%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW219+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.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 05:30:05 PM UTC 2026
% Result : Theorem 6.18s 5.86s
% Output : CNFRefutation 6.35s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1427)
% Comments :
%------------------------------------------------------------------------------
fof(fact_le__SucE,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,c_Nat_OSuc(X14))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> X26 = c_Nat_OSuc(X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_not__less__eq__eq,axiom,
! [X11,X25] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X11),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_not__less__eq,axiom,
! [X11,X25] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Nat_OSuc(X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X25,X11] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X25)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Nat_OSuc(X25))
<=> X11 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_less__antisym,axiom,
! [X26,X14] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X26)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Nat_OSuc(X26))
=> X26 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_less__SucE,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,c_Nat_OSuc(X14))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> X26 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X14] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X14),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_div__Suc,axiom,
! [X22,X21] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(X21),X22) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X21,X22),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21,X22),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22)),X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__Suc) ).
fof(fact_Suc__eq__plus1,axiom,
! [X14] : c_Nat_OSuc(X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(conj_0,hypothesis,
! [X97] :
( ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X97,X10)),v_r)
=> ( ! [X10] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X97,X10))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X10)))))
=> v_thesis____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_Suc__mult__less__cancel1,axiom,
! [X11,X25,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X48)),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X48)),X11))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(fact_Suc__mult__le__cancel1,axiom,
! [X11,X25,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X48)),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X48)),X11))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096,axiom,
? [X7] :
! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X7,X3)),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X7,X3))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096) ).
fof(fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096,axiom,
! [X11] :
? [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X9)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X11))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096) ).
fof(fact_th,axiom,
! [X10] :
? [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X9)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X10))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th) ).
fof(fact_lemma__NBseq__def2,axiom,
! [X33,X34] :
( class_RealVector_Oreal__normed__vector(X34)
=> ( ? [X35] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
& ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X34,hAPP(X33,X10)),X35) )
<=> ? [X36] :
! [X10] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X34,hAPP(X33,X10)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X36))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__NBseq__def2) ).
fof(fact_lemma__NBseq__def,axiom,
! [X33,X34] :
( class_RealVector_Oreal__normed__vector(X34)
=> ( ? [X35] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
& ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X34,hAPP(X33,X10)),X35) )
<=> ? [X36] :
! [X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X34,hAPP(X33,X10)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X36))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__NBseq__def) ).
fof(fact_Bseq__iff1a,axiom,
! [X33,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( c_SEQ_OBseq(X19,X33)
<=> ? [X36] :
! [X10] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(X33,X10)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X36))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__iff1a) ).
fof(fact_Bseq__iff,axiom,
! [X33,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( c_SEQ_OBseq(X19,X33)
<=> ? [X36] :
! [X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(X33,X10)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X36))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__iff) ).
fof(fact_realpow__two__disj,axiom,
! [X12,X4,X19] :
( class_Rings_Oidom(X19)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X19),X4),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X19),X12),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( X4 = X12
| X4 = c_Groups_Ouminus__class_Ouminus(X19,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
fof(fact_power__le__imp__le__base,axiom,
! [X20,X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),c_Nat_OSuc(X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X20),c_Nat_OSuc(X14)))
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> c_Orderings_Oord__class_Oless__eq(X19,X21,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
fof(fact_split__div_H,axiom,
! [X11,X25,X45] :
( hBOOL(hAPP(X45,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X25,X11)))
<=> ( ( X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(X45,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X60] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X60),X25)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),c_Nat_OSuc(X60)))
& hBOOL(hAPP(X45,X60)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div_H) ).
fof(fact_split__div__lemma,axiom,
! [X25,X54,X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11)
=> ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X54),X25)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),c_Nat_OSuc(X54))) )
<=> X54 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X25,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div__lemma) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [X16,X18,X19] :
( class_Rings_Olinordered__ring(X19)
=> ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X16)),c_Groups_Ozero__class_Ozero(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_power_Opower_Opower__Suc,axiom,
! [X11,X24,X85,X86,X19] : hAPP(hAPP(c_Power_Opower_Opower(X19,X86,X85),X24),c_Nat_OSuc(X11)) = hAPP(hAPP(X85,X24),hAPP(hAPP(c_Power_Opower_Opower(X19,X86,X85),X24),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
fof(fact_mod__mult__self4,axiom,
! [X26,X14,X28] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X14),X26)),X14) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X26),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self4) ).
fof(fact_Suc__mult__cancel1,axiom,
! [X11,X25,X48] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X48)),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X48)),X11)
<=> X25 = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(fact_one__less__mult,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26)
=> 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),X26),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).
fof(fact_one__le__mult__iff,axiom,
! [X11,X25] :
( 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),X25),X11))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
fof(fact_divide__less__eq,axiom,
! [X24,X37,X23,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X23,X37),X24)
<=> ( ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> c_Orderings_Oord__class_Oless(X19,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37)) )
& ( ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),X23) )
& ( ~ c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X24) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq) ).
fof(fact_divide__le__eq,axiom,
! [X24,X37,X23,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X23,X37),X24)
<=> ( ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> c_Orderings_Oord__class_Oless__eq(X19,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37)) )
& ( ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),X23) )
& ( ~ c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X24) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq) ).
fof(fact_less__divide__eq,axiom,
! [X37,X23,X24,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X24,c_Rings_Oinverse__class_Odivide(X19,X23,X37))
<=> ( ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),X23) )
& ( ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37)) )
& ( ~ c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,X24,c_Groups_Ozero__class_Ozero(X19)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq) ).
fof(fact_le__divide__eq,axiom,
! [X37,X23,X24,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X24,c_Rings_Oinverse__class_Odivide(X19,X23,X37))
<=> ( ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),X23) )
& ( ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37)) )
& ( ~ c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,X24,c_Groups_Ozero__class_Ozero(X19)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq) ).
fof(fact_power__inject__base,axiom,
! [X20,X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),c_Nat_OSuc(X14)) = hAPP(hAPP(c_Power_Opower__class_Opower(X19),X20),c_Nat_OSuc(X14))
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> X21 = X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__base) ).
fof(fact_int__power__div__base,axiom,
! [X28,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X28)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X28),X26),X28) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X28),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power__div__base) ).
fof(fact_nat__lt__two__imp__zero__or__one,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
fof(fact_n__less__n__mult__m,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
fof(fact_n__less__m__mult__n,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
fof(fact_divmod__int__rel__mod__eq,axiom,
! [X16,X84,X80,X81] :
( X81 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X80),X84),X16)
=> ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X80)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X16)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X80) ) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X80)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X80,X16)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
=> ( X80 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X81,X80) = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).
fof(fact_divmod__int__rel__div__eq,axiom,
! [X79,X16,X80,X81] :
( X81 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X80),X16),X79)
=> ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X80)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X80) ) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X80)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X80,X79)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X79,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
=> ( X80 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X81,X80) = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).
fof(fact_power__Suc__less__one,axiom,
! [X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless(X19,X21,c_Groups_Oone__class_Oone(X19))
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),c_Nat_OSuc(X14)),c_Groups_Oone__class_Oone(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
fof(fact_realpow__Suc__le__self,axiom,
! [X14,X17,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X17)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X17,c_Groups_Oone__class_Oone(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X17),c_Nat_OSuc(X14)),X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
fof(fact_mod__Suc__eq__Suc__mod,axiom,
! [X14,X26] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X26),X14) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14)),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
fof(fact_calculation,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
=> ? [X9] :
! [X32] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X32),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X9)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X32))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_calculation) ).
fof(fact_nat__one__le__power,axiom,
! [X14,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)
=> 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),X30),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
fof(fact_power__gt1,axiom,
! [X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),X21)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),c_Nat_OSuc(X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1) ).
fof(fact_mod__Suc,axiom,
! [X14,X26] :
( ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14)) = X14
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X26),X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14)) != X14
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X26),X14) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc) ).
fof(fact_Suc__less__eq,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X25),c_Nat_OSuc(X11))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_Suc__less__SucD,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X26),c_Nat_OSuc(X14))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_Suc__le__mono,axiom,
! [X25,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X11),c_Nat_OSuc(X25))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_ex__least__nat__less,axiom,
! [X11,X45] :
( ~ hBOOL(hAPP(X45,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X45,X11))
=> ? [X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X39,X11)
& ! [X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X39)
=> ~ hBOOL(hAPP(X45,X57)) )
& hBOOL(hAPP(X45,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
fof(fact_Suc__times__mod__eq,axiom,
! [X26,X28] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X28)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X26)),X28) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__times__mod__eq) ).
fof(fact_split__zmod,axiom,
! [X48,X11,X45] :
( hBOOL(hAPP(X45,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X48)))
<=> ( ( X48 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X45,X11)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
=> ! [X57,X50] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X48)
& X11 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X57),X50) )
=> hBOOL(hAPP(X45,X50)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X57,X50] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X50)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& X11 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X57),X50) )
=> hBOOL(hAPP(X45,X50)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zmod) ).
fof(fact_split__zdiv,axiom,
! [X48,X11,X45] :
( hBOOL(hAPP(X45,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X11,X48)))
<=> ( ( X48 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X45,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
=> ! [X57] :
( ? [X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X48)
& X11 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X57),X50) )
=> hBOOL(hAPP(X45,X57)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X57] :
( ? [X50] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X50)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& X11 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X57),X50) )
=> hBOOL(hAPP(X45,X57)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zdiv) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
! [X52,X18,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),X52)),X18) = hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),c_Nat_OSuc(X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(fact_power__Suc2,axiom,
! [X14,X21,X19] :
( class_Groups_Omonoid__mult(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),c_Nat_OSuc(X14)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc2) ).
fof(fact_reals__Archimedean6a,axiom,
! [X17] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X17)
=> ? [X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X10),X17)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reals__Archimedean6a) ).
fof(fact_mult__Suc,axiom,
! [X14,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X26)),X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
fof(fact_Suc__diff__le,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X26)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X26),X14) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
fof(fact_less__add__Suc1,axiom,
! [X26,X30] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X26))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X26,X30] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X30))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_le__Suc__eq,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,c_Nat_OSuc(X11))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11)
| X25 = c_Nat_OSuc(X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_Suc__mono,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X26),c_Nat_OSuc(X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Nat_OSuc(X11))
<=> ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X50] :
( X25 = c_Nat_OSuc(X50)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X50,X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_le__less__Suc__eq,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Nat_OSuc(X25))
<=> X11 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_power__Suc__0,axiom,
! [X14] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X14) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__0) ).
fof(fact_less__trans__Suc,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X29)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X28)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X30),X28) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_add__Suc__shift,axiom,
! [X14,X26] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X26),X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,c_Nat_OSuc(X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_diff__Suc__eq__diff__pred,axiom,
! [X14,X26] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,c_Nat_OSuc(X14)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
fof(fact_power__Suc,axiom,
! [X14,X21,X19] :
( class_Power_Opower(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),c_Nat_OSuc(X14)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
! [X52,X18,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),c_Nat_OSuc(X52)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),X52)) ),
file('/export/starexec/sandbox/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,
! [X52,X18,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),X52)) = hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),c_Nat_OSuc(X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(fact_add__Suc,axiom,
! [X14,X26] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X26),X14) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_add__Suc__right,axiom,
! [X14,X26] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,c_Nat_OSuc(X14)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_less__Suc__eq,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Nat_OSuc(X11))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11)
| X25 = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__lessD,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X26),X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_Suc__le__lessD,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X26),X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_Suc__le__eq,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X25),X11)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_less__eq__Suc__le,axiom,
! [X25,X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X25)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X11),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__leD,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X26),X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_less__Suc__eq__le,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Nat_OSuc(X11))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_less__iff__Suc__add,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11)
<=> ? [X39] : X11 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_Suc__lessI,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> ( c_Nat_OSuc(X26) != X14
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X26),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_add__leE,axiom,
! [X14,X28,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X28),X14)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_mult__Suc__right,axiom,
! [X14,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),c_Nat_OSuc(X14)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
fof(fact_real__of__nat__Suc__gt__zero,axiom,
! [X14] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X14))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
fof(fact_one__is__add,axiom,
! [X11,X25] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X11)
<=> ( ( X25 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X11 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(fact_add__is__1,axiom,
! [X11,X25] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X11) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X25 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X11 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X19,X34] :
( class_Orderings_Oord(X34)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X19,X34),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X19,X34),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X19,X34),X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_mult__eq__1__iff,axiom,
! [X11,X25] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X11) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X25 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X11 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
fof(fact_less__Suc0,axiom,
! [X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_diff__less__Suc,axiom,
! [X14,X26] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14),c_Nat_OSuc(X26)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
fof(fact_not__square__less__zero,axiom,
! [X21,X19] :
( class_Rings_Olinordered__ring(X19)
=> ~ c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X21),c_Groups_Ozero__class_Ozero(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_mod__if,axiom,
! [X14,X26] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14) = X26 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__if) ).
fof(fact_mod__geq,axiom,
! [X14,X26] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__geq) ).
fof(fact_Suc__leI,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X26),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_less__SucI,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,c_Nat_OSuc(X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_le__imp__less__Suc,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,c_Nat_OSuc(X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_le__SucI,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,c_Nat_OSuc(X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_not__add__less1,axiom,
! [X29,X30] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X29),X30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X30,X29] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X30),X30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_not__real__square__gt__zero,axiom,
! [X4] :
( ~ 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),X4))
<=> X4 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
fof(fact_z3div__def,axiom,
! [X28,X47] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X47)
=> c_SMT_Oz3div(X28,X47) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X28,X47) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X47)
=> c_SMT_Oz3div(X28,X47) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X28,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X47))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_z3div__def) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [X25,X4] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4),X25) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(fact_add__diff__inverse,axiom,
! [X14,X26] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14)) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_less__le__not__le,axiom,
! [X12,X4,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X4,X12)
<=> ( c_Orderings_Oord__class_Oless__eq(X19,X4,X12)
& ~ c_Orderings_Oord__class_Oless__eq(X19,X12,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_real__of__nat__Suc,axiom,
! [X14] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X14)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
fof(fact_power__0__Suc,axiom,
! [X14,X19] :
( ( class_Power_Opower(X19)
& class_Rings_Osemiring__0(X19) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),c_Groups_Ozero__class_Ozero(X19)),c_Nat_OSuc(X14)) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__Suc) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X12,X4,X19] :
( class_Orderings_Olinorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X4,X12)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X4,X12)
<=> X4 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_xt1_I9_J,axiom,
! [X21,X20,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X20,X21)
=> ~ c_Orderings_Oord__class_Oless(X19,X21,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X12,X4,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X4,X12)
<=> ( c_Orderings_Oord__class_Oless(X19,X12,X4)
| X4 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_leD,axiom,
! [X18,X16,X19] :
( class_Orderings_Olinorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X16,X18)
=> ~ c_Orderings_Oord__class_Oless(X19,X18,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__less,axiom,
! [X12,X4,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X4,X12)
<=> c_Orderings_Oord__class_Oless__eq(X19,X12,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [X12,X4,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X19,X4,X12)
<=> c_Orderings_Oord__class_Oless(X19,X12,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_order__less__asym,axiom,
! [X16,X18,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> ~ c_Orderings_Oord__class_Oless(X19,X16,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X20,X21,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ~ c_Orderings_Oord__class_Oless(X19,X20,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X16,X18,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> ~ c_Orderings_Oord__class_Oless(X19,X16,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X16,X18,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> ~ c_Orderings_Oord__class_Oless(X19,X16,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_nat_Oinject,axiom,
! [X41,X42] :
( c_Nat_OSuc(X42) = c_Nat_OSuc(X41)
<=> X42 = X41 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(fact_Suc__inject,axiom,
! [X16,X18] :
( c_Nat_OSuc(X18) = c_Nat_OSuc(X16)
=> X18 = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(fact_mod__1,axiom,
! [X26] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__1) ).
fof(fact_div__1,axiom,
! [X26] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__1) ).
fof(fact_diff__Suc__1,axiom,
! [X14] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X14),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
fof(fact_zero__less__Suc,axiom,
! [X14] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_lessI,axiom,
! [X14] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Nat_OSuc(X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_z3mod__def,axiom,
! [X28,X47] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X47)
=> c_SMT_Oz3mod(X28,X47) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X28,X47) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X47)
=> c_SMT_Oz3mod(X28,X47) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X28,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X47)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_z3mod__def) ).
fof(fact_gr0__conv__Suc,axiom,
! [X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11)
<=> ? [X49] : X11 = c_Nat_OSuc(X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X12,X4,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X4,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X4,X12)
<=> X4 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_norm__not__less__zero,axiom,
! [X18,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X18),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
fof(fact_not__real__of__nat__less__zero,axiom,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).
fof(fact_linorder__cases,axiom,
! [X16,X18,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X18,X16)
=> ( X18 != X16
=> c_Orderings_Oord__class_Oless(X19,X16,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X16,X18,X19] :
( class_Orderings_Olinorder(X19)
=> ( X18 != X16
=> ( ~ c_Orderings_Oord__class_Oless(X19,X18,X16)
=> c_Orderings_Oord__class_Oless(X19,X16,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X4,X12,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X12,X4)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X4,X12)
<=> X4 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X16,X18,X19] :
( class_Rings_Olinordered__idom(X19)
=> ( X18 != X16
=> ( ~ c_Orderings_Oord__class_Oless(X19,X18,X16)
=> c_Orderings_Oord__class_Oless(X19,X16,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_not__leE,axiom,
! [X18,X16,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X19,X16,X18)
=> c_Orderings_Oord__class_Oless(X19,X18,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X16,X18,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X18,X16)
=> c_Orderings_Oord__class_Oless__eq(X19,X16,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_linorder__le__cases,axiom,
! [X16,X18,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X19,X18,X16)
=> c_Orderings_Oord__class_Oless__eq(X19,X16,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_not__one__less__zero,axiom,
! [X19] :
( class_Rings_Olinordered__semidom(X19)
=> ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),c_Groups_Ozero__class_Ozero(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_not__one__le__zero,axiom,
! [X19] :
( class_Rings_Olinordered__semidom(X19)
=> ~ c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oone__class_Oone(X19),c_Groups_Ozero__class_Ozero(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X14] : c_Nat_OSuc(X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_linorder__neqE__nat,axiom,
! [X16,X18] :
( X18 != X16
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X16)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_order__less__irrefl,axiom,
! [X18,X19] :
( class_Orderings_Opreorder(X19)
=> ~ c_Orderings_Oord__class_Oless(X19,X18,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_Suc__not__Zero,axiom,
! [X26] : c_Nat_OSuc(X26) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
fof(fact_nat_Osimps_I3_J,axiom,
! [X43] : c_Nat_OSuc(X43) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(fact_Suc__neq__Zero,axiom,
! [X26] : c_Nat_OSuc(X26) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(fact_Zero__not__Suc,axiom,
! [X26] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [X44] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__neq__Suc,axiom,
! [X26] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_Suc__n__not__n,axiom,
! [X14] : c_Nat_OSuc(X14) != X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X14] : X14 != c_Nat_OSuc(X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_not__less0,axiom,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__nat__zero__code,axiom,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_less__zeroE,axiom,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_less__not__refl,axiom,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_less__irrefl__nat,axiom,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_Bseq__iff3,axiom,
! [X33,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( c_SEQ_OBseq(X19,X33)
<=> ? [X39] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X39)
& ? [X36] :
! [X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,c_Groups_Oplus__class_Oplus(X19,hAPP(X33,X10),c_Groups_Ouminus__class_Ouminus(X19,hAPP(X33,X36)))),X39) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__iff3) ).
fof(fact_Bseq__iff2,axiom,
! [X33,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( c_SEQ_OBseq(X19,X33)
<=> ? [X39] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X39)
& ? [X3] :
! [X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,c_Groups_Oplus__class_Oplus(X19,hAPP(X33,X10),c_Groups_Ouminus__class_Ouminus(X19,X3))),X39) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__iff2) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X19,X34] :
( class_Orderings_Oord(X34)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X19,X34),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X34,hAPP(X2,X3),hAPP(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_BseqI2_H,axiom,
! [X58,X33,X59,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( ! [X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59,X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(X33,X10)),X58) )
=> c_SEQ_OBseq(X19,X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_BseqI2_H) ).
fof(fact_mult_Oprod__diff__prod,axiom,
! [X20,X21,X16,X18,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> c_Groups_Ominus__class_Ominus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)) = c_Groups_Oplus__class_Oplus(X19,c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ominus__class_Ominus(X19,X18,X21)),c_Groups_Ominus__class_Ominus(X19,X16,X20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ominus__class_Ominus(X19,X18,X21)),X20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Groups_Ominus__class_Ominus(X19,X16,X20))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(fact_reduce__poly__simple,axiom,
! [X14,X20] :
( X20 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ( X14 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ? [X9] : 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),X20),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X9),X14)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduce__poly__simple) ).
fof(fact_split__pos__lemma,axiom,
! [X11,X45,X48] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
=> ( hBOOL(hAPP(hAPP(X45,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X11,X48)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X48)))
<=> ! [X57,X50] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X48)
& X11 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X57),X50) )
=> hBOOL(hAPP(hAPP(X45,X57),X50)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__pos__lemma) ).
fof(fact_split__neg__lemma,axiom,
! [X11,X45,X48] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( hBOOL(hAPP(hAPP(X45,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X11,X48)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X48)))
<=> ! [X57,X50] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X50)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& X11 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X57),X50) )
=> hBOOL(hAPP(hAPP(X45,X57),X50)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__neg__lemma) ).
fof(fact_zdiv__zadd1__eq,axiom,
! [X22,X20,X21] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X20),X22) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X22),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X20,X22)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X22),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20,X22)),X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).
fof(fact_div__add1__eq,axiom,
! [X22,X20,X21] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X20),X22) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X21,X22),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X20,X22)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21,X22),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20,X22)),X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add1__eq) ).
fof(fact_div__mod__equality,axiom,
! [X22,X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Divides_Odiv__class_Odiv(X19,X21,X20)),X20),c_Divides_Odiv__class_Omod(X19,X21,X20)),X22) = c_Groups_Oplus__class_Oplus(X19,X21,X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality) ).
fof(fact_zdiv__zmod__equality2,axiom,
! [X28,X20,X21] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20)),X20),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20)),X28) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [X82,X83,X69,X17,X52,X20] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X52),X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X69),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),X69),X83),X82),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X20)
=> ( 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),X69)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X69,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X83,X52) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [X82,X83,X69,X17,X52,X20] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X52),X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X69),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),X69),X83),X82))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X82,X69)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X69)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X69,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,X83) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_mult_Ononneg__bounded,axiom,
! [X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> ? [X35] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
& ! [X76,X77] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X76),X77)),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(X19,X76)),c_RealVector_Onorm__class_Onorm(X19,X77))),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ononneg__bounded) ).
fof(fact_mult_Opos__bounded,axiom,
! [X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> ? [X35] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
& ! [X76,X77] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X76),X77)),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(X19,X76)),c_RealVector_Onorm__class_Onorm(X19,X77))),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Opos__bounded) ).
fof(fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096,axiom,
! [X12] :
( ? [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X9)))),X12) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096) ).
fof(fact_unique__quotient__lemma,axiom,
! [X17,X52,X82,X83,X20] :
( 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),X20),X83),X82),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X52),X17))
=> ( 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,X20)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X83,X52) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [X17,X52,X82,X83,X20] :
( 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),X20),X83),X82),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X52),X17))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,X17)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,X82)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,X83) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_poly__mod__mult__right,axiom,
! [X6,X16,X18,X19] :
( class_Fields_Ofield(X19)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X19),X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X19)),X16),X6)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X19)),X16),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X19),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X19),X18,X16),X6)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X19),X18,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mod__mult__right) ).
fof(fact_eq__add__iff1,axiom,
! [X65,X23,X37,X93,X24,X19] :
( class_Rings_Oring(X19)
=> ( c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X93),X37) = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X23),X93),X65)
<=> c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ominus__class_Ominus(X19,X24,X23)),X93),X37) = X65 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [X65,X23,X37,X93,X24,X19] :
( class_Rings_Oring(X19)
=> ( c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X93),X37) = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X23),X93),X65)
<=> X37 = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ominus__class_Ominus(X19,X23,X24)),X93),X65) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_zdiv__zmult1__eq,axiom,
! [X22,X20,X21] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X20),X22) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X20,X22)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20,X22)),X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).
fof(fact_div__mult1__eq,axiom,
! [X22,X20,X21] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X20),X22) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X20,X22)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20,X22)),X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult1__eq) ).
fof(fact_mult__diff__mult,axiom,
! [X20,X21,X16,X18,X19] :
( class_Rings_Oring(X19)
=> c_Groups_Ominus__class_Ominus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)) = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),c_Groups_Ominus__class_Ominus(X19,X16,X20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ominus__class_Ominus(X19,X18,X21)),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
! [X14,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X14)),X18),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,X18,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
fof(fact_zmult2__lemma__aux4,axiom,
! [X52,X20,X17,X22] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X20)
=> 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),X20),c_Divides_Odiv__class_Omod(tc_Int_Oint,X52,X22)),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).
fof(fact_zmult2__lemma__aux1,axiom,
! [X52,X17,X20,X22] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X22),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),c_Divides_Odiv__class_Omod(tc_Int_Oint,X52,X22)),X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).
fof(fact_zmod__zmult2__eq,axiom,
! [X20,X21,X22] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X22)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20),X22)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).
fof(fact_real__of__nat__div__aux,axiom,
! [X18,X38] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X38)
=> c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X18),c_RealDef_Oreal(tc_Nat_Onat,X38)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X18,X38)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X18,X38)),c_RealDef_Oreal(tc_Nat_Onat,X38))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__div__aux) ).
fof(fact_div__mod__equality2,axiom,
! [X22,X21,X20,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),c_Divides_Odiv__class_Odiv(X19,X21,X20)),c_Divides_Odiv__class_Omod(X19,X21,X20)),X22) = c_Groups_Oplus__class_Oplus(X19,X21,X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality2) ).
fof(fact_combine__common__factor,axiom,
! [X22,X20,X68,X21,X19] :
( class_Rings_Osemiring(X19)
=> c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X68),c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X68),X22)) = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oplus__class_Oplus(X19,X21,X20)),X68),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(fact_convex__bound__lt,axiom,
! [X71,X72,X16,X21,X18,X19] :
( class_Rings_Olinordered__semiring__1__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X21)
=> ( c_Orderings_Oord__class_Oless(X19,X16,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X72)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X71)
=> ( c_Groups_Oplus__class_Oplus(X19,X72,X71) = c_Groups_Oone__class_Oone(X19)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X72),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X71),X16)),X21) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_convex__bound__le,axiom,
! [X71,X72,X16,X21,X18,X19] :
( class_Rings_Olinordered__semiring__1(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X16,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X72)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X71)
=> ( c_Groups_Oplus__class_Oplus(X19,X72,X71) = c_Groups_Oone__class_Oone(X19)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X72),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X71),X16)),X21) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__le) ).
fof(fact_zmult2__lemma__aux2,axiom,
! [X52,X17,X20,X22] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> 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),X20),c_Divides_Odiv__class_Omod(tc_Int_Oint,X52,X22)),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux2) ).
fof(fact_zmult2__lemma__aux3,axiom,
! [X52,X20,X17,X22] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X20)
=> 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),X20),c_Divides_Odiv__class_Omod(tc_Int_Oint,X52,X22)),X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).
fof(fact_mod__lemma,axiom,
! [X52,X20,X17,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X22)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X20)
=> 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),X20),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X52,X22)),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__lemma) ).
fof(fact_mod__mult2__eq,axiom,
! [X22,X20,X21] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X22)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X21,X20),X22)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).
fof(fact_zdiv__zmod__equality,axiom,
! [X28,X21,X20] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20)),X28) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).
fof(fact_BseqI,axiom,
! [X33,X58,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X58)
=> ( ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(X33,X10)),X58)
=> c_SEQ_OBseq(X19,X33) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_BseqI) ).
fof(fact_Bseq__def,axiom,
! [X33,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( c_SEQ_OBseq(X19,X33)
<=> ? [X35] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
& ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(X33,X10)),X35) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__def) ).
fof(fact_left__add__mult__distrib,axiom,
! [X28,X29,X72,X30] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X72),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X72),X28)) = 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,X30,X29)),X72),X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_field__le__mult__one__interval,axiom,
! [X16,X18,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( ! [X9] :
( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X9)
=> ( c_Orderings_Oord__class_Oless(X19,X9,c_Groups_Oone__class_Oone(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X9),X18),X16) ) )
=> c_Orderings_Oord__class_Oless__eq(X19,X18,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).
fof(fact_mod__mult__eq,axiom,
! [X22,X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),X22) = c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Divides_Odiv__class_Omod(X19,X21,X22)),c_Divides_Odiv__class_Omod(X19,X20,X22)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__eq) ).
fof(fact_add__frac__eq,axiom,
! [X27,X18,X6,X16,X19] :
( class_Fields_Ofield(X19)
=> ( X16 != c_Groups_Ozero__class_Ozero(X19)
=> ( X6 != c_Groups_Ozero__class_Ozero(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X16),c_Rings_Oinverse__class_Odivide(X19,X27,X6)) = c_Rings_Oinverse__class_Odivide(X19,c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X27),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__eq) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [X12,X4,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X4),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X12),X12)))
<=> ( X4 != c_Groups_Ozero__class_Ozero(X19)
| X12 != c_Groups_Ozero__class_Ozero(X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X61,X62,X63,X64,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X62),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),X63)),X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [X12,X4,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X4),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X12),X12)),c_Groups_Ozero__class_Ozero(X19))
<=> ( X4 = c_Groups_Ozero__class_Ozero(X19)
& X12 = c_Groups_Ozero__class_Ozero(X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_crossproduct__noteq,axiom,
! [X65,X37,X23,X24,X19] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X19)
=> ( ( X24 != X23
& X37 != X65 )
<=> c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X23),X65)) != c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X65),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X23),X37)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_crossproduct__eq,axiom,
! [X5,X4,X12,X66,X19] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X19)
=> ( c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X66),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X4),X5)) = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X66),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X4),X12))
<=> ( X66 = X4
| X12 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_power__minus,axiom,
! [X14,X21,X19] :
( class_Rings_Oring__1(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),c_Groups_Ouminus__class_Ouminus(X19,X21)),X14) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),c_Groups_Ouminus__class_Ouminus(X19,c_Groups_Oone__class_Oone(X19))),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus) ).
fof(fact_q__neg__lemma,axiom,
! [X82,X83,X69] :
( 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),X69),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),X69)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X83,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
fof(fact_q__pos__lemma,axiom,
! [X82,X83,X69] :
( 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),X69),X83),X82))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X82,X69)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X69)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X83) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_split__div,axiom,
! [X48,X11,X45] :
( hBOOL(hAPP(X45,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X11,X48)))
<=> ( ( X48 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(X45,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( X48 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [X57,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X50,X48)
=> ( X11 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X57),X50)
=> hBOOL(hAPP(X45,X57)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div) ).
fof(fact_mod__diff__eq,axiom,
! [X22,X20,X21,X19] :
( class_Divides_Oring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Ominus__class_Ominus(X19,X21,X20),X22) = c_Divides_Odiv__class_Omod(X19,c_Groups_Ominus__class_Ominus(X19,c_Divides_Odiv__class_Omod(X19,X21,X22),c_Divides_Odiv__class_Omod(X19,X20,X22)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__eq) ).
fof(fact_mod__add__eq,axiom,
! [X22,X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X22) = c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,c_Divides_Odiv__class_Omod(X19,X21,X22),c_Divides_Odiv__class_Omod(X19,X20,X22)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__eq) ).
fof(fact_split__mod,axiom,
! [X48,X11,X45] :
( hBOOL(hAPP(X45,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X11,X48)))
<=> ( ( X48 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(X45,X11)) )
& ( X48 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [X57,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X50,X48)
=> ( X11 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X57),X50)
=> hBOOL(hAPP(X45,X50)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mod) ).
fof(fact_zmod__simps_I4_J,axiom,
! [X20,X22,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Divides_Odiv__class_Omod(X19,X21,X22)),X20),X22) = c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).
fof(fact_mod__mult__left__eq,axiom,
! [X22,X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),X22) = c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Divides_Odiv__class_Omod(X19,X21,X22)),X20),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).
fof(fact_gt__half__sum,axiom,
! [X20,X21,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),c_Groups_Oplus__class_Oplus(X19,c_Groups_Oone__class_Oone(X19),c_Groups_Oone__class_Oone(X19))),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gt__half__sum) ).
fof(fact_less__half__sum,axiom,
! [X20,X21,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> c_Orderings_Oord__class_Oless(X19,X21,c_Rings_Oinverse__class_Odivide(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),c_Groups_Oplus__class_Oplus(X19,c_Groups_Oone__class_Oone(X19),c_Groups_Oone__class_Oone(X19)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__half__sum) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X61,X62,X63,X64,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X62),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X63),X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [X61,X62,X63,X64,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X62),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X63),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X62),X61))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_divide__strict__left__mono,axiom,
! [X22,X21,X20,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X20,X21)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20))
=> c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X22,X21),c_Rings_Oinverse__class_Odivide(X19,X22,X20)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).
fof(fact_divide__left__mono,axiom,
! [X22,X21,X20,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20))
=> c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X22,X21),c_Rings_Oinverse__class_Odivide(X19,X22,X20)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono) ).
fof(fact_divide__strict__left__mono__neg,axiom,
! [X22,X20,X21,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless(X19,X22,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20))
=> c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X22,X21),c_Rings_Oinverse__class_Odivide(X19,X22,X20)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).
fof(fact_divide__left__mono__neg,axiom,
! [X22,X20,X21,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X22,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20))
=> c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X22,X21),c_Rings_Oinverse__class_Odivide(X19,X22,X20)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).
fof(fact_zpower__zmod,axiom,
! [X16,X26,X18] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X18,X26)),X16),X26) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X18),X16),X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zmod) ).
fof(fact_mod__div__equality,axiom,
! [X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Divides_Odiv__class_Odiv(X19,X21,X20)),X20),c_Divides_Odiv__class_Omod(X19,X21,X20)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__equality) ).
fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
! [X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Divides_Odiv__class_Omod(X19,X21,X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Divides_Odiv__class_Odiv(X19,X21,X20)),X20)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).
fof(fact_complex__mod__triangle__sub,axiom,
! [X6,X27] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X27),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X27,X6)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
fof(fact_mult__poly__add__left,axiom,
! [X17,X52,X51,X19] :
( class_Rings_Ocomm__semiring__0(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X19)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X19),X51,X52)),X17) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X19)),X51),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X19)),X52),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
fof(fact_mod__diff__cong,axiom,
! [X69,X20,X70,X22,X21,X19] :
( class_Divides_Oring__div(X19)
=> ( c_Divides_Odiv__class_Omod(X19,X21,X22) = c_Divides_Odiv__class_Omod(X19,X70,X22)
=> ( c_Divides_Odiv__class_Omod(X19,X20,X22) = c_Divides_Odiv__class_Omod(X19,X69,X22)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Ominus__class_Ominus(X19,X21,X20),X22) = c_Divides_Odiv__class_Omod(X19,c_Groups_Ominus__class_Ominus(X19,X70,X69),X22) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__cong) ).
fof(fact_mod__add__cong,axiom,
! [X69,X20,X70,X22,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> ( c_Divides_Odiv__class_Omod(X19,X21,X22) = c_Divides_Odiv__class_Omod(X19,X70,X22)
=> ( c_Divides_Odiv__class_Omod(X19,X20,X22) = c_Divides_Odiv__class_Omod(X19,X69,X22)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X22) = c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X70,X69),X22) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__cong) ).
fof(fact_mod__mult__cong,axiom,
! [X69,X20,X70,X22,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> ( c_Divides_Odiv__class_Omod(X19,X21,X22) = c_Divides_Odiv__class_Omod(X19,X70,X22)
=> ( c_Divides_Odiv__class_Omod(X19,X20,X22) = c_Divides_Odiv__class_Omod(X19,X69,X22)
=> c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),X22) = c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X70),X69),X22) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__cong) ).
fof(fact_power__Suc__less,axiom,
! [X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless(X19,X21,c_Groups_Oone__class_Oone(X19))
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(fact_odd__less__0,axiom,
! [X5] :
( 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),X5),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).
fof(fact_norm__add__less,axiom,
! [X15,X16,X17,X18,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X18),X17)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X16),X15)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,c_Groups_Oplus__class_Oplus(X19,X18,X16)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X17,X15)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__add__less) ).
fof(fact_frac__less2,axiom,
! [X6,X27,X16,X18,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X18)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,X16)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X27)
=> ( c_Orderings_Oord__class_Oless(X19,X27,X6)
=> c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X6),c_Rings_Oinverse__class_Odivide(X19,X16,X27)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less2) ).
fof(fact_frac__less,axiom,
! [X6,X27,X16,X18,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X18)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X27)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X27,X6)
=> c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X6),c_Rings_Oinverse__class_Odivide(X19,X16,X27)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less) ).
fof(fact_frac__le,axiom,
! [X6,X27,X16,X18,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X18)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,X16)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X27)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X27,X6)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X6),c_Rings_Oinverse__class_Odivide(X19,X16,X27)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__le) ).
fof(fact_times__divide__times__eq,axiom,
! [X27,X6,X16,X18,X19] :
( class_Fields_Ofield__inverse__zero(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Rings_Oinverse__class_Odivide(X19,X18,X16)),c_Rings_Oinverse__class_Odivide(X19,X6,X27)) = c_Rings_Oinverse__class_Odivide(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
fof(fact_poly__mult,axiom,
! [X18,X52,X51,X19] :
( class_Rings_Ocomm__semiring__0(X19)
=> hAPP(c_Polynomial_Opoly(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X19)),X51),X52)),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(c_Polynomial_Opoly(X19,X51),X18)),hAPP(c_Polynomial_Opoly(X19,X52),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mult) ).
fof(fact_less__diff__iff,axiom,
! [X11,X25,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X11)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X48),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X48))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(fact_le__diff__iff,axiom,
! [X11,X25,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X11)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X48),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X48))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).
fof(fact_mult__strict__mono,axiom,
! [X38,X22,X20,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless(X19,X22,X38)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X38)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_mult__strict__mono_H,axiom,
! [X38,X22,X20,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless(X19,X22,X38)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X38)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__le__less__imp__less,axiom,
! [X38,X22,X20,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless(X19,X22,X38)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X38)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__less__le__imp__less,axiom,
! [X38,X22,X20,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X22,X38)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X38)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__mono_H,axiom,
! [X38,X22,X20,X21,X19] :
( class_Rings_Oordered__semiring(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X22,X38)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X38)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__mono,axiom,
! [X38,X22,X20,X21,X19] :
( class_Rings_Oordered__semiring(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X22,X38)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X38)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono) ).
fof(fact_norm__mult__less,axiom,
! [X15,X16,X17,X18,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X18),X17)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X16),X15)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X15)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult__less) ).
fof(fact_power__mult__distrib,axiom,
! [X14,X20,X21,X19] :
( class_Groups_Ocomm__monoid__mult(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)),X14) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X20),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X52,X16,X18,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)),X52) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),X52)),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X16),X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_sum__squares__ge__zero,axiom,
! [X16,X18,X19] :
( class_Rings_Olinordered__ring(X19)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X16))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096,axiom,
( ? [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X9)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096) ).
fof(fact_power__less__power__Suc,axiom,
! [X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),X21)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_mult__right__less__imp__less,axiom,
! [X20,X22,X21,X19] :
( class_Rings_Olinordered__semiring(X19)
=> ( c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22))
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless(X19,X21,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [X20,X22,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22))
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless(X19,X21,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_power__less__imp__less__base,axiom,
! [X20,X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X20),X14))
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> c_Orderings_Oord__class_Oless(X19,X21,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_mult__left__less__imp__less,axiom,
! [X20,X21,X22,X19] :
( class_Rings_Olinordered__semiring(X19)
=> ( c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20))
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless(X19,X21,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__left,axiom,
! [X20,X21,X22,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20))
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless(X19,X21,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [X23,X24,X37,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X37),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X37),X23))
<=> c_Orderings_Oord__class_Oless(X19,X24,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__right__le__imp__le,axiom,
! [X20,X22,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22))
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless__eq(X19,X21,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__left__le__imp__le,axiom,
! [X20,X21,X22,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20))
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless__eq(X19,X21,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [X23,X24,X37,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X37),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X37),X23))
<=> c_Orderings_Oord__class_Oless__eq(X19,X24,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [X23,X24,X37,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X37),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X37),X23))
<=> c_Orderings_Oord__class_Oless(X19,X23,X24) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [X23,X24,X37,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X37),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X37),X23))
<=> c_Orderings_Oord__class_Oless__eq(X19,X23,X24) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_power__strict__increasing__iff,axiom,
! [X12,X4,X23,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),X23)
=> ( c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X23),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X23),X12))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [X14,X26,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),X21)
=> ( c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X26),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__le__imp__le__exp,axiom,
! [X14,X26,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X26),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_power__increasing__iff,axiom,
! [X12,X4,X23,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),X23)
=> ( c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X23),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X23),X12))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_poly__power,axiom,
! [X18,X14,X51,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(c_Polynomial_Opoly(X19,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X19)),X51),X14)),X18) = hAPP(hAPP(c_Power_Opower__class_Opower(X19),hAPP(c_Polynomial_Opoly(X19,X51),X18)),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__power) ).
fof(fact_divide_Ononneg__bounded,axiom,
! [X16,X19] :
( class_RealVector_Oreal__normed__field(X19)
=> ? [X35] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,c_Rings_Oinverse__class_Odivide(X19,X3,X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X19,X3)),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Ononneg__bounded) ).
fof(fact_divide_Opos__bounded,axiom,
! [X16,X19] :
( class_RealVector_Oreal__normed__field(X19)
=> ? [X35] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,c_Rings_Oinverse__class_Odivide(X19,X3,X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X19,X3)),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Opos__bounded) ).
fof(fact_le__mult__natfloor,axiom,
! [X20,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X21)),c_RComplete_Onatfloor(X20)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__mult__natfloor) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X38,X22,X20,X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),c_Groups_Oplus__class_Oplus(X19,X22,X38)) = c_Groups_Oplus__class_Oplus(X19,c_Groups_Oplus__class_Oplus(X19,X21,X22),c_Groups_Oplus__class_Oplus(X19,X20,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_zmod__simps_I1_J,axiom,
! [X20,X22,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,c_Divides_Odiv__class_Omod(X19,X21,X22),X20),X22) = c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).
fof(fact_zmod__simps_I2_J,axiom,
! [X22,X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X21,c_Divides_Odiv__class_Omod(X19,X20,X22)),X22) = c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).
fof(fact_mod__diff__left__eq,axiom,
! [X22,X20,X21,X19] :
( class_Divides_Oring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Ominus__class_Ominus(X19,X21,X20),X22) = c_Divides_Odiv__class_Omod(X19,c_Groups_Ominus__class_Ominus(X19,c_Divides_Odiv__class_Omod(X19,X21,X22),X20),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).
fof(fact_mod__add__left__eq,axiom,
! [X22,X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X22) = c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,c_Divides_Odiv__class_Omod(X19,X21,X22),X20),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).
fof(fact_mod__diff__right__eq,axiom,
! [X22,X20,X21,X19] :
( class_Divides_Oring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Ominus__class_Ominus(X19,X21,X20),X22) = c_Divides_Odiv__class_Omod(X19,c_Groups_Ominus__class_Ominus(X19,X21,c_Divides_Odiv__class_Omod(X19,X20,X22)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).
fof(fact_mod__add__right__eq,axiom,
! [X22,X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X22) = c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X21,c_Divides_Odiv__class_Omod(X19,X20,X22)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).
fof(fact_power__strict__decreasing,axiom,
! [X21,X78,X14,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X78)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless(X19,X21,c_Groups_Oone__class_Oone(X19))
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X78),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_power__decreasing,axiom,
! [X21,X78,X14,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X78)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,c_Groups_Oone__class_Oone(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X78),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__decreasing) ).
fof(fact_div__mult__self2,axiom,
! [X22,X21,X20,X19] :
( class_Divides_Osemiring__div(X19)
=> ( X20 != c_Groups_Ozero__class_Ozero(X19)
=> c_Divides_Odiv__class_Odiv(X19,c_Groups_Oplus__class_Oplus(X19,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22)),X20) = c_Groups_Oplus__class_Oplus(X19,X22,c_Divides_Odiv__class_Odiv(X19,X21,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2) ).
fof(fact_div__mult__self1,axiom,
! [X22,X21,X20,X19] :
( class_Divides_Osemiring__div(X19)
=> ( X20 != c_Groups_Ozero__class_Ozero(X19)
=> c_Divides_Odiv__class_Odiv(X19,c_Groups_Oplus__class_Oplus(X19,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)),X20) = c_Groups_Oplus__class_Oplus(X19,X22,c_Divides_Odiv__class_Odiv(X19,X21,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1) ).
fof(fact_divide__add__eq__iff,axiom,
! [X16,X18,X6,X19] :
( class_Fields_Ofield(X19)
=> ( X6 != c_Groups_Ozero__class_Ozero(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X6),X16) = c_Rings_Oinverse__class_Odivide(X19,c_Groups_Oplus__class_Oplus(X19,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X6),X16)),X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
fof(fact_add__frac__num,axiom,
! [X6,X18,X16,X19] :
( class_Fields_Ofield__inverse__zero(X19)
=> ( X16 != c_Groups_Ozero__class_Ozero(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X16),X6) = c_Rings_Oinverse__class_Odivide(X19,c_Groups_Oplus__class_Oplus(X19,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X6),X16)),X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__num) ).
fof(fact_add__divide__eq__iff,axiom,
! [X16,X18,X6,X19] :
( class_Fields_Ofield(X19)
=> ( X6 != c_Groups_Ozero__class_Ozero(X19)
=> c_Groups_Oplus__class_Oplus(X19,X18,c_Rings_Oinverse__class_Odivide(X19,X16,X6)) = c_Rings_Oinverse__class_Odivide(X19,c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X6),X18),X16),X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
fof(fact_add__num__frac,axiom,
! [X18,X6,X16,X19] :
( class_Fields_Ofield__inverse__zero(X19)
=> ( X16 != c_Groups_Ozero__class_Ozero(X19)
=> c_Groups_Oplus__class_Oplus(X19,X6,c_Rings_Oinverse__class_Odivide(X19,X18,X16)) = c_Rings_Oinverse__class_Odivide(X19,c_Groups_Oplus__class_Oplus(X19,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X6),X16)),X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__num__frac) ).
fof(fact_power__strict__mono,axiom,
! [X14,X20,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X20),X14)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__mono) ).
fof(fact_nonzero__power__divide,axiom,
! [X14,X21,X20,X19] :
( class_Fields_Ofield(X19)
=> ( X20 != c_Groups_Ozero__class_Ozero(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),c_Rings_Oinverse__class_Odivide(X19,X21,X20)),X14) = c_Rings_Oinverse__class_Odivide(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X20),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [X23,X24,X37,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X37),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X37),X23))
<=> ( ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
& c_Orderings_Oord__class_Oless(X19,X24,X23) )
| ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
& c_Orderings_Oord__class_Oless(X19,X23,X24) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [X23,X37,X24,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X23),X37))
<=> ( ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
& c_Orderings_Oord__class_Oless(X19,X24,X23) )
| ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
& c_Orderings_Oord__class_Oless(X19,X23,X24) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_mult__left_Ononneg__bounded,axiom,
! [X16,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> ? [X35] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X3),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X19,X3)),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ononneg__bounded) ).
fof(fact_mult__left_Opos__bounded,axiom,
! [X16,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> ? [X35] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X3),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X19,X3)),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).
fof(fact_norm__mult__ineq,axiom,
! [X16,X18,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X19,X18)),c_RealVector_Onorm__class_Onorm(X19,X16))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
fof(fact_mult__right_Ononneg__bounded,axiom,
! [X18,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> ? [X35] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X19,X3)),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ononneg__bounded) ).
fof(fact_mult__right_Opos__bounded,axiom,
! [X18,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> ? [X35] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X19,X3)),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).
fof(fact_mod__mult__right__eq,axiom,
! [X22,X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),X22) = c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Divides_Odiv__class_Omod(X19,X20,X22)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).
fof(fact_mod__mult__mult2,axiom,
! [X20,X22,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Divides_Odiv__class_Omod(X19,X21,X20)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [X20,X26,X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oplus__class_Oplus(X19,X21,X20)),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_power__divide,axiom,
! [X14,X20,X21,X19] :
( class_Fields_Ofield__inverse__zero(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),c_Rings_Oinverse__class_Odivide(X19,X21,X20)),X14) = c_Rings_Oinverse__class_Odivide(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X20),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__divide) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Ocomm__semiring(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oplus__class_Oplus(X19,X21,X20)),X22) = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_mult__left_Oadd,axiom,
! [X31,X16,X18,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oplus__class_Oplus(X19,X18,X16)),X31) = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
fof(fact_mult_Oadd__left,axiom,
! [X20,X70,X21,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oplus__class_Oplus(X19,X21,X70)),X20) = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X70),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oplus__class_Oplus(X19,X21,X20)),X22) = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_zdiv__mono2,axiom,
! [X20,X69,X21] :
( c_Orderings_Oord__class_Oless__eq(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),X69)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X69,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X69)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2) ).
fof(fact_zdiv__mono2__neg,axiom,
! [X20,X69,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X69)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X69,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X69),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X52,X51,X18,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),X51)),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),X52)) = hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [X14,X26,X21,X19] :
( class_Groups_Omonoid__mult(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X14)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X26)),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X62,X63,X64,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),X63)),X62) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),X62)),X63) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_s1,axiom,
! [X12] :
( ? [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X9)),X12) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s1) ).
fof(fact_pos__less__divide__eq,axiom,
! [X23,X24,X37,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( c_Orderings_Oord__class_Oless(X19,X24,c_Rings_Oinverse__class_Odivide(X19,X23,X37))
<=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).
fof(fact_pos__le__divide__eq,axiom,
! [X23,X24,X37,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X24,c_Rings_Oinverse__class_Odivide(X19,X23,X37))
<=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).
fof(fact_neg__divide__less__eq,axiom,
! [X24,X23,X37,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X23,X37),X24)
<=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).
fof(fact_neg__divide__le__eq,axiom,
! [X24,X23,X37,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X23,X37),X24)
<=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).
fof(fact_pos__divide__less__eq,axiom,
! [X24,X23,X37,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X23,X37),X24)
<=> c_Orderings_Oord__class_Oless(X19,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).
fof(fact_pos__divide__le__eq,axiom,
! [X24,X23,X37,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X23,X37),X24)
<=> c_Orderings_Oord__class_Oless__eq(X19,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).
fof(fact_neg__less__divide__eq,axiom,
! [X23,X24,X37,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,X24,c_Rings_Oinverse__class_Odivide(X19,X23,X37))
<=> c_Orderings_Oord__class_Oless(X19,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).
fof(fact_neg__le__divide__eq,axiom,
! [X23,X24,X37,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless__eq(X19,X24,c_Rings_Oinverse__class_Odivide(X19,X23,X37))
<=> c_Orderings_Oord__class_Oless__eq(X19,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).
fof(fact_mult__imp__div__pos__less,axiom,
! [X6,X18,X16,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X16)
=> ( c_Orderings_Oord__class_Oless(X19,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X6),X16))
=> c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X16),X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).
fof(fact_mult__imp__div__pos__le,axiom,
! [X6,X18,X16,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X16)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X6),X16))
=> c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X16),X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).
fof(fact_mult__imp__less__div__pos,axiom,
! [X18,X6,X16,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X16)
=> ( c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X6),X16),X18)
=> c_Orderings_Oord__class_Oless(X19,X6,c_Rings_Oinverse__class_Odivide(X19,X18,X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).
fof(fact_mult__imp__le__div__pos,axiom,
! [X18,X6,X16,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X16)
=> ( c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X6),X16),X18)
=> c_Orderings_Oord__class_Oless__eq(X19,X6,c_Rings_Oinverse__class_Odivide(X19,X18,X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).
fof(fact_add__scale__eq__noteq,axiom,
! [X38,X22,X20,X21,X17,X19] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X19)
=> ( X17 != c_Groups_Ozero__class_Ozero(X19)
=> ( ( X21 = X20
& X22 != X38 )
=> c_Groups_Oplus__class_Oplus(X19,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X17),X22)) != c_Groups_Oplus__class_Oplus(X19,X20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X17),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_nat__power__less__imp__less,axiom,
! [X14,X26,X30] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X26),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X30),X14))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [X11,X25,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X11))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_real__mult__less__iff1,axiom,
! [X12,X4,X5] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X5))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_mult__le__cancel2,axiom,
! [X11,X48,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X48))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [X11,X25,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X11))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_mult__le__cancel1,axiom,
! [X11,X25,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X11))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_real__mult__le__cancel__iff1,axiom,
! [X12,X4,X5] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X5))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [X12,X4,X5] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X12))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
fof(fact_natceiling__eq,axiom,
! [X18,X14] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatceiling(X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__eq) ).
fof(fact_norm__triangle__ineq2,axiom,
! [X20,X21,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X21),c_RealVector_Onorm__class_Onorm(X19,X20)),c_RealVector_Onorm__class_Onorm(X19,c_Groups_Ominus__class_Ominus(X19,X21,X20))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).
fof(fact_norm__triangle__ineq,axiom,
! [X16,X18,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,c_Groups_Oplus__class_Oplus(X19,X18,X16)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X18),c_RealVector_Onorm__class_Onorm(X19,X16))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).
fof(fact_poly__add,axiom,
! [X18,X52,X51,X19] :
( class_Rings_Ocomm__semiring__0(X19)
=> hAPP(c_Polynomial_Opoly(X19,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X19),X51,X52)),X18) = c_Groups_Oplus__class_Oplus(X19,hAPP(c_Polynomial_Opoly(X19,X51),X18),hAPP(c_Polynomial_Opoly(X19,X52),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__add) ).
fof(fact_zmod__simps_I3_J,axiom,
! [X22,X20,X21] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20,X22)),X22) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X20),X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
fof(fact_zmod__zmult1__eq,axiom,
! [X22,X20,X21] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X20),X22) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20,X22)),X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
fof(fact_le__diff__conv2,axiom,
! [X90,X94,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X94)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X90,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X94,X48))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X90,X48),X94) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_zadd__zmult__distrib,axiom,
! [X27,X74,X75] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X75,X74)),X27) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X75),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X74),X27)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_mod__mult__distrib,axiom,
! [X28,X14,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14)),X28) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).
fof(fact_add__mult__distrib,axiom,
! [X28,X14,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X14)),X28) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_real__add__mult__distrib,axiom,
! [X27,X74,X75] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X75,X74)),X27) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X75),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X74),X27)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_mod__div__equality2,axiom,
! [X21,X20,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),c_Divides_Odiv__class_Odiv(X19,X21,X20)),c_Divides_Odiv__class_Omod(X19,X21,X20)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__equality2) ).
fof(fact_norm__power__ineq,axiom,
! [X14,X18,X19] :
( class_RealVector_Oreal__normed__algebra__1(X19)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X19,X18)),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__power__ineq) ).
fof(fact_add__less__imp__less__right,axiom,
! [X20,X22,X21,X19] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X21,X22),c_Groups_Oplus__class_Oplus(X19,X20,X22))
=> c_Orderings_Oord__class_Oless(X19,X21,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__right,axiom,
! [X23,X37,X24,X19] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X24,X37),c_Groups_Oplus__class_Oplus(X19,X23,X37))
<=> c_Orderings_Oord__class_Oless(X19,X24,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__left,axiom,
! [X20,X21,X22,X19] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X22,X21),c_Groups_Oplus__class_Oplus(X19,X22,X20))
=> c_Orderings_Oord__class_Oless(X19,X21,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__cancel__left,axiom,
! [X23,X24,X37,X19] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X37,X24),c_Groups_Oplus__class_Oplus(X19,X37,X23))
<=> c_Orderings_Oord__class_Oless(X19,X24,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__le__imp__le__right,axiom,
! [X20,X22,X21,X19] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oplus__class_Oplus(X19,X21,X22),c_Groups_Oplus__class_Oplus(X19,X20,X22))
=> c_Orderings_Oord__class_Oless__eq(X19,X21,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__right,axiom,
! [X23,X37,X24,X19] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oplus__class_Oplus(X19,X24,X37),c_Groups_Oplus__class_Oplus(X19,X23,X37))
<=> c_Orderings_Oord__class_Oless__eq(X19,X24,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__left,axiom,
! [X20,X21,X22,X19] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oplus__class_Oplus(X19,X22,X21),c_Groups_Oplus__class_Oplus(X19,X22,X20))
=> c_Orderings_Oord__class_Oless__eq(X19,X21,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__cancel__left,axiom,
! [X23,X24,X37,X19] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oplus__class_Oplus(X19,X37,X24),c_Groups_Oplus__class_Oplus(X19,X37,X23))
<=> c_Orderings_Oord__class_Oless__eq(X19,X24,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [X14,X26,X28] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X26)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X14)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X28),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X28)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_real__of__nat__div4,axiom,
! [X18,X14] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X14,X18)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),c_RealDef_Oreal(tc_Nat_Onat,X18))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__div4) ).
fof(fact_power__gt1__lemma,axiom,
! [X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),X21)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_zpower__zadd__distrib,axiom,
! [X6,X16,X18] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X18),X16)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X18),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X11,X25,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X25),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X11))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X11,X25,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X25),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X11))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_self__quotient__aux2,axiom,
! [X52,X17,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ( X21 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X52))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_power__one__over,axiom,
! [X14,X21,X19] :
( class_Fields_Ofield__inverse__zero(X19)
=> c_Rings_Oinverse__class_Odivide(X19,c_Groups_Oone__class_Oone(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)) = hAPP(hAPP(c_Power_Opower__class_Opower(X19),c_Rings_Oinverse__class_Odivide(X19,c_Groups_Oone__class_Oone(X19),X21)),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__over) ).
fof(fact_divide__strict__right__mono,axiom,
! [X22,X20,X21,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X21,X22),c_Rings_Oinverse__class_Odivide(X19,X20,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).
fof(fact_divide__right__mono,axiom,
! [X22,X20,X21,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X21,X22),c_Rings_Oinverse__class_Odivide(X19,X20,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono) ).
fof(fact_divide__strict__right__mono__neg,axiom,
! [X22,X21,X20,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X20,X21)
=> ( c_Orderings_Oord__class_Oless(X19,X22,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X21,X22),c_Rings_Oinverse__class_Odivide(X19,X20,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).
fof(fact_divide__right__mono__neg,axiom,
! [X22,X20,X21,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X22,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X20,X22),c_Rings_Oinverse__class_Odivide(X19,X21,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).
fof(fact_self__quotient__aux1,axiom,
! [X52,X17,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ( X21 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X52))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X52) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_zmod__zdiv__equality,axiom,
! [X20,X21] : X21 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [X20,X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14) = hAPP(hAPP(c_Power_Opower__class_Opower(X19),X20),X14)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
=> X21 = X20 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [X26,X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X26),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oplus__class_Oplus(X19,X21,c_Groups_Oone__class_Oone(X19))),X26) ),
file('/export/starexec/sandbox/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,
! [X21,X26,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> c_Groups_Oplus__class_Oplus(X19,X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oplus__class_Oplus(X19,X21,c_Groups_Oone__class_Oone(X19))),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_natfloor__eq,axiom,
! [X18,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),X18)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatfloor(X18) = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__eq) ).
fof(fact_mult__right__le__one__le,axiom,
! [X16,X18,X19] :
( class_Rings_Olinordered__idom(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X18)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X16)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X16,c_Groups_Oone__class_Oone(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16),X18) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_mult__left__le__one__le,axiom,
! [X16,X18,X19] :
( class_Rings_Olinordered__idom(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X18)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X16)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X16,c_Groups_Oone__class_Oone(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X18),X18) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_norm__ratiotest__lemma,axiom,
! [X16,X18,X22,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),c_RealVector_Onorm__class_Onorm(X19,X16)))
=> X18 = c_Groups_Ozero__class_Ozero(X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).
fof(fact_mult__strict__right__mono,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Olinordered__comm__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_power__mono,axiom,
! [X14,X20,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X20),X14)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono) ).
fof(fact_mult__right__mono,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Oordered__semiring(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono) ).
fof(fact_comm__mult__left__mono,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Oordered__comm__semiring(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Oordered__semiring(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [X22,X21,X20,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X20,X21)
=> ( c_Orderings_Oord__class_Oless(X19,X22,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [X22,X21,X20,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X20,X21)
=> ( c_Orderings_Oord__class_Oless(X19,X22,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_mult__right__mono__neg,axiom,
! [X22,X21,X20,X19] :
( class_Rings_Oordered__ring(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X22,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_mult__left__mono__neg,axiom,
! [X22,X21,X20,X19] :
( class_Rings_Oordered__ring(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X22,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_le__add__diff,axiom,
! [X26,X14,X28] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X26),X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(fact_add__strict__mono,axiom,
! [X38,X22,X20,X21,X19] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless(X19,X22,X38)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X21,X22),c_Groups_Oplus__class_Oplus(X19,X20,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_add__le__less__mono,axiom,
! [X38,X22,X20,X21,X19] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless(X19,X22,X38)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X21,X22),c_Groups_Oplus__class_Oplus(X19,X20,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X38,X22,X20,X21,X19] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X22,X38)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X21,X22),c_Groups_Oplus__class_Oplus(X19,X20,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_add__mono,axiom,
! [X38,X22,X20,X21,X19] :
( class_Groups_Oordered__ab__semigroup__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X22,X38)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oplus__class_Oplus(X19,X21,X22),c_Groups_Oplus__class_Oplus(X19,X20,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_mod__pos__neg__trivial,axiom,
! [X20,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X20),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).
fof(fact_power__strict__increasing,axiom,
! [X21,X78,X14,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X78)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),X21)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X78)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_power__increasing,axiom,
! [X21,X78,X14,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X78)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oone__class_Oone(X19),X21)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X78)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing) ).
fof(fact_add__divide__distrib,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Odivision__ring(X19)
=> c_Rings_Oinverse__class_Odivide(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X22) = c_Groups_Oplus__class_Oplus(X19,c_Rings_Oinverse__class_Odivide(X19,X21,X22),c_Rings_Oinverse__class_Odivide(X19,X20,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__distrib) ).
fof(fact_divide_Oadd,axiom,
! [X31,X16,X18,X19] :
( class_RealVector_Oreal__normed__field(X19)
=> c_Rings_Oinverse__class_Odivide(X19,c_Groups_Oplus__class_Oplus(X19,X18,X16),X31) = c_Groups_Oplus__class_Oplus(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X31),c_Rings_Oinverse__class_Odivide(X19,X16,X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Oadd) ).
fof(fact_zdiv__mono1,axiom,
! [X20,X70,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X70)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X70,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1) ).
fof(fact_div__le__mono2,axiom,
! [X28,X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X28,X14),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X28,X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono2) ).
fof(fact_zdiv__mono1__neg,axiom,
! [X20,X70,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X70)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,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,X70,X20),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).
fof(fact_zadd__zless__mono,axiom,
! [X6,X88,X27,X89] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X89,X27)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X88,X6)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X89,X88),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_diff__less__mono,axiom,
! [X22,X20,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(fact_diff__less__mono2,axiom,
! [X47,X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X47)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X47,X14),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X47,X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_add__less__mono,axiom,
! [X47,X28,X29,X30] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X29)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X47)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X28),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X47)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_add__le__mono,axiom,
! [X47,X28,X29,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X29)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X47)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X28),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X47)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_mod__mult__self2,axiom,
! [X22,X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22)),X20) = c_Divides_Odiv__class_Omod(X19,X21,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2) ).
fof(fact_mod__mult__self1,axiom,
! [X20,X22,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)),X20) = c_Divides_Odiv__class_Omod(X19,X21,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [X12,X4,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X4),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X12),X12)) = c_Groups_Ozero__class_Ozero(X19)
<=> ( X4 = c_Groups_Ozero__class_Ozero(X19)
& X12 = c_Groups_Ozero__class_Ozero(X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_mod__mult__mult1,axiom,
! [X20,X21,X22,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),c_Divides_Odiv__class_Omod(X19,X21,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).
fof(fact_mult__right_Oadd,axiom,
! [X16,X18,X67,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X67),c_Groups_Oplus__class_Oplus(X19,X18,X16)) = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X67),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X67),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_mult_Oadd__right,axiom,
! [X69,X20,X21,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Groups_Oplus__class_Oplus(X19,X20,X69)) = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X6,X16,X18,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),c_Groups_Oplus__class_Oplus(X19,X16,X6)) = c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_mult__less__cancel1,axiom,
! [X11,X25,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X11))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [X11,X48,X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X48))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
! [X23,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X24,X23))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X24)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
fof(fact_zero__less__mult__pos2,axiom,
! [X21,X20,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X21))
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [X20,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20))
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_power__commutes,axiom,
! [X14,X21,X19] :
( class_Groups_Omonoid__mult(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [X22,X20,X21,X19] :
( class_Groups_Oab__semigroup__mult(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)),X22) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [X62,X63,X64,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),X63)),X62) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X63),X62)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X61,X62,X64,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X62),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),X62)),X61) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_nat__less__real__le,axiom,
! [X25,X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X25)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
fof(fact_nat__le__real__less,axiom,
! [X25,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X25)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X25),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__real__less) ).
fof(fact_power__mult,axiom,
! [X14,X26,X21,X19] :
( class_Groups_Omonoid__mult(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X14)) = hAPP(hAPP(c_Power_Opower__class_Opower(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X26)),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X52,X51,X18,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),X51)),X52) = hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_zmult__zless__mono2,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X30,X29)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X28)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X28),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X28),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_mult__less__mono1,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X29)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X28)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X28)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X29)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X28)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_real__mult__less__mono2,axiom,
! [X16,X18,X6] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X16)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
fof(fact_less__diff__conv,axiom,
! [X48,X94,X90] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X90,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X94,X48))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X90,X48),X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(fact_le__diff__conv,axiom,
! [X90,X48,X94] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X94,X48),X90)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X94,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X90,X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(fact_mult__le__mono,axiom,
! [X47,X28,X29,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X29)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X47)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X47)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
fof(fact_poly__div__mult__right,axiom,
! [X6,X16,X18,X19] :
( class_Fields_Ofield(X19)
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X19),X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X19)),X16),X6)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X19),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X19),X18,X16),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__div__mult__right) ).
fof(fact_add__diff__assoc2,axiom,
! [X30,X29,X28] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X29)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X28),X30) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X30),X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc2,axiom,
! [X30,X29,X28] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X29)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X30),X28) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X28),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_diff__add__assoc,axiom,
! [X30,X29,X28] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X29)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X29),X28) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_diff__diff__right,axiom,
! [X30,X29,X28] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X29)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X28)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X28),X29) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).
fof(fact_add__diff__assoc,axiom,
! [X30,X29,X28] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X29)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X28)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X29),X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
! [X24,X23] :
( c_Orderings_Oord__class_Oless(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,X24,X23))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
fof(fact_neg__imp__zdiv__neg__iff,axiom,
! [X24,X23] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X24,X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
fof(fact_pos__imp__zdiv__neg__iff,axiom,
! [X24,X23] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X24,X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
! [X24,X23] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,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,X24,X23))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
fof(fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096,axiom,
? [X40] :
! [X8] :
( ? [X3] :
( ? [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X9)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8,X3) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8,X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096) ).
fof(fact_s,axiom,
! [X8] :
( ? [X3] :
( ? [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X9)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8,X3) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8,v_s____) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s) ).
fof(fact_pos__imp__zdiv__pos__iff,axiom,
! [X90,X48] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X90,X48))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,X90) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
fof(fact_divide__less__0__iff,axiom,
! [X23,X24,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X24,X23),c_Groups_Ozero__class_Ozero(X19))
<=> ( ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X24)
& c_Orderings_Oord__class_Oless(X19,X23,c_Groups_Ozero__class_Ozero(X19)) )
| ( c_Orderings_Oord__class_Oless(X19,X24,c_Groups_Ozero__class_Ozero(X19))
& c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X23) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).
fof(fact_divide__le__0__iff,axiom,
! [X23,X24,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X24,X23),c_Groups_Ozero__class_Ozero(X19))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X24)
& c_Orderings_Oord__class_Oless__eq(X19,X23,c_Groups_Ozero__class_Ozero(X19)) )
| ( c_Orderings_Oord__class_Oless__eq(X19,X24,c_Groups_Ozero__class_Ozero(X19))
& c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X23) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).
fof(fact_zero__less__divide__iff,axiom,
! [X23,X24,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Rings_Oinverse__class_Odivide(X19,X24,X23))
<=> ( ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X24)
& c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X23) )
| ( c_Orderings_Oord__class_Oless(X19,X24,c_Groups_Ozero__class_Ozero(X19))
& c_Orderings_Oord__class_Oless(X19,X23,c_Groups_Ozero__class_Ozero(X19)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).
fof(fact_zero__le__divide__iff,axiom,
! [X23,X24,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),c_Rings_Oinverse__class_Odivide(X19,X24,X23))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X24)
& c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X23) )
| ( c_Orderings_Oord__class_Oless__eq(X19,X24,c_Groups_Ozero__class_Ozero(X19))
& c_Orderings_Oord__class_Oless__eq(X19,X23,c_Groups_Ozero__class_Ozero(X19)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).
fof(fact_natfloor__div__nat,axiom,
! [X16,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X18)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16)
=> c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X18,c_RealDef_Oreal(tc_Nat_Onat,X16))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X18),X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__div__nat) ).
fof(fact_mod__mult__self3,axiom,
! [X26,X14,X28] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X14),X26),X14) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self3) ).
fof(fact_zdiv__zmult2__eq,axiom,
! [X20,X21,X22] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X22)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
fof(fact_mult__le__0__iff,axiom,
! [X23,X24,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X23),c_Groups_Ozero__class_Ozero(X19))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X24)
& c_Orderings_Oord__class_Oless__eq(X19,X23,c_Groups_Ozero__class_Ozero(X19)) )
| ( c_Orderings_Oord__class_Oless__eq(X19,X24,c_Groups_Ozero__class_Ozero(X19))
& c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X23) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [X23,X24,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X23))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X24)
& c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X23) )
| ( c_Orderings_Oord__class_Oless__eq(X19,X24,c_Groups_Ozero__class_Ozero(X19))
& c_Orderings_Oord__class_Oless__eq(X19,X23,c_Groups_Ozero__class_Ozero(X19)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_DeMoivre2,axiom,
! [X14,X21,X17] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(X17,X21)),X14) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X17),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X14)),X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DeMoivre2) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [X74,X75,X27] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X75,X74)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27),X75),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27),X74)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_mod__mult__distrib2,axiom,
! [X14,X26,X28] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).
fof(fact_add__mult__distrib2,axiom,
! [X14,X26,X28] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X14)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_mod__minus__eq,axiom,
! [X20,X21,X19] :
( class_Divides_Oring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Ouminus__class_Ouminus(X19,X21),X20) = c_Divides_Odiv__class_Omod(X19,c_Groups_Ouminus__class_Ouminus(X19,c_Divides_Odiv__class_Omod(X19,X21,X20)),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__minus__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X26,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> c_Groups_Oplus__class_Oplus(X19,X26,X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oplus__class_Oplus(X19,c_Groups_Oone__class_Oone(X19),c_Groups_Oone__class_Oone(X19))),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_nat__mult__div__cancel1,axiom,
! [X14,X26,X28] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X28)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X14)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).
fof(fact_real__two__squares__add__zero__iff,axiom,
! [X12,X4] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X12)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X4 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X12 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
fof(fact_divide__neg__pos,axiom,
! [X16,X18,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X16)
=> c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X16),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__pos) ).
fof(fact_divide__pos__neg,axiom,
! [X16,X18,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X18)
=> ( c_Orderings_Oord__class_Oless(X19,X16,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X16),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__neg) ).
fof(fact_divide__nonneg__neg,axiom,
! [X16,X18,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X18)
=> ( c_Orderings_Oord__class_Oless(X19,X16,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X16),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).
fof(fact_divide__nonpos__pos,axiom,
! [X16,X18,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X16)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X16),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).
fof(fact_add__neg__neg,axiom,
! [X20,X21,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,X20,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_add__nonpos__neg,axiom,
! [X20,X21,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,X20,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [X20,X21,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X20,X21,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_add__pos__pos,axiom,
! [X20,X21,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Oplus__class_Oplus(X19,X21,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__nonneg__pos,axiom,
! [X20,X21,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Oplus__class_Oplus(X19,X21,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X20,X21,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Oplus__class_Oplus(X19,X21,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_divide__pos__pos,axiom,
! [X16,X18,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X18)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X16)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Rings_Oinverse__class_Odivide(X19,X18,X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__pos) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X20,X21,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Oplus__class_Oplus(X19,X21,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_divide__nonneg__pos,axiom,
! [X16,X18,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X18)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X16)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),c_Rings_Oinverse__class_Odivide(X19,X18,X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).
fof(fact_divide__neg__neg,axiom,
! [X16,X18,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,X16,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Rings_Oinverse__class_Odivide(X19,X18,X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__neg) ).
fof(fact_divide__nonpos__neg,axiom,
! [X16,X18,X19] :
( class_Fields_Olinordered__field(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,X16,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),c_Rings_Oinverse__class_Odivide(X19,X18,X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).
fof(fact_poly__bound__exists,axiom,
! [X51,X17] :
? [X49] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X49)
& ! [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9),X17)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X51),X9)),X49) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__bound__exists) ).
fof(fact_add__gr__0,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X11))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_real__0__le__divide__iff,axiom,
! [X12,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4,X12))
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| 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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__le__divide__iff) ).
fof(fact_zpower__zpower,axiom,
! [X6,X16,X18] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X18),X16)),X6) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(fact_zmult__assoc,axiom,
! [X73,X74,X75] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X75),X74)),X73) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X75),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X74),X73)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(fact_nat__mult__assoc,axiom,
! [X28,X14,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X14)),X28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_real__mult__assoc,axiom,
! [X73,X74,X75] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X75),X74)),X73) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X75),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X74),X73)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
fof(fact_mult__neg__pos,axiom,
! [X20,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__pos__neg,axiom,
! [X20,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless(X19,X20,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [X20,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless(X19,X20,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X21),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_split__mult__neg__le,axiom,
! [X20,X21,X19] :
( class_Rings_Oordered__cancel__semiring(X19)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
& c_Orderings_Oord__class_Oless__eq(X19,X20,c_Groups_Ozero__class_Ozero(X19)) )
| ( c_Orderings_Oord__class_Oless__eq(X19,X21,c_Groups_Ozero__class_Ozero(X19))
& c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X20) ) )
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),c_Groups_Ozero__class_Ozero(X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [X20,X21,X19] :
( class_Rings_Oordered__cancel__semiring(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [X20,X21,X19] :
( class_Rings_Oordered__cancel__semiring(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [X20,X21,X19] :
( class_Rings_Oordered__cancel__semiring(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X21),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_less__1__mult,axiom,
! [X14,X26,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),X26)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),X14)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X26),X14)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(fact_mult__pos__pos,axiom,
! [X20,X21,X19] :
( class_Rings_Olinordered__semiring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_split__mult__pos__le,axiom,
! [X20,X21,X19] :
( class_Rings_Oordered__ring(X19)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
& c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X20) )
| ( c_Orderings_Oord__class_Oless__eq(X19,X21,c_Groups_Ozero__class_Ozero(X19))
& c_Orderings_Oord__class_Oless__eq(X19,X20,c_Groups_Ozero__class_Ozero(X19)) ) )
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [X20,X21,X19] :
( class_Rings_Oordered__cancel__semiring(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X20)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_mult__neg__neg,axiom,
! [X20,X21,X19] :
( class_Rings_Olinordered__ring__strict(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless(X19,X20,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [X20,X21,X19] :
( class_Rings_Oordered__ring(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,c_Groups_Ozero__class_Ozero(X19))
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_add__strict__right__mono,axiom,
! [X22,X20,X21,X19] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X21,X22),c_Groups_Oplus__class_Oplus(X19,X20,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X22,X20,X21,X19] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X22,X21),c_Groups_Oplus__class_Oplus(X19,X22,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_add__right__mono,axiom,
! [X22,X20,X21,X19] :
( class_Groups_Oordered__ab__semigroup__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oplus__class_Oplus(X19,X21,X22),c_Groups_Oplus__class_Oplus(X19,X20,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X22,X20,X21,X19] :
( class_Groups_Oordered__ab__semigroup__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oplus__class_Oplus(X19,X22,X21),c_Groups_Oplus__class_Oplus(X19,X22,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_zminus__zmod,axiom,
! [X26,X18] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X18,X26)),X26) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X18),X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zmod) ).
fof(fact_realpow__pos__nth__unique,axiom,
! [X21,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)
=> ? [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),X14) = X21
& ! [X8] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X8),X14) = X21 )
=> X8 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__pos__nth__unique) ).
fof(fact_one__less__power,axiom,
! [X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),X21)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(fact_incseq__def,axiom,
! [X33,X19] :
( class_Orderings_Oorder(X19)
=> ( c_SEQ_Oincseq(X19,X33)
<=> ! [X49,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49,X10)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(X33,X49),hAPP(X33,X10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_incseq__def) ).
fof(fact_decseq__def,axiom,
! [X33,X19] :
( class_Orderings_Oorder(X19)
=> ( c_SEQ_Odecseq(X19,X33)
<=> ! [X49,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49,X10)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(X33,X10),hAPP(X33,X49)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decseq__def) ).
fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
! [X14,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X14)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,c_RealDef_Oreal(tc_Nat_Onat,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
fof(fact_add__strict__increasing2,axiom,
! [X22,X20,X21,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless(X19,X20,X22)
=> c_Orderings_Oord__class_Oless(X19,X20,c_Groups_Oplus__class_Oplus(X19,X21,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X22,X20,X21,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,X22)
=> c_Orderings_Oord__class_Oless(X19,X20,c_Groups_Oplus__class_Oplus(X19,X21,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_pos__add__strict,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless(X19,X20,X22)
=> c_Orderings_Oord__class_Oless(X19,X20,c_Groups_Oplus__class_Oplus(X19,X21,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_add__increasing,axiom,
! [X22,X20,X21,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,X22)
=> c_Orderings_Oord__class_Oless__eq(X19,X20,c_Groups_Oplus__class_Oplus(X19,X21,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X21,X20,X22,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X22)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,X21)
=> c_Orderings_Oord__class_Oless__eq(X19,X20,c_Groups_Oplus__class_Oplus(X19,X21,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_real__minus__mult__self__le,axiom,
! [X18,X72] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X72),X72)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).
fof(fact_s1m,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X6),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s1m) ).
fof(fact_zadd__strict__right__mono,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X30,X29)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,X28),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X29,X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_add__less__mono1,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X29)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X28),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_zadd__left__mono,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X30,X29)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X28,X30),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X28,X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_diff__le__mono,axiom,
! [X47,X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X47),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__le__mono2,axiom,
! [X47,X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X47,X14),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X47,X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_div__le__mono,axiom,
! [X28,X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,X28),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X14,X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono) ).
fof(fact_add__le__mono1,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X29)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X28),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_real__add__left__mono,axiom,
! [X6,X16,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,X18),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_div__add__self1,axiom,
! [X21,X20,X19] :
( class_Divides_Osemiring__div(X19)
=> ( X20 != c_Groups_Ozero__class_Ozero(X19)
=> c_Divides_Odiv__class_Odiv(X19,c_Groups_Oplus__class_Oplus(X19,X20,X21),X20) = c_Groups_Oplus__class_Oplus(X19,c_Divides_Odiv__class_Odiv(X19,X21,X20),c_Groups_Oone__class_Oone(X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self1) ).
fof(fact_div__add__self2,axiom,
! [X21,X20,X19] :
( class_Divides_Osemiring__div(X19)
=> ( X20 != c_Groups_Ozero__class_Ozero(X19)
=> c_Divides_Odiv__class_Odiv(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X20) = c_Groups_Oplus__class_Oplus(X19,c_Divides_Odiv__class_Odiv(X19,X21,X20),c_Groups_Oone__class_Oone(X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self2) ).
fof(fact_mod__minus__cong,axiom,
! [X70,X20,X21,X19] :
( class_Divides_Oring__div(X19)
=> ( c_Divides_Odiv__class_Omod(X19,X21,X20) = c_Divides_Odiv__class_Omod(X19,X70,X20)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Ouminus__class_Ouminus(X19,X21),X20) = c_Divides_Odiv__class_Omod(X19,c_Groups_Ouminus__class_Ouminus(X19,X70),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__minus__cong) ).
fof(fact_div__neg__pos__less0,axiom,
! [X20,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).
fof(fact_div__nonneg__neg__le0,axiom,
! [X20,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,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,X21,X20),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).
fof(fact_div__nonpos__pos__le0,axiom,
! [X20,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X16,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X18,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X16,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X16)
=> 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,X18,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X16,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X16)
=> 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,X18,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_eq__diff__iff,axiom,
! [X11,X25,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X11)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X48) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X48)
<=> X25 = X11 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_int__div__less__self,axiom,
! [X28,X18] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X28)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X18,X28),X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__div__less__self) ).
fof(fact_diff__less,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14),X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).
fof(fact_div__less__dividend,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X14)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,X14),X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less__dividend) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X24,X19] :
( class_Groups_Olinordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Oplus__class_Oplus(X19,X24,X24))
<=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X24,X19] :
( class_Groups_Olinordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Oplus__class_Oplus(X19,X24,X24))
<=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X24,X19] :
( class_Groups_Olinordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X24,X24),c_Groups_Ozero__class_Ozero(X19))
<=> c_Orderings_Oord__class_Oless(X19,X24,c_Groups_Ozero__class_Ozero(X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_even__less__0__iff,axiom,
! [X24,X19] :
( class_Rings_Olinordered__idom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,X24,X24),c_Groups_Ozero__class_Ozero(X19))
<=> c_Orderings_Oord__class_Oless(X19,X24,c_Groups_Ozero__class_Ozero(X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X24,X19] :
( class_Groups_Olinordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oplus__class_Oplus(X19,X24,X24),c_Groups_Ozero__class_Ozero(X19))
<=> c_Orderings_Oord__class_Oless__eq(X19,X24,c_Groups_Ozero__class_Ozero(X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_rcis__mult,axiom,
! [X20,X91,X21,X92] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X92,X21)),c_Complex_Orcis(X91,X20)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X92),X91),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rcis__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X22) = c_Groups_Oplus__class_Oplus(X19,c_Groups_Oplus__class_Oplus(X19,X21,X22),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X22) = c_Groups_Oplus__class_Oplus(X19,X21,c_Groups_Oplus__class_Oplus(X19,X20,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X22,X20,X21,X19] :
( class_Groups_Oab__semigroup__add(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X22) = c_Groups_Oplus__class_Oplus(X19,X21,c_Groups_Oplus__class_Oplus(X19,X20,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X38,X22,X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> c_Groups_Oplus__class_Oplus(X19,X21,c_Groups_Oplus__class_Oplus(X19,X22,X38)) = c_Groups_Oplus__class_Oplus(X19,c_Groups_Oplus__class_Oplus(X19,X21,X22),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X38,X22,X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> c_Groups_Oplus__class_Oplus(X19,X21,c_Groups_Oplus__class_Oplus(X19,X22,X38)) = c_Groups_Oplus__class_Oplus(X19,X22,c_Groups_Oplus__class_Oplus(X19,X21,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_real__0__less__add__iff,axiom,
! [X12,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,X4,X12))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
fof(fact_real__0__le__add__iff,axiom,
! [X12,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X12))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).
fof(fact_real__add__less__0__iff,axiom,
! [X12,X4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
fof(fact_real__add__le__0__iff,axiom,
! [X12,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
fof(fact_div__mult__mult1__if,axiom,
! [X20,X21,X22,X19] :
( class_Divides_Osemiring__div(X19)
=> ( ( X22 = c_Groups_Ozero__class_Ozero(X19)
=> c_Divides_Odiv__class_Odiv(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)) = c_Groups_Ozero__class_Ozero(X19) )
& ( X22 != c_Groups_Ozero__class_Ozero(X19)
=> c_Divides_Odiv__class_Odiv(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)) = c_Divides_Odiv__class_Odiv(X19,X21,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).
fof(fact_div__mult__mult1,axiom,
! [X20,X21,X22,X19] :
( class_Divides_Osemiring__div(X19)
=> ( X22 != c_Groups_Ozero__class_Ozero(X19)
=> c_Divides_Odiv__class_Odiv(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)) = c_Divides_Odiv__class_Odiv(X19,X21,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1) ).
fof(fact_div__mult__mult2,axiom,
! [X20,X21,X22,X19] :
( class_Divides_Osemiring__div(X19)
=> ( X22 != c_Groups_Ozero__class_Ozero(X19)
=> c_Divides_Odiv__class_Odiv(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22)) = c_Divides_Odiv__class_Odiv(X19,X21,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult2) ).
fof(fact_mult__divide__mult__cancel__left,axiom,
! [X20,X21,X22,X19] :
( class_Fields_Ofield__inverse__zero(X19)
=> ( X22 != c_Groups_Ozero__class_Ozero(X19)
=> c_Rings_Oinverse__class_Odivide(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X22),X20)) = c_Rings_Oinverse__class_Odivide(X19,X21,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
fof(fact_mult__divide__mult__cancel__right,axiom,
! [X20,X21,X22,X19] :
( class_Fields_Ofield__inverse__zero(X19)
=> ( X22 != c_Groups_Ozero__class_Ozero(X19)
=> c_Rings_Oinverse__class_Odivide(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X22)) = c_Rings_Oinverse__class_Odivide(X19,X21,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [X11,X25] :
( 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),X25),X11))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_real__mult__order,axiom,
! [X16,X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X16)
=> 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),X18),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__order) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X16,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X16)
=> 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),X18),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_le__cube,axiom,
! [X26] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X26))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
fof(fact_times__divide__eq__right,axiom,
! [X22,X20,X21,X19] :
( class_Rings_Odivision__ring(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Rings_Oinverse__class_Odivide(X19,X20,X22)) = c_Rings_Oinverse__class_Odivide(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
fof(fact_diff__eq__diff__less,axiom,
! [X65,X37,X23,X24,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Groups_Ominus__class_Ominus(X19,X24,X23) = c_Groups_Ominus__class_Ominus(X19,X37,X65)
=> ( c_Orderings_Oord__class_Oless(X19,X24,X23)
<=> c_Orderings_Oord__class_Oless(X19,X37,X65) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [X65,X37,X23,X24,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Groups_Ominus__class_Ominus(X19,X24,X23) = c_Groups_Ominus__class_Ominus(X19,X37,X65)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X24,X23)
<=> c_Orderings_Oord__class_Oless__eq(X19,X37,X65) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_mult__le__mono1,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X29)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X29)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
fof(fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5),v_r)
=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X5)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X61,X62,X64,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X62),X61)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X64),X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_diff__cancel,axiom,
! [X14,X26,X28] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X26),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X14)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__cancel2,axiom,
! [X14,X28,X26] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X28),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X28)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__diff__left,axiom,
! [X28,X29,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X29),X28) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_zadd__assoc,axiom,
! [X73,X74,X75] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X75,X74),X73) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X75,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X74,X73)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_nat__add__assoc,axiom,
! [X28,X14,X26] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X14),X28) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_zadd__left__commute,axiom,
! [X6,X16,X18] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,X6)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [X6,X16,X18] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X6)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_zless__add1__eq,axiom,
! [X5,X66] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X66,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X66,X5)
| X66 = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_mth2,axiom,
? [X9] :
! [X3] :
( ? [X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X13),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X13)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mth2) ).
fof(fact_add1__zle__eq,axiom,
! [X5,X66] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X66,c_Groups_Oone__class_Oone(tc_Int_Oint)),X5)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X66,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zle__add1__eq__le,axiom,
! [X5,X66] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X66,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X66,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_zero__less__diff,axiom,
! [X25,X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X25))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(fact_less__add__eq__less,axiom,
! [X14,X26,X47,X28] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X47)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X47) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_natfloor__add,axiom,
! [X21,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,c_RealDef_Oreal(tc_Nat_Onat,X21))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X18),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__add) ).
fof(fact_natceiling__add,axiom,
! [X21,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,c_RealDef_Oreal(tc_Nat_Onat,X21))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X18),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__add) ).
fof(fact_add__lessD1,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X29),X28)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_add__leD1,axiom,
! [X14,X28,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X28),X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X14,X28,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X28),X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_div__mult2__eq,axiom,
! [X22,X20,X21] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X22)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X21,X20),X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult2__eq) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X12,X4,X19] :
( class_Groups_Oordered__comm__monoid__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X12)
=> ( c_Groups_Oplus__class_Oplus(X19,X4,X12) = c_Groups_Ozero__class_Ozero(X19)
<=> ( X4 = c_Groups_Ozero__class_Ozero(X19)
& X12 = c_Groups_Ozero__class_Ozero(X19) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_frac__eq__eq,axiom,
! [X66,X4,X5,X12,X19] :
( class_Fields_Ofield(X19)
=> ( X12 != c_Groups_Ozero__class_Ozero(X19)
=> ( X5 != c_Groups_Ozero__class_Ozero(X19)
=> ( c_Rings_Oinverse__class_Odivide(X19,X4,X12) = c_Rings_Oinverse__class_Odivide(X19,X66,X5)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X4),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X66),X12) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
fof(fact_le__mod__geq,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X26)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__mod__geq) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [X11,X4] :
( 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),X4),X11))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4)
| X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [X11,X4] :
( 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),X4),X11))
<=> ( X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_nat__mult__div__cancel__disj,axiom,
! [X14,X26,X28] :
( ( X28 = 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),X28),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X14)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X28 != 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),X28),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X14)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
fof(fact_real__divide__square__eq,axiom,
! [X21,X17] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X17)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X21,X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__divide__square__eq) ).
fof(fact_realpow__pos__nth,axiom,
! [X21,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)
=> ? [X87] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X87)
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X87),X14) = X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__pos__nth) ).
fof(fact_power__inject__exp,axiom,
! [X11,X25,X24,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),X24)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X19),X24),X25) = hAPP(hAPP(c_Power_Opower__class_Opower(X19),X24),X11)
<=> X25 = X11 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(fact_less__natfloor,axiom,
! [X14,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_RealDef_Oreal(tc_Nat_Onat,X14))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X18),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__natfloor) ).
fof(fact_natceiling__le__eq,axiom,
! [X24,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_Nat_Onat,c_RComplete_Onatceiling(X4),X24)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,c_RealDef_Oreal(tc_Nat_Onat,X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).
fof(fact_le__natfloor__eq,axiom,
! [X24,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_Nat_Onat,X24,c_RComplete_Onatfloor(X4))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X24),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).
fof(fact_zero__less__power,axiom,
! [X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(fact_one__le__power,axiom,
! [X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oone__class_Oone(X19),X21)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oone__class_Oone(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__power) ).
fof(fact_zero__le__power,axiom,
! [X14,X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X21)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power) ).
fof(fact_natfloor__add__one,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X18),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__add__one) ).
fof(fact_natceiling__add__one,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X18),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__add__one) ).
fof(fact_odd__nonzero,axiom,
! [X6] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X6),X6) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(fact_power_Opower_Opower__0,axiom,
! [X24,X85,X86,X19] : hAPP(hAPP(c_Power_Opower_Opower(X19,X86,X85),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X86,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(fact_le__imp__0__less,axiom,
! [X6] :
( 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),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_neg__mod__conj,axiom,
! [X21,X20] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__conj) ).
fof(fact_neg__mod__sign,axiom,
! [X21,X20] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__sign) ).
fof(fact_pos__mod__conj,axiom,
! [X21,X20] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__conj) ).
fof(fact_pos__mod__sign,axiom,
! [X21,X20] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__sign) ).
fof(fact_norm__mult,axiom,
! [X16,X18,X19] :
( class_RealVector_Oreal__normed__div__algebra(X19)
=> c_RealVector_Onorm__class_Onorm(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X19,X18)),c_RealVector_Onorm__class_Onorm(X19,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult) ).
fof(fact_zless__imp__add1__zle,axiom,
! [X6,X27] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,c_Groups_Oone__class_Oone(tc_Int_Oint)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_pos__mod__bound,axiom,
! [X21,X20] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
fof(fact_mod__less__divisor,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
fof(fact_zmod__le__nonneg__dividend,axiom,
! [X28,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,X28),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).
fof(fact_mod__le__divisor,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__le__divisor) ).
fof(fact_neg__mod__bound,axiom,
! [X21,X20] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
fof(fact_poly__mod__minus__left,axiom,
! [X16,X18,X19] :
( class_Fields_Ofield(X19)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X19),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X19),X18),X16) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X19),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X19),X18,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mod__minus__left) ).
fof(fact_poly__div__minus__left,axiom,
! [X16,X18,X19] :
( class_Fields_Ofield(X19)
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X19),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X19),X18),X16) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X19),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X19),X18,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__div__minus__left) ).
fof(fact_poly__div__minus__right,axiom,
! [X16,X18,X19] :
( class_Fields_Ofield(X19)
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X19),X18,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X19),X16)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X19),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X19),X18,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__div__minus__right) ).
fof(fact_le__add__diff__inverse2,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X26)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14),X14) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_diff__diff__cancel,axiom,
! [X14,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X14)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X30)) = X30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_le__add__diff__inverse,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X26)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14)) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_le__funE,axiom,
! [X4,X1,X2,X19,X34] :
( class_Orderings_Oord(X34)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X19,X34),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X34,hAPP(X2,X4),hAPP(X1,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_le__funD,axiom,
! [X4,X1,X2,X19,X34] :
( class_Orderings_Oord(X34)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X19,X34),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X34,hAPP(X2,X4),hAPP(X1,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_less__imp__diff__less,axiom,
! [X14,X28,X29] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X28)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X14),X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X6,X16,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X16)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add1,axiom,
! [X26,X29,X30] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X29)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X16,X6,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_trans__less__add2,axiom,
! [X26,X29,X30] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X29)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X6,X16,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add1,axiom,
! [X26,X29,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X29)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X16,X6,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_trans__le__add2,axiom,
! [X26,X29,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X29)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_norm__divide,axiom,
! [X20,X21,X19] :
( ( class_Fields_Ofield__inverse__zero(X19)
& class_RealVector_Oreal__normed__field(X19) )
=> c_RealVector_Onorm__class_Onorm(X19,c_Rings_Oinverse__class_Odivide(X19,X21,X20)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X21),c_RealVector_Onorm__class_Onorm(X19,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__divide) ).
fof(fact_nonzero__norm__divide,axiom,
! [X21,X20,X19] :
( class_RealVector_Oreal__normed__field(X19)
=> ( X20 != c_Groups_Ozero__class_Ozero(X19)
=> c_RealVector_Onorm__class_Onorm(X19,c_Rings_Oinverse__class_Odivide(X19,X21,X20)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X21),c_RealVector_Onorm__class_Onorm(X19,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__norm__divide) ).
fof(fact_zmod__zminus2,axiom,
! [X20,X21] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X21),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [X11,X25,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X11)
<=> X25 = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [X14,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> 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),X18),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_order__less__trans,axiom,
! [X6,X16,X18,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> ( c_Orderings_Oord__class_Oless(X19,X16,X6)
=> c_Orderings_Oord__class_Oless(X19,X18,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X6,X16,X18,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,X16)
=> ( c_Orderings_Oord__class_Oless(X19,X16,X6)
=> c_Orderings_Oord__class_Oless(X19,X18,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X6,X16,X18,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X16,X6)
=> c_Orderings_Oord__class_Oless(X19,X18,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X6,X18,X16,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X16,X18)
=> ( c_Orderings_Oord__class_Oless(X19,X6,X16)
=> c_Orderings_Oord__class_Oless(X19,X6,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_xt1_I8_J,axiom,
! [X6,X18,X16,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X16,X18)
=> ( c_Orderings_Oord__class_Oless(X19,X6,X16)
=> c_Orderings_Oord__class_Oless(X19,X6,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X6,X18,X16,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X16,X18)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X6,X16)
=> c_Orderings_Oord__class_Oless(X19,X6,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__trans,axiom,
! [X6,X16,X18,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,X16)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X16,X6)
=> c_Orderings_Oord__class_Oless__eq(X19,X18,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X6,X18,X16,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X16,X18)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X6,X16)
=> c_Orderings_Oord__class_Oless__eq(X19,X6,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_minus__add__distrib,axiom,
! [X20,X21,X19] :
( class_Groups_Oab__group__add(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20)) = c_Groups_Oplus__class_Oplus(X19,c_Groups_Ouminus__class_Ouminus(X19,X21),c_Groups_Ouminus__class_Ouminus(X19,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_minus__add,axiom,
! [X20,X21,X19] :
( class_Groups_Ogroup__add(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20)) = c_Groups_Oplus__class_Oplus(X19,c_Groups_Ouminus__class_Ouminus(X19,X20),c_Groups_Ouminus__class_Ouminus(X19,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add) ).
fof(fact_real__natfloor__add__one__gt,axiom,
! [X18] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X18)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).
fof(fact_div__mult__self1__is__m,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X26),X14) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).
fof(fact_div__mult__self__is__m,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X14),X14) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).
fof(fact_neg__less__iff__less,axiom,
! [X24,X23,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ouminus__class_Ouminus(X19,X23),c_Groups_Ouminus__class_Ouminus(X19,X24))
<=> c_Orderings_Oord__class_Oless(X19,X24,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_compl__le__compl__iff,axiom,
! [X12,X4,X19] :
( class_Lattices_Oboolean__algebra(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ouminus__class_Ouminus(X19,X4),c_Groups_Ouminus__class_Ouminus(X19,X12))
<=> c_Orderings_Oord__class_Oless__eq(X19,X12,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_neg__le__iff__le,axiom,
! [X24,X23,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ouminus__class_Ouminus(X19,X23),c_Groups_Ouminus__class_Ouminus(X19,X24))
<=> c_Orderings_Oord__class_Oless__eq(X19,X24,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_div__pos__pos__trivial,axiom,
! [X20,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X20)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).
fof(fact_zdiv__eq__0__iff,axiom,
! [X48,X90] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X90,X48) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( X48 = 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),X90)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X90,X48) )
| ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X90,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X90) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(fact_div__neg__neg__trivial,axiom,
! [X20,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,X21)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).
fof(fact_mult__left_Ominus,axiom,
! [X16,X18,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ouminus__class_Ouminus(X19,X18)),X16) = c_Groups_Ouminus__class_Ouminus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
fof(fact_mult_Ominus__left,axiom,
! [X20,X21,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ouminus__class_Ouminus(X19,X21)),X20) = c_Groups_Ouminus__class_Ouminus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
fof(fact_minus__mult__left,axiom,
! [X20,X21,X19] :
( class_Rings_Oring(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ouminus__class_Ouminus(X19,X21)),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__left) ).
fof(fact_mod__pos__pos__trivial,axiom,
! [X20,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X20)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20) = X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).
fof(fact_mod__neg__neg__trivial,axiom,
! [X20,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,X21)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20) = X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).
fof(fact_le__imp__diff__is__add,axiom,
! [X48,X94,X90] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X90,X94)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X94,X90) = X48
<=> X94 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X90) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_mod__mod__trivial,axiom,
! [X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Divides_Odiv__class_Omod(X19,X21,X20),X20) = c_Divides_Odiv__class_Omod(X19,X21,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).
fof(fact_mod__add__self1,axiom,
! [X21,X20,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X20,X21),X20) = c_Divides_Odiv__class_Omod(X19,X21,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self1) ).
fof(fact_mod__add__self2,axiom,
! [X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X20) = c_Divides_Odiv__class_Omod(X19,X21,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self2) ).
fof(fact_norm__power,axiom,
! [X14,X18,X19] :
( class_RealVector_Oreal__normed__div__algebra(X19)
=> c_RealVector_Onorm__class_Onorm(X19,hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),X14)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X19,X18)),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__power) ).
fof(fact_add__minus__cancel,axiom,
! [X20,X21,X19] :
( class_Groups_Ogroup__add(X19)
=> c_Groups_Oplus__class_Oplus(X19,X21,c_Groups_Oplus__class_Oplus(X19,c_Groups_Ouminus__class_Ouminus(X19,X21),X20)) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_zle__trans,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X30,X29)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X29,X28)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X30,X28) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(fact_le__trans,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X29)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X28)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X28) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_real__le__trans,axiom,
! [X28,X29,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X30,X29)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X29,X28)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X30,X28) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_real__of__nat__mult,axiom,
! [X14,X26] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X14)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X26)),c_RealDef_Oreal(tc_Nat_Onat,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).
fof(fact_poly__minus,axiom,
! [X18,X51,X19] :
( class_Rings_Ocomm__ring(X19)
=> hAPP(c_Polynomial_Opoly(X19,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X19),X51)),X18) = c_Groups_Ouminus__class_Ouminus(X19,hAPP(c_Polynomial_Opoly(X19,X51),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__minus) ).
fof(fact_minus__less__iff,axiom,
! [X23,X24,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ouminus__class_Ouminus(X19,X24),X23)
<=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ouminus__class_Ouminus(X19,X23),X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).
fof(fact_minus__le__iff,axiom,
! [X23,X24,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ouminus__class_Ouminus(X19,X24),X23)
<=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ouminus__class_Ouminus(X19,X23),X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__iff) ).
fof(fact_less__minus__iff,axiom,
! [X23,X24,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X24,c_Groups_Ouminus__class_Ouminus(X19,X23))
<=> c_Orderings_Oord__class_Oless(X19,X23,c_Groups_Ouminus__class_Ouminus(X19,X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__iff) ).
fof(fact_le__minus__iff,axiom,
! [X23,X24,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X24,c_Groups_Ouminus__class_Ouminus(X19,X23))
<=> c_Orderings_Oord__class_Oless__eq(X19,X23,c_Groups_Ouminus__class_Ouminus(X19,X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__iff) ).
fof(fact_zmod__zminus__zminus,axiom,
! [X20,X21] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X21),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus__zminus) ).
fof(fact_real__of__nat__add,axiom,
! [X14,X26] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X14)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X26),c_RealDef_Oreal(tc_Nat_Onat,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
fof(fact_zminus__zadd__distrib,axiom,
! [X27,X6] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,X27)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X6),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X27)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_nonzero__minus__divide__right,axiom,
! [X21,X20,X19] :
( class_Rings_Odivision__ring(X19)
=> ( X20 != c_Groups_Ozero__class_Ozero(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,c_Rings_Oinverse__class_Odivide(X19,X21,X20)) = c_Rings_Oinverse__class_Odivide(X19,X21,c_Groups_Ouminus__class_Ouminus(X19,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).
fof(fact_mult__left__idem,axiom,
! [X20,X21,X19] :
( class_Lattices_Oab__semigroup__idem__mult(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__idem) ).
fof(fact_real__of__nat__less__iff,axiom,
! [X25,X11] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11),c_RealDef_Oreal(tc_Nat_Onat,X25))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
fof(fact_real__of__nat__le__iff,axiom,
! [X25,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11),c_RealDef_Oreal(tc_Nat_Onat,X25))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
fof(fact_divide_Ominus,axiom,
! [X16,X18,X19] :
( class_RealVector_Oreal__normed__field(X19)
=> c_Rings_Oinverse__class_Odivide(X19,c_Groups_Ouminus__class_Ouminus(X19,X18),X16) = c_Groups_Ouminus__class_Ouminus(X19,c_Rings_Oinverse__class_Odivide(X19,X18,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Ominus) ).
fof(fact_minus__divide__left,axiom,
! [X20,X21,X19] :
( class_Rings_Odivision__ring(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,c_Rings_Oinverse__class_Odivide(X19,X21,X20)) = c_Rings_Oinverse__class_Odivide(X19,c_Groups_Ouminus__class_Ouminus(X19,X21),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__left) ).
fof(fact_minus__divide__right,axiom,
! [X20,X21,X19] :
( class_Fields_Ofield__inverse__zero(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,c_Rings_Oinverse__class_Odivide(X19,X21,X20)) = c_Rings_Oinverse__class_Odivide(X19,X21,c_Groups_Ouminus__class_Ouminus(X19,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__right) ).
fof(fact_neg__less__0__iff__less,axiom,
! [X24,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ouminus__class_Ouminus(X19,X24),c_Groups_Ozero__class_Ozero(X19))
<=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_neg__le__0__iff__le,axiom,
! [X24,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ouminus__class_Ouminus(X19,X24),c_Groups_Ozero__class_Ozero(X19))
<=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_neg__0__less__iff__less,axiom,
! [X24,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Ouminus__class_Ouminus(X19,X24))
<=> c_Orderings_Oord__class_Oless(X19,X24,c_Groups_Ozero__class_Ozero(X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_neg__0__le__iff__le,axiom,
! [X24,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Ouminus__class_Ouminus(X19,X24))
<=> c_Orderings_Oord__class_Oless__eq(X19,X24,c_Groups_Ozero__class_Ozero(X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_mult__right_Ominus,axiom,
! [X18,X67,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X67),c_Groups_Ouminus__class_Ouminus(X19,X18)) = c_Groups_Ouminus__class_Ouminus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X67),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
fof(fact_mult_Ominus__right,axiom,
! [X20,X21,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Groups_Ouminus__class_Ouminus(X19,X20)) = c_Groups_Ouminus__class_Ouminus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
fof(fact_minus__mult__right,axiom,
! [X20,X21,X19] :
( class_Rings_Oring(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Groups_Ouminus__class_Ouminus(X19,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__right) ).
fof(fact_compl__mono,axiom,
! [X16,X18,X19] :
( class_Lattices_Oboolean__algebra(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,X16)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ouminus__class_Ouminus(X19,X16),c_Groups_Ouminus__class_Ouminus(X19,X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__mono) ).
fof(fact_le__imp__neg__le,axiom,
! [X20,X21,X19] :
( class_Groups_Oordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ouminus__class_Ouminus(X19,X20),c_Groups_Ouminus__class_Ouminus(X19,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_zero__less__two,axiom,
! [X19] :
( class_Rings_Olinordered__semidom(X19)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Oplus__class_Oplus(X19,c_Groups_Oone__class_Oone(X19),c_Groups_Oone__class_Oone(X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_minus__add__cancel,axiom,
! [X20,X21,X19] :
( class_Groups_Ogroup__add(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Ouminus__class_Ouminus(X19,X21),c_Groups_Oplus__class_Oplus(X19,X21,X20)) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_neg__less__nonneg,axiom,
! [X24,X19] :
( class_Groups_Olinordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ouminus__class_Ouminus(X19,X24),X24)
<=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_minus__le__self__iff,axiom,
! [X24,X19] :
( class_Groups_Olinordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ouminus__class_Ouminus(X19,X24),X24)
<=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_less__minus__self__iff,axiom,
! [X24,X19] :
( class_Rings_Olinordered__idom(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X24,c_Groups_Ouminus__class_Ouminus(X19,X24))
<=> c_Orderings_Oord__class_Oless(X19,X24,c_Groups_Ozero__class_Ozero(X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_le__minus__self__iff,axiom,
! [X24,X19] :
( class_Groups_Olinordered__ab__group__add(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X24,c_Groups_Ouminus__class_Ouminus(X19,X24))
<=> c_Orderings_Oord__class_Oless__eq(X19,X24,c_Groups_Ozero__class_Ozero(X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_power__real__of__nat,axiom,
! [X14,X26] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X26)),X14) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__real__of__nat) ).
fof(fact_zmult__zminus,axiom,
! [X27,X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X6)),X27) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6),X27)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zminus) ).
fof(fact_real__of__nat__power,axiom,
! [X14,X26] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X14)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X26)),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__power) ).
fof(fact_nat__less__cases,axiom,
! [X45,X11,X25] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11)
=> hBOOL(hAPP(hAPP(X45,X11),X25)) )
=> ( ( X25 = X11
=> hBOOL(hAPP(hAPP(X45,X11),X25)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X25)
=> hBOOL(hAPP(hAPP(X45,X11),X25)) )
=> hBOOL(hAPP(hAPP(X45,X11),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_minus__mult__minus,axiom,
! [X20,X21,X19] :
( class_Rings_Oring(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ouminus__class_Ouminus(X19,X21)),c_Groups_Ouminus__class_Ouminus(X19,X20)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_minus__mult__commute,axiom,
! [X20,X21,X19] :
( class_Rings_Oring(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ouminus__class_Ouminus(X19,X21)),X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Groups_Ouminus__class_Ouminus(X19,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_square__eq__iff,axiom,
! [X23,X24,X19] :
( class_Rings_Oidom(X19)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X23),X23)
<=> ( X24 = X23
| X24 = c_Groups_Ouminus__class_Ouminus(X19,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__iff) ).
fof(fact_BseqD,axiom,
! [X33,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( c_SEQ_OBseq(X19,X33)
=> ? [X35] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
& ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,hAPP(X33,X10)),X35) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_BseqD) ).
fof(fact_natfloor__power,axiom,
! [X14,X18] :
( X18 = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X18))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X18),X14)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X18)),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__power) ).
fof(fact_minus__diff__eq,axiom,
! [X20,X21,X19] :
( class_Groups_Oab__group__add(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,c_Groups_Ominus__class_Ominus(X19,X21,X20)) = c_Groups_Ominus__class_Ominus(X19,X20,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_xt1_I5_J,axiom,
! [X18,X16,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X16,X18)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,X16)
=> X18 = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__antisym,axiom,
! [X16,X18,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,X16)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X16,X18)
=> X18 = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_order__antisym__conv,axiom,
! [X4,X12,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X12,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X4,X12)
<=> X4 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__eq__iff,axiom,
! [X12,X4,X19] :
( class_Orderings_Oorder(X19)
=> ( X4 = X12
<=> ( c_Orderings_Oord__class_Oless__eq(X19,X4,X12)
& c_Orderings_Oord__class_Oless__eq(X19,X12,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
! [X11] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X11))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
fof(fact_less__add__one,axiom,
! [X21,X19] :
( class_Rings_Olinordered__semidom(X19)
=> c_Orderings_Oord__class_Oless(X19,X21,c_Groups_Oplus__class_Oplus(X19,X21,c_Groups_Oone__class_Oone(X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_add__right__imp__eq,axiom,
! [X22,X21,X20,X19] :
( class_Groups_Ocancel__semigroup__add(X19)
=> ( c_Groups_Oplus__class_Oplus(X19,X20,X21) = c_Groups_Oplus__class_Oplus(X19,X22,X21)
=> X20 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [X37,X24,X23,X19] :
( class_Groups_Ocancel__semigroup__add(X19)
=> ( c_Groups_Oplus__class_Oplus(X19,X23,X24) = c_Groups_Oplus__class_Oplus(X19,X37,X24)
<=> X23 = X37 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__imp__eq,axiom,
! [X22,X20,X21,X19] :
( class_Groups_Ocancel__ab__semigroup__add(X19)
=> ( c_Groups_Oplus__class_Oplus(X19,X21,X20) = c_Groups_Oplus__class_Oplus(X19,X21,X22)
=> X20 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X22,X20,X21,X19] :
( class_Groups_Ocancel__semigroup__add(X19)
=> ( c_Groups_Oplus__class_Oplus(X19,X21,X20) = c_Groups_Oplus__class_Oplus(X19,X21,X22)
=> X20 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X37,X23,X24,X19] :
( class_Groups_Ocancel__semigroup__add(X19)
=> ( c_Groups_Oplus__class_Oplus(X19,X24,X23) = c_Groups_Oplus__class_Oplus(X19,X24,X37)
<=> X23 = X37 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_natceiling__le,axiom,
! [X21,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,c_RealDef_Oreal(tc_Nat_Onat,X21))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X18),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le) ).
fof(fact_le__natfloor,axiom,
! [X21,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X18),X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_RComplete_Onatfloor(X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor) ).
fof(fact_order__root,axiom,
! [X24,X53,X19] :
( class_Rings_Oidom(X19)
=> ( hAPP(c_Polynomial_Opoly(X19,X53),X24) = c_Groups_Ozero__class_Ozero(X19)
<=> ( X53 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19))
| c_Polynomial_Oorder(X19,X24,X53) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__root) ).
fof(fact_diffs0__imp__equal,axiom,
! [X14,X26] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X26) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X26 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_real__natfloor__le,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X18)),X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natfloor__le) ).
fof(fact_nonzero__minus__divide__divide,axiom,
! [X21,X20,X19] :
( class_Rings_Odivision__ring(X19)
=> ( X20 != c_Groups_Ozero__class_Ozero(X19)
=> c_Rings_Oinverse__class_Odivide(X19,c_Groups_Ouminus__class_Ouminus(X19,X21),c_Groups_Ouminus__class_Ouminus(X19,X20)) = c_Rings_Oinverse__class_Odivide(X19,X21,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).
fof(fact_mod__div__trivial,axiom,
! [X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Odiv(X19,c_Divides_Odiv__class_Omod(X19,X21,X20),X20) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__trivial) ).
fof(fact_div__mult__self1__is__id,axiom,
! [X21,X20,X19] :
( class_Divides_Osemiring__div(X19)
=> ( X20 != c_Groups_Ozero__class_Ozero(X19)
=> c_Divides_Odiv__class_Odiv(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X21),X20) = X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).
fof(fact_div__mult__self2__is__id,axiom,
! [X21,X20,X19] :
( class_Divides_Osemiring__div(X19)
=> ( X20 != c_Groups_Ozero__class_Ozero(X19)
=> c_Divides_Odiv__class_Odiv(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),X20) = X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).
fof(fact_zero__le__square,axiom,
! [X21,X19] :
( class_Rings_Olinordered__ring(X19)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(fact_zle__antisym,axiom,
! [X27,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,X27)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X27,X6)
=> X6 = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(fact_le__antisym,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X26)
=> X26 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_real__le__antisym,axiom,
! [X27,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X27)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X6)
=> X6 = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(fact_add__diff__cancel,axiom,
! [X20,X21,X19] :
( class_Groups_Ogroup__add(X19)
=> c_Groups_Ominus__class_Ominus(X19,c_Groups_Oplus__class_Oplus(X19,X21,X20),X20) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [X20,X21,X19] :
( class_Groups_Ogroup__add(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Ominus__class_Ominus(X19,X21,X20),X20) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X11) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X25 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X11 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_nat__add__right__cancel,axiom,
! [X11,X48,X25] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X48) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X48)
<=> X25 = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X11,X25,X48] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X25) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X11)
<=> X25 = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_mod__mult__self1__is__0,axiom,
! [X21,X20,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X21),X20) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).
fof(fact_mod__mult__self2__is__0,axiom,
! [X20,X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20),X20) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).
fof(fact_minus__divide__divide,axiom,
! [X20,X21,X19] :
( class_Fields_Ofield__inverse__zero(X19)
=> c_Rings_Oinverse__class_Odivide(X19,c_Groups_Ouminus__class_Ouminus(X19,X21),c_Groups_Ouminus__class_Ouminus(X19,X20)) = c_Rings_Oinverse__class_Odivide(X19,X21,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__divide) ).
fof(fact_poly__mod__minus__right,axiom,
! [X16,X18,X19] :
( class_Fields_Ofield(X19)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X19),X18,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X19),X16)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X19),X18,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mod__minus__right) ).
fof(fact_zmod__zminus1__not__zero,axiom,
! [X47,X28] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X28),X47) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X28,X47) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus1__not__zero) ).
fof(fact_zmod__zminus2__not__zero,axiom,
! [X47,X28] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X28,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X47)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X28,X47) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2__not__zero) ).
fof(fact_le__Suc__ex__iff,axiom,
! [X55,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X55)
<=> ? [X10] : X55 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(fact_le__iff__add,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11)
<=> ? [X39] : X11 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_zmod__eq__0__iff,axiom,
! [X65,X25] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X65) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ? [X60] : X25 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X65),X60) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
fof(fact_mod__eq__0__iff,axiom,
! [X65,X25] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,X65) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ? [X60] : X25 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X65),X60) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).
fof(fact_zmod__zdiv__trivial,axiom,
! [X20,X21] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20),X20) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).
fof(fact_diff__add__0,axiom,
! [X26,X14] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X26)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(fact_diff__add__inverse,axiom,
! [X26,X14] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X26),X14) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [X14,X26] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X14),X14) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_diff__le__self,axiom,
! [X14,X26] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14),X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(fact_mod__less__eq__dividend,axiom,
! [X14,X26] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14),X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
fof(fact_div__le__dividend,axiom,
! [X14,X26] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,X14),X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__dividend) ).
fof(fact_le__add1,axiom,
! [X26,X14] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X26)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X26,X14] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_divide__eq__eq,axiom,
! [X24,X37,X23,X19] :
( class_Fields_Ofield__inverse__zero(X19)
=> ( c_Rings_Oinverse__class_Odivide(X19,X23,X37) = X24
<=> ( ( X37 != c_Groups_Ozero__class_Ozero(X19)
=> X23 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37) )
& ( X37 = c_Groups_Ozero__class_Ozero(X19)
=> X24 = c_Groups_Ozero__class_Ozero(X19) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
fof(fact_eq__divide__eq,axiom,
! [X37,X23,X24,X19] :
( class_Fields_Ofield__inverse__zero(X19)
=> ( X24 = c_Rings_Oinverse__class_Odivide(X19,X23,X37)
<=> ( ( X37 != c_Groups_Ozero__class_Ozero(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37) = X23 )
& ( X37 = c_Groups_Ozero__class_Ozero(X19)
=> X24 = c_Groups_Ozero__class_Ozero(X19) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
fof(fact_le__natfloor__eq__one,axiom,
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X4))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
fof(fact_natceiling__le__eq__one,axiom,
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X4),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).
fof(fact_nonzero__eq__divide__eq,axiom,
! [X23,X24,X37,X19] :
( class_Rings_Odivision__ring(X19)
=> ( X37 != c_Groups_Ozero__class_Ozero(X19)
=> ( X24 = c_Rings_Oinverse__class_Odivide(X19,X23,X37)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37) = X23 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
fof(fact_nonzero__divide__eq__eq,axiom,
! [X24,X23,X37,X19] :
( class_Rings_Odivision__ring(X19)
=> ( X37 != c_Groups_Ozero__class_Ozero(X19)
=> ( c_Rings_Oinverse__class_Odivide(X19,X23,X37) = X24
<=> X23 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
fof(fact_divide__eq__imp,axiom,
! [X21,X20,X22,X19] :
( class_Rings_Odivision__ring(X19)
=> ( X22 != c_Groups_Ozero__class_Ozero(X19)
=> ( X20 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22)
=> c_Rings_Oinverse__class_Odivide(X19,X20,X22) = X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__imp) ).
fof(fact_eq__divide__imp,axiom,
! [X20,X21,X22,X19] :
( class_Rings_Odivision__ring(X19)
=> ( X22 != c_Groups_Ozero__class_Ozero(X19)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X22) = X20
=> X21 = c_Rings_Oinverse__class_Odivide(X19,X20,X22) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
fof(fact_zdiv__zminus__zminus,axiom,
! [X20,X21] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X21),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).
fof(fact_zdiv__zminus2,axiom,
! [X20,X21] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X21),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).
fof(fact_mult__cancel2,axiom,
! [X11,X48,X25] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X48) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X48)
<=> ( X25 = X11
| X48 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
fof(fact_real__mult__right__cancel,axiom,
! [X23,X24,X37] :
( X37 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X37) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X37)
<=> X24 = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [X11,X25,X48] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X11)
<=> ( X48 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X25 = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_mult__cancel1,axiom,
! [X11,X25,X48] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X11)
<=> ( X25 = X11
| X48 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(fact_real__mult__left__cancel,axiom,
! [X23,X24,X37] :
( X37 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X37),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X37),X23)
<=> X24 = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
fof(fact_xt1_I11_J,axiom,
! [X21,X20,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,X21)
=> ( X21 != X20
=> c_Orderings_Oord__class_Oless(X19,X20,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [X20,X21,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> ( X21 != X20
=> c_Orderings_Oord__class_Oless(X19,X21,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X16,X18,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,X16)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
| X18 = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__neq__le__trans,axiom,
! [X20,X21,X19] :
( class_Orderings_Oorder(X19)
=> ( X21 != X20
=> ( c_Orderings_Oord__class_Oless__eq(X19,X21,X20)
=> c_Orderings_Oord__class_Oless(X19,X21,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__less,axiom,
! [X12,X4,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X4,X12)
<=> ( c_Orderings_Oord__class_Oless(X19,X4,X12)
| X4 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__le,axiom,
! [X12,X4,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X4,X12)
<=> ( c_Orderings_Oord__class_Oless__eq(X19,X4,X12)
& X4 != X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_xt1_I12_J,axiom,
! [X20,X21,X19] :
( class_Orderings_Oorder(X19)
=> ( X21 != X20
=> ( c_Orderings_Oord__class_Oless__eq(X19,X20,X21)
=> c_Orderings_Oord__class_Oless(X19,X20,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [X18,X19] :
( class_Rings_Ocomm__ring__1(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ouminus__class_Ouminus(X19,c_Groups_Oone__class_Oone(X19))),X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(fact_natfloor__mono,axiom,
! [X16,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X18),c_RComplete_Onatfloor(X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__mono) ).
fof(fact_natceiling__mono,axiom,
! [X16,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X18),c_RComplete_Onatceiling(X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__mono) ).
fof(fact_order__less__imp__le,axiom,
! [X16,X18,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> c_Orderings_Oord__class_Oless__eq(X19,X18,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_zero__less__norm__iff,axiom,
! [X4,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X19,X4))
<=> X4 != c_Groups_Ozero__class_Ozero(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(fact_complex__mod__minus__le__complex__mod,axiom,
! [X18] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X18)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(fact_le__square,axiom,
! [X26] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X26)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
fof(fact_diff__minus__eq__add,axiom,
! [X20,X21,X19] :
( class_Groups_Ogroup__add(X19)
=> c_Groups_Ominus__class_Ominus(X19,X21,c_Groups_Ouminus__class_Ouminus(X19,X20)) = c_Groups_Oplus__class_Oplus(X19,X21,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_norm__le__zero__iff,axiom,
! [X4,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X4),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X4 = c_Groups_Ozero__class_Ozero(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
fof(fact_diff__is__0__eq,axiom,
! [X11,X25] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_zless__le,axiom,
! [X66,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X66)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X66)
& X5 != X66 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
fof(fact_nat__less__le,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11)
& X25 != X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11)
| X25 = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_le__neq__implies__less,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> ( X26 != X14
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_real__less__def,axiom,
! [X12,X4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,X12)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X12)
& X4 != X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(fact_less__eq__real__def,axiom,
! [X12,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X12)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,X12)
| X4 = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_diff__is__0__eq_H,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(fact_div__less,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less) ).
fof(fact_uminus__apply,axiom,
! [X4,X56,X34,X19] :
( class_Groups_Ouminus(X19)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X34,X19),X56),X4) = c_Groups_Ouminus__class_Ouminus(X19,hAPP(X56,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__apply) ).
fof(fact_mod__less,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X16,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_less__imp__le__nat,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X14,X26] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
| X26 = X14 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_real__of__nat__one,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__one) ).
fof(fact_mult__poly__0__left,axiom,
! [X52,X19] :
( class_Rings_Ocomm__semiring__0(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X19)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19))),X52) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
! [X11] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_real__add__minus__iff,axiom,
! [X24,X4] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X24)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X4 = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
fof(fact_power__eq__0__iff,axiom,
! [X11,X24,X19] :
( ( class_Power_Opower(X19)
& class_Rings_Omult__zero(X19)
& class_Rings_Ono__zero__divisors(X19)
& class_Rings_Ozero__neq__one(X19) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X19),X24),X11) = c_Groups_Ozero__class_Ozero(X19)
<=> ( X24 = c_Groups_Ozero__class_Ozero(X19)
& X11 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_square__eq__1__iff,axiom,
! [X4,X19] :
( class_Rings_Oring__1__no__zero__divisors(X19)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X4),X4) = c_Groups_Oone__class_Oone(X19)
<=> ( X4 = c_Groups_Oone__class_Oone(X19)
| X4 = c_Groups_Ouminus__class_Ouminus(X19,c_Groups_Oone__class_Oone(X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_linorder__neq__iff,axiom,
! [X12,X4,X19] :
( class_Orderings_Olinorder(X19)
=> ( X4 != X12
<=> ( c_Orderings_Oord__class_Oless(X19,X4,X12)
| c_Orderings_Oord__class_Oless(X19,X12,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X16,X18,X19] :
( class_Orderings_Olinorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
| X18 = X16
| c_Orderings_Oord__class_Oless(X19,X16,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_linorder__le__less__linear,axiom,
! [X16,X18,X19] :
( class_Orderings_Olinorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,X16)
| c_Orderings_Oord__class_Oless(X19,X16,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_linorder__linear,axiom,
! [X16,X18,X19] :
( class_Orderings_Olinorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X18,X16)
| c_Orderings_Oord__class_Oless__eq(X19,X16,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X22,X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> c_Groups_Oplus__class_Oplus(X19,X21,X22) = c_Groups_Oplus__class_Oplus(X19,X22,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_minus__unique,axiom,
! [X20,X21,X19] :
( class_Groups_Ogroup__add(X19)
=> ( c_Groups_Oplus__class_Oplus(X19,X21,X20) = c_Groups_Ozero__class_Ozero(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,X21) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__unique) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [X23,X24,X19] :
( class_Groups_Ogroup__add(X19)
=> ( X24 = c_Groups_Ouminus__class_Ouminus(X19,X23)
<=> c_Groups_Oplus__class_Oplus(X19,X24,X23) = c_Groups_Ozero__class_Ozero(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_add__eq__0__iff,axiom,
! [X12,X4,X19] :
( class_Groups_Ogroup__add(X19)
=> ( c_Groups_Oplus__class_Oplus(X19,X4,X12) = c_Groups_Ozero__class_Ozero(X19)
<=> X12 = c_Groups_Ouminus__class_Ouminus(X19,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
fof(fact_mult__poly__0__right,axiom,
! [X51,X19] :
( class_Rings_Ocomm__semiring__0(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X19)),X51),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X20,X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X20),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_zless__linear,axiom,
! [X16,X18] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,X16)
| X18 = X16
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(fact_nat__neq__iff,axiom,
! [X11,X25] :
( X25 != X11
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_right__inverse__eq,axiom,
! [X24,X23,X19] :
( class_Rings_Odivision__ring(X19)
=> ( X23 != c_Groups_Ozero__class_Ozero(X19)
=> ( c_Rings_Oinverse__class_Odivide(X19,X24,X23) = c_Groups_Oone__class_Oone(X19)
<=> X24 = X23 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
fof(fact_zle__linear,axiom,
! [X27,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,X27)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X27,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(fact_nat__le__linear,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_real__le__linear,axiom,
! [X27,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X27)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_mult__eq__0__iff,axiom,
! [X23,X24,X19] :
( class_Rings_Oring__no__zero__divisors(X19)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X23) = c_Groups_Ozero__class_Ozero(X19)
<=> ( X24 = c_Groups_Ozero__class_Ozero(X19)
| X23 = c_Groups_Ozero__class_Ozero(X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_no__zero__divisors,axiom,
! [X20,X21,X19] :
( class_Rings_Ono__zero__divisors(X19)
=> ( X21 != c_Groups_Ozero__class_Ozero(X19)
=> ( X20 != c_Groups_Ozero__class_Ozero(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20) != c_Groups_Ozero__class_Ozero(X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_divisors__zero,axiom,
! [X20,X21,X19] :
( class_Rings_Ono__zero__divisors(X19)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X20) = c_Groups_Ozero__class_Ozero(X19)
=> ( X21 = c_Groups_Ozero__class_Ozero(X19)
| X20 = c_Groups_Ozero__class_Ozero(X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).
fof(fact_zadd__commute,axiom,
! [X27,X6] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,X27) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(fact_nat__add__commute,axiom,
! [X14,X26] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_double__eq__0__iff,axiom,
! [X24,X19] :
( class_Groups_Olinordered__ab__group__add(X19)
=> ( c_Groups_Oplus__class_Oplus(X19,X24,X24) = c_Groups_Ozero__class_Ozero(X19)
<=> X24 = c_Groups_Ozero__class_Ozero(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X24,X19] :
( class_Groups_Olinordered__ab__group__add(X19)
=> ( c_Groups_Ozero__class_Ozero(X19) = c_Groups_Oplus__class_Oplus(X19,X24,X24)
<=> X24 = c_Groups_Ozero__class_Ozero(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_eq__iff__diff__eq__0,axiom,
! [X23,X24,X19] :
( class_Groups_Oab__group__add(X19)
=> ( X24 = X23
<=> c_Groups_Ominus__class_Ominus(X19,X24,X23) = c_Groups_Ozero__class_Ozero(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_right__minus__eq,axiom,
! [X23,X24,X19] :
( class_Groups_Ogroup__add(X19)
=> ( c_Groups_Ominus__class_Ominus(X19,X24,X23) = c_Groups_Ozero__class_Ozero(X19)
<=> X24 = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(fact_field__power__not__zero,axiom,
! [X14,X21,X19] :
( class_Rings_Oring__1__no__zero__divisors(X19)
=> ( X21 != c_Groups_Ozero__class_Ozero(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),X14) != c_Groups_Ozero__class_Ozero(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_real__add__eq__0__iff,axiom,
! [X12,X4] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X12) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X12 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(fact_add__0__iff,axiom,
! [X24,X23,X19] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X19)
=> ( X23 = c_Groups_Oplus__class_Oplus(X19,X23,X24)
<=> X24 = c_Groups_Ozero__class_Ozero(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_poly__zero,axiom,
! [X53,X19] :
( ( class_Int_Oring__char__0(X19)
& class_Rings_Oidom(X19) )
=> ( c_Polynomial_Opoly(X19,X53) = c_Polynomial_Opoly(X19,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)))
<=> X53 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__zero) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X16,X18,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> X16 != X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X16,X18,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> X18 != X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X16,X18,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> X18 != X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_natfloor__neg,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatfloor(X18) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__neg) ).
fof(fact_natceiling__neg,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatceiling(X18) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__neg) ).
fof(fact_neq0__conv,axiom,
! [X11] :
( X11 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_le__0__eq,axiom,
! [X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(fact_zmult__commute,axiom,
! [X27,X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6),X27) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(fact_nat__mult__commute,axiom,
! [X14,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X14) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_real__mult__commute,axiom,
! [X27,X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X27) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact_ab__left__minus,axiom,
! [X21,X19] :
( class_Groups_Oab__group__add(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Ouminus__class_Ouminus(X19,X21),X21) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__left__minus) ).
fof(fact_left__minus,axiom,
! [X21,X19] :
( class_Groups_Ogroup__add(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Ouminus__class_Ouminus(X19,X21),X21) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__minus) ).
fof(fact_right__minus,axiom,
! [X21,X19] :
( class_Groups_Ogroup__add(X19)
=> c_Groups_Oplus__class_Oplus(X19,X21,c_Groups_Ouminus__class_Ouminus(X19,X21)) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus) ).
fof(fact_add__is__0,axiom,
! [X11,X25] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(fact_gr__implies__not0,axiom,
! [X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> X14 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_norm__ge__zero,axiom,
! [X18,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X19,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
fof(fact_power__0__left,axiom,
! [X14,X19] :
( ( class_Power_Opower(X19)
& class_Rings_Osemiring__0(X19) )
=> ( ( X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),c_Groups_Ozero__class_Ozero(X19)),X14) = c_Groups_Oone__class_Oone(X19) )
& ( X14 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),c_Groups_Ozero__class_Ozero(X19)),X14) = c_Groups_Ozero__class_Ozero(X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left) ).
fof(fact_add__eq__self__zero,axiom,
! [X14,X26] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X14) = X26
=> X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_real__natceiling__ge,axiom,
! [X18] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X18))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).
fof(fact_poly__1,axiom,
! [X18,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(c_Polynomial_Opoly(X19,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X19))),X18) = c_Groups_Oone__class_Oone(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__1) ).
fof(fact_poly__0,axiom,
! [X18,X19] :
( class_Rings_Ocomm__semiring__0(X19)
=> hAPP(c_Polynomial_Opoly(X19,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19))),X18) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__0) ).
fof(fact_less__not__refl2,axiom,
! [X26,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X26)
=> X26 != X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__not__refl3,axiom,
! [X46,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X46)
=> X15 != X46 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_add__poly__code_I1_J,axiom,
! [X52,X19] :
( class_Groups_Ocomm__monoid__add(X19)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X19),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)),X52) = X52 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(fact_add__poly__code_I2_J,axiom,
! [X51,X19] :
( class_Groups_Ocomm__monoid__add(X19)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X19),X51,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19))) = X51 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(fact_mth1,axiom,
? [X3,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X9)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mth1) ).
fof(fact_mult__is__0,axiom,
! [X11,X25] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
fof(fact_mult__eq__self__implies__10,axiom,
! [X14,X26] :
( X26 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X14)
=> ( X14 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X26 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [X11,X25] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X11) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X25 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X11 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [X11,X25] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X11)
<=> ( X25 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X11 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_real__of__nat__ge__zero,axiom,
! [X14] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [X6] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X6),X6) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_power__power__power,axiom,
! [X19] :
( class_Power_Opower(X19)
=> c_Power_Opower__class_Opower(X19) = c_Power_Opower_Opower(X19,c_Groups_Oone__class_Oone(X19),c_Groups_Otimes__class_Otimes(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(fact_power__one,axiom,
! [X14,X19] :
( class_Groups_Omonoid__mult(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),c_Groups_Oone__class_Oone(X19)),X14) = c_Groups_Oone__class_Oone(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_mult__zero__left,axiom,
! [X21,X19] :
( class_Rings_Omult__zero(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ozero__class_Ozero(X19)),X21) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(fact_mult_Ozero__left,axiom,
! [X20,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ozero__class_Ozero(X19)),X20) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
fof(fact_mult__left_Ozero,axiom,
! [X16,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ozero__class_Ozero(X19)),X16) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Ozero__class_Ozero(X19)),X21) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_divide__self__if,axiom,
! [X21,X19] :
( class_Rings_Odivision__ring__inverse__zero(X19)
=> ( ( X21 = c_Groups_Ozero__class_Ozero(X19)
=> c_Rings_Oinverse__class_Odivide(X19,X21,X21) = c_Groups_Ozero__class_Ozero(X19) )
& ( X21 != c_Groups_Ozero__class_Ozero(X19)
=> c_Rings_Oinverse__class_Odivide(X19,X21,X21) = c_Groups_Oone__class_Oone(X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self__if) ).
fof(fact_zero__less__one,axiom,
! [X19] :
( class_Rings_Olinordered__semidom(X19)
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Oone__class_Oone(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_zero__le__one,axiom,
! [X19] :
( class_Rings_Olinordered__semidom(X19)
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),c_Groups_Oone__class_Oone(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_mult__1,axiom,
! [X21,X19] :
( class_Groups_Ocomm__monoid__mult(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oone__class_Oone(X19)),X21) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
fof(fact_mult__1__left,axiom,
! [X21,X19] :
( class_Groups_Omonoid__mult(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oone__class_Oone(X19)),X21) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),c_Groups_Oone__class_Oone(X19)),X21) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_mod__0,axiom,
! [X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,c_Groups_Ozero__class_Ozero(X19),X21) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__0) ).
fof(fact_div__0,axiom,
! [X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Odiv(X19,c_Groups_Ozero__class_Ozero(X19),X21) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__0) ).
fof(fact_divide__zero__left,axiom,
! [X21,X19] :
( class_Rings_Odivision__ring(X19)
=> c_Rings_Oinverse__class_Odivide(X19,c_Groups_Ozero__class_Ozero(X19),X21) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero__left) ).
fof(fact_divide_Ozero,axiom,
! [X16,X19] :
( class_RealVector_Oreal__normed__field(X19)
=> c_Rings_Oinverse__class_Odivide(X19,c_Groups_Ozero__class_Ozero(X19),X16) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Ozero) ).
fof(fact_mod__by__1,axiom,
! [X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,X21,c_Groups_Oone__class_Oone(X19)) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__1) ).
fof(fact_div__by__0,axiom,
! [X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Odiv(X19,X21,c_Groups_Ozero__class_Ozero(X19)) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__0) ).
fof(fact_divide__zero,axiom,
! [X21,X19] :
( class_Rings_Odivision__ring__inverse__zero(X19)
=> c_Rings_Oinverse__class_Odivide(X19,X21,c_Groups_Ozero__class_Ozero(X19)) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero) ).
fof(fact_div__self,axiom,
! [X21,X19] :
( class_Divides_Osemiring__div(X19)
=> ( X21 != c_Groups_Ozero__class_Ozero(X19)
=> c_Divides_Odiv__class_Odiv(X19,X21,X21) = c_Groups_Oone__class_Oone(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__self) ).
fof(fact_divide__self,axiom,
! [X21,X19] :
( class_Rings_Odivision__ring(X19)
=> ( X21 != c_Groups_Ozero__class_Ozero(X19)
=> c_Rings_Oinverse__class_Odivide(X19,X21,X21) = c_Groups_Oone__class_Oone(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self) ).
fof(fact_mult__zero__right,axiom,
! [X21,X19] :
( class_Rings_Omult__zero(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Groups_Ozero__class_Ozero(X19)) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(fact_mult_Ozero__right,axiom,
! [X21,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Groups_Ozero__class_Ozero(X19)) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
fof(fact_mult__right_Ozero,axiom,
! [X18,X19] :
( class_RealVector_Oreal__normed__algebra(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),c_Groups_Ozero__class_Ozero(X19)) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Groups_Ozero__class_Ozero(X19)) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Ozero__class_Ozero(X19),X21) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add__0,axiom,
! [X21,X19] :
( class_Groups_Ocomm__monoid__add(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Ozero__class_Ozero(X19),X21) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_add__0__left,axiom,
! [X21,X19] :
( class_Groups_Omonoid__add(X19)
=> c_Groups_Oplus__class_Oplus(X19,c_Groups_Ozero__class_Ozero(X19),X21) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_diff__0__right,axiom,
! [X21,X19] :
( class_Groups_Ogroup__add(X19)
=> c_Groups_Ominus__class_Ominus(X19,X21,c_Groups_Ozero__class_Ozero(X19)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(fact_mod__by__0,axiom,
! [X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,X21,c_Groups_Ozero__class_Ozero(X19)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__0) ).
fof(fact_div__by__1,axiom,
! [X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Odiv(X19,X21,c_Groups_Oone__class_Oone(X19)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> c_Groups_Oplus__class_Oplus(X19,X21,c_Groups_Ozero__class_Ozero(X19)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X21,X19] :
( class_Groups_Ocomm__monoid__add(X19)
=> c_Groups_Oplus__class_Oplus(X19,X21,c_Groups_Ozero__class_Ozero(X19)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_add__0__right,axiom,
! [X21,X19] :
( class_Groups_Omonoid__add(X19)
=> c_Groups_Oplus__class_Oplus(X19,X21,c_Groups_Ozero__class_Ozero(X19)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_divide__1,axiom,
! [X21,X19] :
( class_Rings_Odivision__ring(X19)
=> c_Rings_Oinverse__class_Odivide(X19,X21,c_Groups_Oone__class_Oone(X19)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__1) ).
fof(fact_power__0,axiom,
! [X21,X19] :
( class_Power_Opower(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X18,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [X21,X19] :
( class_Groups_Ocomm__monoid__mult(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Groups_Oone__class_Oone(X19)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_mult__1__right,axiom,
! [X21,X19] :
( class_Groups_Omonoid__mult(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Groups_Oone__class_Oone(X19)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X21,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),c_Groups_Oone__class_Oone(X19)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_diff__self,axiom,
! [X21,X19] :
( class_Groups_Ogroup__add(X19)
=> c_Groups_Ominus__class_Ominus(X19,X21,X21) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
fof(fact_mod__self,axiom,
! [X21,X19] :
( class_Divides_Osemiring__div(X19)
=> c_Divides_Odiv__class_Omod(X19,X21,X21) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__self) ).
fof(fact_order__eq__refl,axiom,
! [X16,X18,X19] :
( class_Orderings_Opreorder(X19)
=> ( X18 = X16
=> c_Orderings_Oord__class_Oless__eq(X19,X18,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_power__one__right,axiom,
! [X21,X19] :
( class_Groups_Omonoid__mult(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),X21),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X18,X19] :
( class_Rings_Ocomm__semiring__1(X19)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X19),X18),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_zero__le__natfloor,axiom,
! [X18] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).
fof(fact_zero__le__natceiling,axiom,
! [X18] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).
fof(fact_order__refl,axiom,
! [X18,X19] :
( class_Orderings_Opreorder(X19)
=> c_Orderings_Oord__class_Oless__eq(X19,X18,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(fact_norm__minus__cancel,axiom,
! [X18,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> c_RealVector_Onorm__class_Onorm(X19,c_Groups_Ouminus__class_Ouminus(X19,X18)) = c_RealVector_Onorm__class_Onorm(X19,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).
fof(fact_poly__eq__iff,axiom,
! [X54,X53,X19] :
( ( class_Int_Oring__char__0(X19)
& class_Rings_Oidom(X19) )
=> ( c_Polynomial_Opoly(X19,X53) = c_Polynomial_Opoly(X19,X54)
<=> X53 = X54 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(fact_times_Oidem,axiom,
! [X21,X19] :
( class_Lattices_Oab__semigroup__idem__mult(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X21) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times_Oidem) ).
fof(fact_mult__idem,axiom,
! [X18,X19] :
( class_Lattices_Oab__semigroup__idem__mult(X19)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X18) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__idem) ).
fof(fact_gr0I,axiom,
! [X14] :
( X14 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_zdiv__self,axiom,
! [X21] :
( X21 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X21) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__self) ).
fof(fact_diff__0__eq__0,axiom,
! [X14] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(fact_zmod__zero,axiom,
! [X20] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zero) ).
fof(fact_zdiv__zero,axiom,
! [X20] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zero) ).
fof(fact_DIVISION__BY__ZERO,axiom,
! [X21] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
fof(fact_zadd__0,axiom,
! [X6] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X14] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [X26] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_zadd__0__right,axiom,
! [X6] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X26] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_eq__imp__le,axiom,
! [X14,X26] :
( X26 = X14
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X14] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X14] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_minus__poly__code_I1_J,axiom,
! [X19] :
( class_Groups_Oab__group__add(X19)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X19),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(fact_diff__self__eq__0,axiom,
! [X26] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X26) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(fact_zmod__self,axiom,
! [X21] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__self) ).
fof(fact_mult__0,axiom,
! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
fof(fact_compl__eq__compl__iff,axiom,
! [X12,X4,X19] :
( class_Lattices_Oboolean__algebra(X19)
=> ( c_Groups_Ouminus__class_Ouminus(X19,X4) = c_Groups_Ouminus__class_Ouminus(X19,X12)
<=> X4 = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [X23,X24,X19] :
( class_Groups_Ogroup__add(X19)
=> ( c_Groups_Ouminus__class_Ouminus(X19,X24) = c_Groups_Ouminus__class_Ouminus(X19,X23)
<=> X24 = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_zmult__1,axiom,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X6) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(fact_nat__mult__1,axiom,
! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X14) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_real__mult__1,axiom,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X6) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_zle__refl,axiom,
! [X27] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X27,X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(fact_le__refl,axiom,
! [X14] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_real__le__refl,axiom,
! [X27] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(fact_mult__0__right,axiom,
! [X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(fact_zmult__1__right,axiom,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(fact_nat__mult__1__right,axiom,
! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_double__compl,axiom,
! [X18,X19] :
( class_Lattices_Oboolean__algebra(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,c_Groups_Ouminus__class_Ouminus(X19,X18)) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__compl) ).
fof(fact_minus__minus,axiom,
! [X21,X19] :
( class_Groups_Ogroup__add(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,c_Groups_Ouminus__class_Ouminus(X19,X21)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(fact_minus__equation__iff,axiom,
! [X23,X24,X19] :
( class_Groups_Ogroup__add(X19)
=> ( c_Groups_Ouminus__class_Ouminus(X19,X24) = X23
<=> c_Groups_Ouminus__class_Ouminus(X19,X23) = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_equation__minus__iff,axiom,
! [X23,X24,X19] :
( class_Groups_Ogroup__add(X19)
=> ( X24 = c_Groups_Ouminus__class_Ouminus(X19,X23)
<=> X23 = c_Groups_Ouminus__class_Ouminus(X19,X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_psize__eq__0__iff,axiom,
! [X53,X19] :
( class_Groups_Ozero(X19)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X19,X53) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X53 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
fof(fact_real__of__nat__inject,axiom,
! [X25,X11] :
( c_RealDef_Oreal(tc_Nat_Onat,X11) = c_RealDef_Oreal(tc_Nat_Onat,X25)
<=> X11 = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [X24,X19] :
( class_Groups_Ogroup__add(X19)
=> ( c_Groups_Ozero__class_Ozero(X19) = c_Groups_Ouminus__class_Ouminus(X19,X24)
<=> c_Groups_Ozero__class_Ozero(X19) = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [X24,X19] :
( class_Groups_Ogroup__add(X19)
=> ( c_Groups_Ouminus__class_Ouminus(X19,X24) = c_Groups_Ozero__class_Ozero(X19)
<=> X24 = c_Groups_Ozero__class_Ozero(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_norm__eq__zero,axiom,
! [X4,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ( c_RealVector_Onorm__class_Onorm(X19,X4) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X4 = c_Groups_Ozero__class_Ozero(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
fof(arity_fun__Groups_Ouminus,axiom,
! [X96,X95] :
( class_Groups_Ouminus(X95)
=> class_Groups_Ouminus(tc_fun(X96,X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(arity_fun__Lattices_Oboolean__algebra,axiom,
! [X96,X95] :
( class_Lattices_Oboolean__algebra(X95)
=> class_Lattices_Oboolean__algebra(tc_fun(X96,X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X96,X95] :
( class_Orderings_Oorder(X95)
=> class_Orderings_Oorder(tc_fun(X96,X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X96,X95] :
( class_Orderings_Oord(X95)
=> class_Orderings_Oord(tc_fun(X96,X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X96,X95] :
( class_Orderings_Opreorder(X95)
=> class_Orderings_Opreorder(tc_fun(X96,X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(fact_zminus__zminus,axiom,
! [X6] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X6)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(fact_neg__equal__zero,axiom,
! [X24,X19] :
( class_Groups_Olinordered__ab__group__add(X19)
=> ( c_Groups_Ouminus__class_Ouminus(X19,X24) = X24
<=> X24 = c_Groups_Ozero__class_Ozero(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_equal__neg__zero,axiom,
! [X24,X19] :
( class_Groups_Olinordered__ab__group__add(X19)
=> ( X24 = c_Groups_Ouminus__class_Ouminus(X19,X24)
<=> X24 = c_Groups_Ozero__class_Ozero(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_minus__zero,axiom,
! [X19] :
( class_Groups_Ogroup__add(X19)
=> c_Groups_Ouminus__class_Ouminus(X19,c_Groups_Ozero__class_Ozero(X19)) = c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(fact_norm__one,axiom,
! [X19] :
( class_RealVector_Oreal__normed__algebra__1(X19)
=> c_RealVector_Onorm__class_Onorm(X19,c_Groups_Oone__class_Oone(X19)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__one) ).
fof(fact_norm__zero,axiom,
! [X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> c_RealVector_Onorm__class_Onorm(X19,c_Groups_Ozero__class_Ozero(X19)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__zero) ).
fof(fact_natfloor__real__of__nat,axiom,
! [X14] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X14)) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
fof(fact_natceiling__real__of__nat,axiom,
! [X14] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X14)) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
fof(fact_real__of__nat__zero__iff,axiom,
! [X11] :
( c_RealDef_Oreal(tc_Nat_Onat,X11) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).
fof(fact_zero__neq__one,axiom,
! [X19] :
( class_Rings_Ozero__neq__one(X19)
=> c_Groups_Ozero__class_Ozero(X19) != c_Groups_Oone__class_Oone(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [X19] :
( class_Rings_Ozero__neq__one(X19)
=> c_Groups_Oone__class_Oone(X19) != c_Groups_Ozero__class_Ozero(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(fact_rcis__zero__mod,axiom,
! [X21] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rcis__zero__mod) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
! [X95] :
( class_Groups_Ocancel__comm__monoid__add(X95)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
! [X95] :
( class_Rings_Ocomm__ring__1(X95)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
! [X95] :
( class_Rings_Ocomm__semiring__0(X95)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(arity_Polynomial__Opoly__Power_Opower,axiom,
! [X95] :
( class_Rings_Ocomm__semiring__1(X95)
=> class_Power_Opower(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
! [X95] :
( class_Rings_Ocomm__ring__1(X95)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(arity_Polynomial__Opoly__Divides_Oring__div,axiom,
! [X95] :
( class_Fields_Ofield(X95)
=> class_Divides_Oring__div(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Oring__div) ).
fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
! [X95] :
( class_Rings_Ocomm__semiring__0(X95)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
! [X95] :
( class_Rings_Ocomm__semiring__0(X95)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
! [X95] :
( class_Rings_Ocomm__semiring__0(X95)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
! [X95] :
( class_Rings_Ocomm__semiring__1(X95)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
! [X95] :
( class_Rings_Ocomm__semiring__1(X95)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
! [X95] :
( class_Rings_Ocomm__semiring__0(X95)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
! [X95] :
( class_Rings_Ocomm__ring(X95)
=> class_Rings_Oring(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
! [X95] :
( class_Fields_Ofield(X95)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
! [X95] :
( class_Groups_Oab__group__add(X95)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
! [X95] :
( class_Rings_Ocomm__semiring__0(X95)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [X95] :
( class_Rings_Ocomm__semiring__1(X95)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
! [X95] :
( class_Rings_Ocomm__ring(X95)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
! [X95] :
( class_Groups_Oab__group__add(X95)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
! [X95] :
( class_Rings_Ocomm__semiring__1(X95)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
! [X95] :
( class_Groups_Ocomm__monoid__add(X95)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
! [X95] :
( class_Groups_Ocomm__monoid__add(X95)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
! [X95] :
( class_Rings_Ocomm__semiring__1(X95)
=> class_Groups_Oone(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
! [X95] :
( class_Groups_Ocancel__comm__monoid__add(X95)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
! [X95] :
( class_Groups_Ocancel__comm__monoid__add(X95)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
! [X95] :
( class_Groups_Ocomm__monoid__add(X95)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
! [X95] :
( class_Groups_Ozero(X95)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
! [X95] :
( class_Rings_Olinordered__idom(X95)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
! [X95] :
( class_Groups_Oab__group__add(X95)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X95)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(conj_1,conjecture,
v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096) ).
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/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_rp,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp) ).
fof(fact_real__of__nat__1,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__1) ).
fof(fact_real__of__nat__zero,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
fof(fact_zminus__0,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__0) ).
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/sandbox/benchmark/theBenchmark.p',fact_natfloor__one) ).
fof(fact_natfloor__zero,axiom,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__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/sandbox/benchmark/theBenchmark.p',fact_natceiling__one) ).
fof(fact_natceiling__zero,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__zero) ).
fof(fact_int__0__neq__1,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Int__Oint__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(arity_RealDef__Oreal__Power_Opower,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
fof(arity_Int__Oint__Divides_Oring__div,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
fof(arity_Int__Oint__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
fof(arity_Int__Oint__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(arity_Nat__Onat__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(arity_Int__Oint__Rings_Oring,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(arity_RealDef__Oreal__Rings_Oring,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_HOL__Obool__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(arity_Int__Oint__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).
fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(arity_Int__Oint__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
fof(arity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_Int__Oint__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
fof(arity_RealDef__Oreal__Groups_Oone,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(arity_Int__Oint__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(i_0_1257,plain,
! [X11,X48,X45] :
( epred2_3(X45,X48,X11)
<=> ( ( X48 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X45,X11)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
=> ! [X57,X50] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X48)
& X11 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X57),X50) )
=> hBOOL(hAPP(X45,X50)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X57,X50] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X50)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& X11 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X57),X50) )
=> hBOOL(hAPP(X45,X50)) ) ) ) ),
introduced(definition) ).
fof(i_0_1258,plain,
! [X11,X48,X45] :
( epred1_3(X45,X48,X11)
<=> ( ( X48 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X45,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
=> ! [X57] :
( ? [X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X48)
& X11 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X57),X50) )
=> hBOOL(hAPP(X45,X57)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X57] :
( ? [X50] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X50)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& X11 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X57),X50) )
=> hBOOL(hAPP(X45,X57)) ) ) ) ),
introduced(definition) ).
fof(i_0_1259,plain,
! [X14,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,c_Nat_OSuc(X14))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> X26 = c_Nat_OSuc(X14) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_1260,plain,
! [X11,X25] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X11),X25) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_1261,plain,
! [X11,X25] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Nat_OSuc(X25)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_1262,plain,
! [X25,X11] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X25)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Nat_OSuc(X25))
<=> X11 = X25 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_1263,plain,
! [X26,X14] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X26)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Nat_OSuc(X26))
=> X26 = X14 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_1264,plain,
! [X14,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,c_Nat_OSuc(X14))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> X26 = X14 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_1265,plain,
! [X14] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X14),X14),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_1266,plain,
! [X4921,X4922] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(X4922),X4921) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4922,X4921),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4921)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4922,X4921),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4921)),X4921)),
inference(variable_rename,[status(thm)],[fact_div__Suc]) ).
fof(i_0_1267,plain,
! [X3459] : c_Nat_OSuc(X3459) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3459,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_1268,hypothesis,
! [X5868] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X5868,esk76_1(X5868))),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X5868,esk77_1(X5868)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk77_1(X5868))))))
| v_thesis____ ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])]) ).
fof(i_0_1269,plain,
! [X4750,X4751,X4752] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4752)),X4751),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4752)),X4750))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4751,X4750) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4751,X4750)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4752)),X4751),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4752)),X4750)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])]) ).
fof(i_0_1270,plain,
! [X4757,X4758,X4759] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4759)),X4758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4759)),X4757))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4758,X4757) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4758,X4757)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4759)),X4758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4759)),X4757)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])]) ).
fof(i_0_1271,plain,
! [X2959] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(esk2_0,X2959)),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(esk2_0,X2959))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X2959))))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096])]) ).
fof(i_0_1272,plain,
! [X2968] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk6_1(X2968)),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk6_1(X2968))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X2968))))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096])]) ).
fof(i_0_1273,plain,
! [X2966] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk5_1(X2966)),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk5_1(X2966))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X2966))))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_th])]) ).
fof(i_0_1274,plain,
! [X3157,X3158,X3159,X3162,X3163,X3166] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3159)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3158,hAPP(X3157,esk16_3(X3157,X3158,X3159))),X3159)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3158,hAPP(X3157,X3162)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk17_2(X3157,X3158))))
| ~ class_RealVector_Oreal__normed__vector(X3158) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk19_2(X3157,X3158))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3158,hAPP(X3157,esk18_3(X3157,X3158,X3163))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3163)))
| ~ class_RealVector_Oreal__normed__vector(X3158) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3158,hAPP(X3157,X3166)),esk19_2(X3157,X3158))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3158,hAPP(X3157,esk18_3(X3157,X3158,X3163))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3163)))
| ~ class_RealVector_Oreal__normed__vector(X3158) ) ),
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_1275,plain,
! [X3147,X3148,X3149,X3152,X3153,X3156] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3149)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3148,hAPP(X3147,esk12_3(X3147,X3148,X3149))),X3149)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3148,hAPP(X3147,X3152)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk13_2(X3147,X3148))))
| ~ class_RealVector_Oreal__normed__vector(X3148) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk15_2(X3147,X3148))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3148,hAPP(X3147,esk14_3(X3147,X3148,X3153))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3153)))
| ~ class_RealVector_Oreal__normed__vector(X3148) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3148,hAPP(X3147,X3156)),esk15_2(X3147,X3148))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3148,hAPP(X3147,esk14_3(X3147,X3148,X3153))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3153)))
| ~ class_RealVector_Oreal__normed__vector(X3148) ) ),
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_1276,plain,
! [X4043,X4044,X4046,X4047] :
( ( ~ c_SEQ_OBseq(X4044,X4043)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4044,hAPP(X4043,X4046)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk36_2(X4043,X4044))))
| ~ class_RealVector_Oreal__normed__vector(X4044) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4044,hAPP(X4043,esk37_3(X4043,X4044,X4047))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4047)))
| c_SEQ_OBseq(X4044,X4043)
| ~ class_RealVector_Oreal__normed__vector(X4044) ) ),
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_1277,plain,
! [X4049,X4050,X4052,X4053] :
( ( ~ c_SEQ_OBseq(X4050,X4049)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4050,hAPP(X4049,X4052)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk38_2(X4049,X4050))))
| ~ class_RealVector_Oreal__normed__vector(X4050) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4050,hAPP(X4049,esk39_3(X4049,X4050,X4053))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4053)))
| c_SEQ_OBseq(X4050,X4049)
| ~ class_RealVector_Oreal__normed__vector(X4050) ) ),
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_1278,plain,
! [X5146,X5147,X5148] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X5148),X5147),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X5148),X5146),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X5147 = X5146
| X5147 = c_Groups_Ouminus__class_Ouminus(X5148,X5146)
| ~ class_Rings_Oidom(X5148) )
& ( X5147 != X5146
| hAPP(hAPP(c_Power_Opower__class_Opower(X5148),X5147),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X5148),X5146),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X5148) )
& ( X5147 != c_Groups_Ouminus__class_Ouminus(X5148,X5146)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5148),X5147),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X5148),X5146),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X5148) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__two__disj])])]) ).
fof(i_0_1279,plain,
! [X5254,X5255,X5256,X5257] :
( ~ class_Rings_Olinordered__semidom(X5257)
| ~ c_Orderings_Oord__class_Oless__eq(X5257,hAPP(hAPP(c_Power_Opower__class_Opower(X5257),X5256),c_Nat_OSuc(X5255)),hAPP(hAPP(c_Power_Opower__class_Opower(X5257),X5254),c_Nat_OSuc(X5255)))
| ~ c_Orderings_Oord__class_Oless__eq(X5257,c_Groups_Ozero__class_Ozero(X5257),X5254)
| c_Orderings_Oord__class_Oless__eq(X5257,X5256,X5254) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base])]) ).
fof(i_0_1280,plain,
! [X4133,X4134,X4135,X4137,X4138,X4139,X4140] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4133),esk53_3(X4133,X4134,X4135)),X4134)
| X4133 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X4135,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4134,X4133))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4134,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4133),c_Nat_OSuc(esk53_3(X4133,X4134,X4135))))
| X4133 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X4135,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4134,X4133))) )
& ( hBOOL(hAPP(X4135,esk53_3(X4133,X4134,X4135)))
| X4133 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X4135,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4134,X4133))) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4133),esk53_3(X4133,X4134,X4135)),X4134)
| hBOOL(hAPP(X4135,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X4135,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4134,X4133))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4134,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4133),c_Nat_OSuc(esk53_3(X4133,X4134,X4135))))
| hBOOL(hAPP(X4135,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X4135,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4134,X4133))) )
& ( hBOOL(hAPP(X4135,esk53_3(X4133,X4134,X4135)))
| hBOOL(hAPP(X4135,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X4135,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4134,X4133))) )
& ( X4137 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X4139,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4139,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4138,X4137))) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4137),X4140),X4138)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4138,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4137),c_Nat_OSuc(X4140)))
| ~ hBOOL(hAPP(X4139,X4140))
| hBOOL(hAPP(X4139,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4138,X4137))) ) ),
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_1281,plain,
! [X4141,X4142,X4143] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4143),X4142),X4141)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4141,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4143),c_Nat_OSuc(X4142)))
| X4142 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4141,X4143)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4143) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4143),X4142),X4141)
| X4142 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4141,X4143)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4143) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4141,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4143),c_Nat_OSuc(X4142)))
| X4142 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4141,X4143)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4143) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div__lemma])])]) ).
fof(i_0_1282,plain,
! [X16,X18,X19] :
( class_Rings_Olinordered__ring(X19)
=> ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Oplus__class_Oplus(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X16),X16)),c_Groups_Ozero__class_Ozero(X19)) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(i_0_1283,plain,
! [X5452,X5453,X5454,X5455,X5456] : hAPP(hAPP(c_Power_Opower_Opower(X5456,X5455,X5454),X5453),c_Nat_OSuc(X5452)) = hAPP(hAPP(X5454,X5453),hAPP(hAPP(c_Power_Opower_Opower(X5456,X5455,X5454),X5453),X5452)),
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc]) ).
fof(i_0_1284,plain,
! [X4478,X4479,X4480] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4480),X4479),X4478)),X4479) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X4478),X4479),
inference(variable_rename,[status(thm)],[fact_mod__mult__self4]) ).
fof(i_0_1285,plain,
! [X4389,X4390,X4391] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4391)),X4390) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4391)),X4389)
| X4390 = X4389 )
& ( X4390 != X4389
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4391)),X4390) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4391)),X4389) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])]) ).
fof(i_0_1286,plain,
! [X4903,X4904] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4904)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4903)
| 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),X4903),X4904)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])]) ).
fof(i_0_1287,plain,
! [X4909,X4910] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4910)
| ~ 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),X4910),X4909)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4909)
| ~ 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),X4910),X4909)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4910)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4909)
| 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),X4910),X4909)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])]) ).
fof(i_0_1288,plain,
! [X24,X37,X23,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless(X19,c_Rings_Oinverse__class_Odivide(X19,X23,X37),X24)
<=> ( ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> c_Orderings_Oord__class_Oless(X19,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37)) )
& ( ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),X23) )
& ( ~ c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X24) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).
fof(i_0_1289,plain,
! [X24,X37,X23,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,c_Rings_Oinverse__class_Odivide(X19,X23,X37),X24)
<=> ( ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> c_Orderings_Oord__class_Oless__eq(X19,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37)) )
& ( ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),X23) )
& ( ~ c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X24) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__le__eq]) ).
fof(i_0_1290,plain,
! [X37,X23,X24,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X24,c_Rings_Oinverse__class_Odivide(X19,X23,X37))
<=> ( ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),X23) )
& ( ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37)) )
& ( ~ c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless(X19,X24,c_Groups_Ozero__class_Ozero(X19)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).
fof(i_0_1291,plain,
! [X37,X23,X24,X19] :
( class_Fields_Olinordered__field__inverse__zero(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X24,c_Rings_Oinverse__class_Odivide(X19,X23,X37))
<=> ( ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37),X23) )
& ( ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X37)
=> ( ( c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X24),X37)) )
& ( ~ c_Orderings_Oord__class_Oless(X19,X37,c_Groups_Ozero__class_Ozero(X19))
=> c_Orderings_Oord__class_Oless__eq(X19,X24,c_Groups_Ozero__class_Ozero(X19)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__divide__eq]) ).
fof(i_0_1292,plain,
! [X5250,X5251,X5252,X5253] :
( ~ class_Rings_Olinordered__semidom(X5253)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5253),X5252),c_Nat_OSuc(X5251)) != hAPP(hAPP(c_Power_Opower__class_Opower(X5253),X5250),c_Nat_OSuc(X5251))
| ~ c_Orderings_Oord__class_Oless__eq(X5253,c_Groups_Ozero__class_Ozero(X5253),X5252)
| ~ c_Orderings_Oord__class_Oless__eq(X5253,c_Groups_Ozero__class_Ozero(X5253),X5250)
| X5252 = X5250 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__base])]) ).
fof(i_0_1293,plain,
! [X5612,X5613] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5613)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5612)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5612),X5613),X5612) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5612),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5613,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_1294,plain,
! [X3691] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3691,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X3691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3691 = 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_1295,plain,
! [X4905,X4906] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4906)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4905)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4906,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4906),X4905)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])]) ).
fof(i_0_1296,plain,
! [X4907,X4908] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4908)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4907)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4908,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4907),X4908)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n])]) ).
fof(i_0_1297,plain,
! [X16,X84,X80,X81] :
( X81 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X80),X84),X16)
=> ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X80)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X16)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X80) ) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X80)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X80,X16)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
=> ( X80 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X81,X80) = X16 ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod__eq]) ).
fof(i_0_1298,plain,
! [X79,X16,X80,X81] :
( X81 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X80),X16),X79)
=> ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X80)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X80) ) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X80)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X80,X79)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X79,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
=> ( X80 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X81,X80) = X16 ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div__eq]) ).
fof(i_0_1299,plain,
! [X5291,X5292,X5293] :
( ~ class_Rings_Olinordered__semidom(X5293)
| ~ c_Orderings_Oord__class_Oless(X5293,c_Groups_Ozero__class_Ozero(X5293),X5292)
| ~ c_Orderings_Oord__class_Oless(X5293,X5292,c_Groups_Oone__class_Oone(X5293))
| c_Orderings_Oord__class_Oless(X5293,hAPP(hAPP(c_Power_Opower__class_Opower(X5293),X5292),c_Nat_OSuc(X5291)),c_Groups_Oone__class_Oone(X5293)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])]) ).
fof(i_0_1300,plain,
! [X5149,X5150,X5151] :
( ~ class_Rings_Olinordered__semidom(X5151)
| ~ c_Orderings_Oord__class_Oless__eq(X5151,c_Groups_Ozero__class_Ozero(X5151),X5150)
| ~ c_Orderings_Oord__class_Oless__eq(X5151,X5150,c_Groups_Oone__class_Oone(X5151))
| c_Orderings_Oord__class_Oless__eq(X5151,hAPP(hAPP(c_Power_Opower__class_Opower(X5151),X5150),c_Nat_OSuc(X5149)),X5150) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__Suc__le__self])]) ).
fof(i_0_1301,plain,
! [X4394,X4395] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X4395),X4394) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4395,X4394)),X4394),
inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__Suc__mod]) ).
fof(i_0_1302,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
=> ? [X9] :
! [X32] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X32),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X9)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X32))) ) ),
inference(fof_simplification,[status(thm)],[fact_calculation]) ).
fof(i_0_1303,plain,
! [X5165,X5166] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5166)
| 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),X5166),X5165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])]) ).
fof(i_0_1304,plain,
! [X5266,X5267,X5268] :
( ~ class_Rings_Olinordered__semidom(X5268)
| ~ c_Orderings_Oord__class_Oless(X5268,c_Groups_Oone__class_Oone(X5268),X5267)
| c_Orderings_Oord__class_Oless(X5268,c_Groups_Oone__class_Oone(X5268),hAPP(hAPP(c_Power_Opower__class_Opower(X5268),X5267),c_Nat_OSuc(X5266))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])]) ).
fof(i_0_1305,plain,
! [X4530,X4531] :
( ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4531,X4530)) != X4530
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X4531),X4530) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4531,X4530)) = X4530
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X4531),X4530) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4531,X4530)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__Suc])]) ).
fof(i_0_1306,plain,
! [X3621,X3622] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3622),c_Nat_OSuc(X3621))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3622,X3621) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3622,X3621)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3622),c_Nat_OSuc(X3621)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_1307,plain,
! [X3604,X3605] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3605),c_Nat_OSuc(X3604))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3605,X3604) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_1308,plain,
! [X3511,X3512] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3512),c_Nat_OSuc(X3511))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3512,X3511) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3512,X3511)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3512),c_Nat_OSuc(X3511)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_1309,plain,
! [X11,X45] :
( ~ hBOOL(hAPP(X45,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X45,X11))
=> ? [X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X39,X11)
& ! [X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X39)
=> ~ hBOOL(hAPP(X45,X57)) )
& hBOOL(hAPP(X45,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).
fof(i_0_1310,plain,
! [X4522,X4523] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X4523)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4523),X4522)),X4523) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__times__mod__eq])]) ).
fof(i_0_1311,axiom,
! [X48,X11,X45] :
( hBOOL(hAPP(X45,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X48)))
<=> epred2_3(X45,X48,X11) ),
inference(apply_def,[status(thm)],[fact_split__zmod,c_0_1257]) ).
fof(i_0_1312,axiom,
! [X48,X11,X45] :
( hBOOL(hAPP(X45,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X11,X48)))
<=> epred1_3(X45,X48,X11) ),
inference(apply_def,[status(thm)],[fact_split__zdiv,c_0_1258]) ).
fof(i_0_1313,plain,
! [X5125,X5126,X5127] :
( ~ class_Rings_Ocomm__semiring__1(X5127)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5127),hAPP(hAPP(c_Power_Opower__class_Opower(X5127),X5126),X5125)),X5126) = hAPP(hAPP(c_Power_Opower__class_Opower(X5127),X5126),c_Nat_OSuc(X5125)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])]) ).
fof(i_0_1314,plain,
! [X5231,X5232,X5233] :
( ~ class_Groups_Omonoid__mult(X5233)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5233),X5232),c_Nat_OSuc(X5231)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5233),hAPP(hAPP(c_Power_Opower__class_Opower(X5233),X5232),X5231)),X5232) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])]) ).
fof(i_0_1315,plain,
! [X4019] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,esk35_1(X4019)),X4019)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4019) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4019,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk35_1(X4019))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4019) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reals__Archimedean6a])])])]) ).
fof(i_0_1316,plain,
! [X4755,X4756] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4756)),X4755) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4755,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4756),X4755)),
inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).
fof(i_0_1317,plain,
! [X5784,X5785] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5785,X5784)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X5784),X5785) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5784,X5785)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])]) ).
fof(i_0_1318,plain,
! [X3469,X3470] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3470,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3470,X3469))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_1319,plain,
! [X3467,X3468] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3468,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3467,X3468))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_1320,plain,
! [X3513,X3514] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3514,c_Nat_OSuc(X3513))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3514,X3513)
| X3514 = c_Nat_OSuc(X3513) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3514,X3513)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3514,c_Nat_OSuc(X3513)) )
& ( X3514 != c_Nat_OSuc(X3513)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3514,c_Nat_OSuc(X3513)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_1321,plain,
! [X3507,X3508] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3508,c_Nat_OSuc(X3507))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3508,X3507)
| X3508 = c_Nat_OSuc(X3507) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1259])]) ).
fof(i_0_1322,plain,
! [X3457,X3458] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3458,X3457)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3458),c_Nat_OSuc(X3457)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_1323,plain,
! [X3632,X3633,X3635,X3636,X3637] :
( ( X3633 = c_Nat_OSuc(esk26_2(X3632,X3633))
| X3633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3633,c_Nat_OSuc(X3632)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk26_2(X3632,X3633),X3632)
| X3633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3633,c_Nat_OSuc(X3632)) )
& ( X3636 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3636,c_Nat_OSuc(X3635)) )
& ( X3636 != c_Nat_OSuc(X3637)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3637,X3635)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3636,c_Nat_OSuc(X3635)) ) ),
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_1324,plain,
! [X3648,X3649] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3648,c_Nat_OSuc(X3649))
| X3648 = X3649
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3649,X3648) )
& ( X3648 != X3649
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3648,c_Nat_OSuc(X3649))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3649,X3648) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
fof(i_0_1325,plain,
! [X3515,X3516] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3516,X3515)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3515),X3516) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3515),X3516)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3516,X3515) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1260])]) ).
fof(i_0_1326,plain,
! [X3625,X3626] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3626,X3625)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3625,c_Nat_OSuc(X3626)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3625,c_Nat_OSuc(X3626))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3626,X3625) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1261])]) ).
fof(i_0_1327,plain,
! [X5178] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5178) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_power__Suc__0]) ).
fof(i_0_1328,plain,
! [X3610,X3611,X3612] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3612,X3611)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3611,X3610)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3612),X3610) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_1329,plain,
! [X3652,X3653] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X3653),X3652) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3653,c_Nat_OSuc(X3652)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_1330,plain,
! [X5641,X5642] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5642,c_Nat_OSuc(X5641)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5642,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5641),
inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).
fof(i_0_1331,plain,
! [X5234,X5235,X5236] :
( ~ class_Power_Opower(X5236)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5236),X5235),c_Nat_OSuc(X5234)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5236),X5235),hAPP(hAPP(c_Power_Opower__class_Opower(X5236),X5235),X5234)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])]) ).
fof(i_0_1332,plain,
! [X5119,X5120,X5121] :
( ~ class_Rings_Ocomm__semiring__1(X5121)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5121),X5120),c_Nat_OSuc(X5119)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5121),X5120),hAPP(hAPP(c_Power_Opower__class_Opower(X5121),X5120),X5119)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])]) ).
fof(i_0_1333,plain,
! [X5122,X5123,X5124] :
( ~ class_Rings_Ocomm__semiring__1(X5124)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5124),X5123),hAPP(hAPP(c_Power_Opower__class_Opower(X5124),X5123),X5122)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5124),X5123),c_Nat_OSuc(X5122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])]) ).
fof(i_0_1334,plain,
! [X3654,X3655] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X3655),X3654) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3655,X3654)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_1335,plain,
! [X3656,X3657] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3657,c_Nat_OSuc(X3656)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3657,X3656)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_1336,plain,
! [X3623,X3624] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3624,c_Nat_OSuc(X3623))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3624,X3623)
| X3624 = X3623 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3624,X3623)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3624,c_Nat_OSuc(X3623)) )
& ( X3624 != X3623
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3624,c_Nat_OSuc(X3623)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_1337,plain,
! [X3619,X3620] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3620,c_Nat_OSuc(X3619))
| X3620 = X3619
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3620,X3619) )
& ( X3620 != X3619
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3620,c_Nat_OSuc(X3619))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3620,X3619) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1262])])]) ).
fof(i_0_1338,plain,
! [X3617,X3618] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3618,X3617)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3618,c_Nat_OSuc(X3617))
| X3617 = X3618 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1263])]) ).
fof(i_0_1339,plain,
! [X3608,X3609] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3609,c_Nat_OSuc(X3608))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3609,X3608)
| X3609 = X3608 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1264])]) ).
fof(i_0_1340,plain,
! [X3606,X3607] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3607),X3606)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3607,X3606) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_1341,plain,
! [X3650,X3651] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3651),X3650)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3651,X3650) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_1342,plain,
! [X3642,X3643] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3643),X3642)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3643,X3642) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3643,X3642)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3643),X3642) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_1343,plain,
! [X3638,X3639] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3639,X3638)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3639),X3638) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3639),X3638)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3639,X3638) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_1344,plain,
! [X3505,X3506] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3506),X3505)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3506,X3505) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_1345,plain,
! [X3640,X3641] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3641,c_Nat_OSuc(X3640))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3641,X3640) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3641,X3640)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3641,c_Nat_OSuc(X3640)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_1346,plain,
! [X3461,X3462,X3464,X3465,X3466] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3462,X3461)
| X3461 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3462,esk20_2(X3461,X3462))) )
& ( X3464 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3465,X3466))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3465,X3464) ) ),
inference(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_1347,plain,
! [X3613,X3614] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3614,X3613)
| c_Nat_OSuc(X3614) = X3613
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3614),X3613) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_1348,plain,
! [X14,X28,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X28),X14)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X14)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X14) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_1349,plain,
! [X4753,X4754] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4754),c_Nat_OSuc(X4753)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4754,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4754),X4753)),
inference(variable_rename,[status(thm)],[fact_mult__Suc__right]) ).
fof(i_0_1350,plain,
! [X3096] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3096))),
inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc__gt__zero]) ).
fof(i_0_1351,plain,
! [X3658,X3659] :
( ( X3659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3659 = 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,X3659,X3658) )
& ( X3658 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3659 = 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,X3659,X3658) )
& ( X3659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3658 = 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,X3659,X3658) )
& ( X3658 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3658 = 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,X3659,X3658) )
& ( X3659 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3658 != 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,X3659,X3658) )
& ( X3659 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3658 != 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,X3659,X3658) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_1352,plain,
! [X3660,X3661] :
( ( X3661 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3661 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3661,X3660) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3660 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3661 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3661,X3660) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3661 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3660 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3661,X3660) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3660 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3660 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3661,X3660) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3661 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3660 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3661,X3660) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3661 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3660 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3661,X3660) = 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_1353,plain,
! [X1,X2,X19,X34] :
( class_Orderings_Oord(X34)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X19,X34),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X19,X34),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X19,X34),X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_1354,plain,
! [X4734,X4735] :
( ( X4735 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4735),X4734) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4734 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4735),X4734) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4735 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4734 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4735),X4734) = 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_1355,plain,
! [X3631] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3631,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X3631 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3631 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3631,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_1356,plain,
! [X5792,X5793] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5793,X5792),c_Nat_OSuc(X5793)),
inference(variable_rename,[status(thm)],[fact_diff__less__Suc]) ).
fof(i_0_1357,plain,
! [X21,X19] :
( class_Rings_Olinordered__ring(X19)
=> ~ c_Orderings_Oord__class_Oless(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X21),X21),c_Groups_Ozero__class_Ozero(X19)) ),
inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).
fof(i_0_1358,plain,
! [X14,X26] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14) = X26 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14),X14) ) ),
inference(fof_simplification,[status(thm)],[fact_mod__if]) ).
fof(i_0_1359,plain,
! [X14,X26] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X14) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14),X14) ),
inference(fof_simplification,[status(thm)],[fact_mod__geq]) ).
fof(i_0_1360,plain,
! [X3517] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3517),X3517),
inference(variable_rename,[status(thm)],[i_0_1265]) ).
fof(i_0_1361,plain,
! [X3646,X3647] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3647,X3646)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3647),X3646) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_1362,plain,
! [X3615,X3616] :
( ~ c_Orderings_Oord__class_Oless(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__SucI])]) ).
fof(i_0_1363,plain,
! [X3644,X3645] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3645,X3644)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3645,c_Nat_OSuc(X3644)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_1364,plain,
! [X3509,X3510] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3510,X3509)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3510,c_Nat_OSuc(X3509)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_1365,plain,
! [X29,X30] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X29),X30),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_1366,plain,
! [X30,X29] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X30),X30),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_1367,plain,
! [X4] :
( ~ 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),X4))
<=> X4 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[fact_not__real__square__gt__zero]) ).
fof(i_0_1368,plain,
! [X28,X47] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X47)
=> c_SMT_Oz3div(X28,X47) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X28,X47) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X47)
=> c_SMT_Oz3div(X28,X47) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X28,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X47))) ) ),
inference(fof_simplification,[status(thm)],[fact_z3div__def]) ).
fof(i_0_1369,plain,
! [X5179,X5180] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5180),X5179) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X5179 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X5180 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X5179 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5180),X5179) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X5180 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5180),X5179) = 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_1370,plain,
! [X14,X26] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X14)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X14)) = X26 ),
inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).
fof(i_0_1371,plain,
! [X12,X4,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X4,X12)
<=> ( c_Orderings_Oord__class_Oless__eq(X19,X4,X12)
& ~ c_Orderings_Oord__class_Oless__eq(X19,X12,X4) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_1372,plain,
! [X2983] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X2983)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2983),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc]) ).
fof(i_0_1373,plain,
! [X5225,X5226] :
( ~ class_Power_Opower(X5226)
| ~ class_Rings_Osemiring__0(X5226)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5226),c_Groups_Ozero__class_Ozero(X5226)),c_Nat_OSuc(X5225)) = c_Groups_Ozero__class_Ozero(X5226) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])]) ).
fof(i_0_1374,plain,
! [X12,X4,X19] :
( class_Orderings_Olinorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X4,X12)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X4,X12)
<=> X4 = X12 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_1375,plain,
! [X21,X20,X19] :
( class_Orderings_Oorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X20,X21)
=> ~ c_Orderings_Oord__class_Oless(X19,X21,X20) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_1376,plain,
! [X12,X4,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X4,X12)
<=> ( c_Orderings_Oord__class_Oless(X19,X12,X4)
| X4 = X12 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_1377,plain,
! [X18,X16,X19] :
( class_Orderings_Olinorder(X19)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X16,X18)
=> ~ c_Orderings_Oord__class_Oless(X19,X18,X16) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_1378,plain,
! [X12,X4,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X4,X12)
<=> c_Orderings_Oord__class_Oless__eq(X19,X12,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_1379,plain,
! [X12,X4,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X19,X4,X12)
<=> c_Orderings_Oord__class_Oless(X19,X12,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_1380,plain,
! [X16,X18,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> ~ c_Orderings_Oord__class_Oless(X19,X16,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_1381,plain,
! [X20,X21,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X21,X20)
=> ~ c_Orderings_Oord__class_Oless(X19,X20,X21) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_1382,plain,
! [X16,X18,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> ~ c_Orderings_Oord__class_Oless(X19,X16,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_1383,plain,
! [X16,X18,X19] :
( class_Orderings_Opreorder(X19)
=> ( c_Orderings_Oord__class_Oless(X19,X18,X16)
=> ~ c_Orderings_Oord__class_Oless(X19,X16,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_1384,plain,
! [X3495,X3496] :
( ( c_Nat_OSuc(X3496) != c_Nat_OSuc(X3495)
| X3496 = X3495 )
& ( X3496 != X3495
| c_Nat_OSuc(X3496) = c_Nat_OSuc(X3495) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_1385,plain,
! [X3493,X3494] :
( c_Nat_OSuc(X3494) != c_Nat_OSuc(X3493)
| X3494 = X3493 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_1386,plain,
! [X4529] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4529,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mod__1]) ).
fof(i_0_1387,plain,
! [X4101] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4101,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X4101,
inference(variable_rename,[status(thm)],[fact_div__1]) ).
fof(i_0_1388,plain,
! [X5640] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X5640),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X5640,
inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).
fof(i_0_1389,plain,
! [X3455] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X3455)),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_1390,plain,
! [X3456] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3456,c_Nat_OSuc(X3456)),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_1391,plain,
! [X28,X47] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X47)
=> c_SMT_Oz3mod(X28,X47) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X28,X47) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X47)
=> c_SMT_Oz3mod(X28,X47) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X28,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X47)) ) ),
inference(fof_simplification,[status(thm)],[fact_z3mod__def]) ).
fof(i_0_1392,plain,
! [X3627,X3629,X3630] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3627)
| X3627 = c_Nat_OSuc(esk25_1(X3627)) )
& ( X3629 != c_Nat_OSuc(X3630)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3629) ) ),
inference(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_1393,plain,
! [X12,X4,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X4,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X19,X4,X12)
<=> X4 = X12 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_1394,plain,
! [X18,X19] :
( class_RealVector_Oreal__normed__vector(X19)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X19,X18),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero]) ).
fof(i_0_1395,plain,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_simplification,[status(thm)],[fact_not__real__of__nat__less__zero]) ).
fof(i_0_1396,plain,
! [X16,X18,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X18,X16)
=> ( X18 != X16
=> c_Orderings_Oord__class_Oless(X19,X16,X18) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_1397,plain,
! [X16,X18,X19] :
( class_Orderings_Olinorder(X19)
=> ( X18 != X16
=> ( ~ c_Orderings_Oord__class_Oless(X19,X18,X16)
=> c_Orderings_Oord__class_Oless(X19,X16,X18) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_1398,plain,
! [X4,X12,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X12,X4)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X4,X12)
<=> X4 = X12 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_1399,plain,
! [X16,X18,X19] :
( class_Rings_Olinordered__idom(X19)
=> ( X18 != X16
=> ( ~ c_Orderings_Oord__class_Oless(X19,X18,X16)
=> c_Orderings_Oord__class_Oless(X19,X16,X18) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_1400,plain,
! [X18,X16,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X19,X16,X18)
=> c_Orderings_Oord__class_Oless(X19,X18,X16) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_1401,plain,
! [X16,X18,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless(X19,X18,X16)
=> c_Orderings_Oord__class_Oless__eq(X19,X16,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_1402,plain,
! [X16,X18,X19] :
( class_Orderings_Olinorder(X19)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X19,X18,X16)
=> c_Orderings_Oord__class_Oless__eq(X19,X16,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_1403,plain,
! [X19] :
( class_Rings_Olinordered__semidom(X19)
=> ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Oone__class_Oone(X19),c_Groups_Ozero__class_Ozero(X19)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_1404,plain,
! [X19] :
( class_Rings_Olinordered__semidom(X19)
=> ~ c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oone__class_Oone(X19),c_Groups_Ozero__class_Ozero(X19)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_1405,plain,
! [X3460] : c_Nat_OSuc(X3460) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3460),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_1406,plain,
! [X16,X18] :
( X18 != X16
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X16)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_1407,plain,
! [X18,X19] :
( class_Orderings_Opreorder(X19)
=> ~ c_Orderings_Oord__class_Oless(X19,X18,X18) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_1408,plain,
! [X3502] : c_Nat_OSuc(X3502) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_1409,plain,
! [X3501] : c_Nat_OSuc(X3501) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_1410,plain,
! [X3499] : c_Nat_OSuc(X3499) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_1411,plain,
! [X3504] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X3504),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_1412,plain,
! [X3503] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X3503),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_1413,plain,
! [X3500] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X3500),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_1414,plain,
! [X3497] : c_Nat_OSuc(X3497) != X3497,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_1415,plain,
! [X3498] : X3498 != c_Nat_OSuc(X3498),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_1416,plain,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_1417,plain,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_1418,plain,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_1419,plain,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X14),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_1420,plain,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X14),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_1421,plain,
! [X4102,X4103,X4106,X4107,X4108] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk44_2(X4102,X4103))
| ~ c_SEQ_OBseq(X4103,X4102)
| ~ class_RealVector_Oreal__normed__vector(X4103) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4103,c_Groups_Oplus__class_Oplus(X4103,hAPP(X4102,X4106),c_Groups_Ouminus__class_Ouminus(X4103,hAPP(X4102,esk45_2(X4102,X4103))))),esk44_2(X4102,X4103))
| ~ c_SEQ_OBseq(X4103,X4102)
| ~ class_RealVector_Oreal__normed__vector(X4103) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4107)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4103,c_Groups_Oplus__class_Oplus(X4103,hAPP(X4102,esk46_4(X4102,X4103,X4107,X4108)),c_Groups_Ouminus__class_Ouminus(X4103,hAPP(X4102,X4108)))),X4107)
| c_SEQ_OBseq(X4103,X4102)
| ~ class_RealVector_Oreal__normed__vector(X4103) ) ),
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__iff3])])])])]) ).
fof(i_0_1422,plain,
! [X4110,X4111,X4114,X4115,X4116] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk47_2(X4110,X4111))
| ~ c_SEQ_OBseq(X4111,X4110)
| ~ class_RealVector_Oreal__normed__vector(X4111) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4111,c_Groups_Oplus__class_Oplus(X4111,hAPP(X4110,X4114),c_Groups_Ouminus__class_Ouminus(X4111,esk48_2(X4110,X4111)))),esk47_2(X4110,X4111))
| ~ c_SEQ_OBseq(X4111,X4110)
| ~ class_RealVector_Oreal__normed__vector(X4111) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4115)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4111,c_Groups_Oplus__class_Oplus(X4111,hAPP(X4110,esk49_4(X4110,X4111,X4115,X4116)),c_Groups_Ouminus__class_Ouminus(X4111,X4116))),X4115)
| c_SEQ_OBseq(X4111,X4110)
| ~ class_RealVector_Oreal__normed__vector(X4111) ) ),
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__iff2])])])])]) ).
fof(i_0_1423,plain,
! [X3715,X3716,X3717,X3718,X3719] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3717,X3718),X3716,X3715)
| c_Orderings_Oord__class_Oless__eq(X3718,hAPP(X3716,X3719),hAPP(X3715,X3719))
| ~ class_Orderings_Oord(X3718) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3718,hAPP(X3716,esk29_4(X3715,X3716,X3717,X3718)),hAPP(X3715,esk29_4(X3715,X3716,X3717,X3718)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3717,X3718),X3716,X3715)
| ~ class_Orderings_Oord(X3718) ) ),
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_1424,plain,
! [X4128,X4129,X4130,X4131] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4130,esk52_4(X4128,X4129,X4130,X4131))
| c_SEQ_OBseq(X4131,X4129)
| ~ class_RealVector_Oreal__normed__vector(X4131) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4131,hAPP(X4129,esk52_4(X4128,X4129,X4130,X4131))),X4128)
| c_SEQ_OBseq(X4131,X4129)
| ~ class_RealVector_Oreal__normed__vector(X4131) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_BseqI2_H])])])]) ).
fof(i_0_1425,plain,
! [X5630,X5631,X5632,X5633,X5634] :
( ~ class_RealVector_Oreal__normed__algebra(X5634)
| c_Groups_Ominus__class_Ominus(X5634,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5634),X5633),X5632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5634),X5631),X5630)) = c_Groups_Oplus__class_Oplus(X5634,c_Groups_Oplus__class_Oplus(X5634,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5634),c_Groups_Ominus__class_Ominus(X5634,X5633,X5631)),c_Groups_Ominus__class_Ominus(X5634,X5632,X5630)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5634),c_Groups_Ominus__class_Ominus(X5634,X5633,X5631)),X5630)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5634),X5631),c_Groups_Ominus__class_Ominus(X5634,X5632,X5630))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod])]) ).
cnf(i_0_1426,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),X2)),
inference(split_conjunct,[status(thm)],[i_0_1266]) ).
cnf(i_0_1427,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_1267]) ).
cnf(i_0_1428,hypothesis,
( v_thesis____
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X1,esk76_1(X1))),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X1,esk77_1(X1)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk77_1(X1)))))) ),
inference(split_conjunct,[status(thm)],[i_0_1268]) ).
fof(i_0_1429,plain,
! [X5314,X5315] :
( X5315 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X5314 = 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),X5315),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk68_2(X5314,X5315)),X5314)))),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_1430,plain,
! [X5420,X5421,X5422,X5423,X5424] :
( ( ~ hBOOL(hAPP(hAPP(X5421,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5420,X5422)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5420,X5422)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5424)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5424,X5422)
| X5420 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5422),X5423),X5424)
| hBOOL(hAPP(hAPP(X5421,X5423),X5424))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5422) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk71_3(X5420,X5421,X5422))
| hBOOL(hAPP(hAPP(X5421,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5420,X5422)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5420,X5422)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5422) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk71_3(X5420,X5421,X5422),X5422)
| hBOOL(hAPP(hAPP(X5421,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5420,X5422)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5420,X5422)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5422) )
& ( X5420 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5422),esk70_3(X5420,X5421,X5422)),esk71_3(X5420,X5421,X5422))
| hBOOL(hAPP(hAPP(X5421,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5420,X5422)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5420,X5422)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5422) )
& ( ~ hBOOL(hAPP(hAPP(X5421,esk70_3(X5420,X5421,X5422)),esk71_3(X5420,X5421,X5422)))
| hBOOL(hAPP(hAPP(X5421,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5420,X5422)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5420,X5422)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5422) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__pos__lemma])])])])]) ).
fof(i_0_1431,plain,
! [X5427,X5428,X5429,X5430,X5431] :
( ( ~ hBOOL(hAPP(hAPP(X5428,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5427,X5429)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5427,X5429)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5429,X5431)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5431,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5427 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5429),X5430),X5431)
| hBOOL(hAPP(hAPP(X5428,X5430),X5431))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5429,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5429,esk73_3(X5427,X5428,X5429))
| hBOOL(hAPP(hAPP(X5428,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5427,X5429)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5427,X5429)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5429,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk73_3(X5427,X5428,X5429),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(hAPP(X5428,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5427,X5429)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5427,X5429)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5429,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( X5427 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5429),esk72_3(X5427,X5428,X5429)),esk73_3(X5427,X5428,X5429))
| hBOOL(hAPP(hAPP(X5428,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5427,X5429)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5427,X5429)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5429,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ hBOOL(hAPP(hAPP(X5428,esk72_3(X5427,X5428,X5429)),esk73_3(X5427,X5428,X5429)))
| hBOOL(hAPP(hAPP(X5428,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5427,X5429)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5427,X5429)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5429,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__neg__lemma])])])])]) ).
fof(i_0_1432,plain,
! [X5478,X5479,X5480] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5480,X5479),X5478) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5480,X5478),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5479,X5478)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5480,X5478),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5479,X5478)),X5478)),
inference(variable_rename,[status(thm)],[fact_zdiv__zadd1__eq]) ).
fof(i_0_1433,plain,
! [X4709,X4710,X4711] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4711,X4710),X4709) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4711,X4709),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4710,X4709)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4711,X4709),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4710,X4709)),X4709)),
inference(variable_rename,[status(thm)],[fact_div__add1__eq]) ).
cnf(i_0_1434,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_1269]) ).
cnf(i_0_1435,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_1270]) ).
cnf(i_0_1436,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(esk2_0,X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))))),
inference(split_conjunct,[status(thm)],[i_0_1271]) ).
cnf(i_0_1437,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk6_1(X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))))),
inference(split_conjunct,[status(thm)],[i_0_1272]) ).
cnf(i_0_1438,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk5_1(X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))))),
inference(split_conjunct,[status(thm)],[i_0_1273]) ).
fof(i_0_1439,plain,
! [X4166,X4167,X4168,X4169] :
( ~ class_Divides_Osemiring__div(X4169)
| c_Groups_Oplus__class_Oplus(X4169,c_Groups_Oplus__class_Oplus(X4169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4169),c_Divides_Odiv__class_Odiv(X4169,X4168,X4167)),X4167),c_Divides_Odiv__class_Omod(X4169,X4168,X4167)),X4166) = c_Groups_Oplus__class_Oplus(X4169,X4168,X4166) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality])]) ).
cnf(i_0_1440,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk17_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,esk16_3(X3,X2,X1))),X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1274]) ).
cnf(i_0_1441,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk13_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,esk12_3(X3,X2,X1))),X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1275]) ).
fof(i_0_1442,plain,
! [X5437,X5438,X5439] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5439,X5438)),X5438),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5439,X5438)),X5437) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5439,X5437),
inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality2]) ).
cnf(i_0_1443,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk19_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk18_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1274]) ).
cnf(i_0_1444,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk15_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk14_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1275]) ).
fof(i_0_1445,plain,
! [X5351,X5352,X5353,X5354,X5355,X5356] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5356),X5355),X5354) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5353),X5352),X5351)
| ~ 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),X5353),X5352),X5351),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5354,X5356)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5351)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5353)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5353,X5356)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5352,X5355) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).
fof(i_0_1446,plain,
! [X5362,X5363,X5364,X5365,X5366,X5367] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5367),X5366),X5365) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5364),X5363),X5362)
| ~ 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),X5364),X5363),X5362))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5362,X5364)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5365)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5364)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5364,X5367)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5366,X5363) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).
fof(i_0_1447,plain,
! [X5093,X5095,X5096] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk64_1(X5093))
| ~ class_RealVector_Oreal__normed__algebra(X5093) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5093,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5093),X5095),X5096)),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(X5093,X5095)),c_RealVector_Onorm__class_Onorm(X5093,X5096))),esk64_1(X5093)))
| ~ class_RealVector_Oreal__normed__algebra(X5093) ) ),
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_1448,plain,
! [X5075,X5077,X5078] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk60_1(X5075))
| ~ class_RealVector_Oreal__normed__algebra(X5075) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5075),X5077),X5078)),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(X5075,X5077)),c_RealVector_Onorm__class_Onorm(X5075,X5078))),esk60_1(X5075)))
| ~ class_RealVector_Oreal__normed__algebra(X5075) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Opos__bounded])])])])]) ).
fof(i_0_1449,plain,
! [X2970,X2971,X2972] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2971),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2971)))),X2970)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X2970) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk7_1(X2972)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X2972) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk7_1(X2972))))),X2972)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X2972) ) ),
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__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096])])])])])]) ).
cnf(i_0_1450,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk19_2(X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk18_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1274]) ).
cnf(i_0_1451,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk15_2(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk14_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1275]) ).
fof(i_0_1452,plain,
! [X5368,X5369,X5370,X5371,X5372] :
( ~ 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),X5372),X5371),X5370),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5372),X5369),X5368))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5370)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5370,X5372)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5368,X5372)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5371,X5369) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).
fof(i_0_1453,plain,
! [X5357,X5358,X5359,X5360,X5361] :
( ~ 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),X5361),X5360),X5359),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5361),X5358),X5357))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5357,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5361,X5357)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5361,X5359)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5358,X5360) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).
cnf(i_0_1454,plain,
( c_SEQ_OBseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk37_3(X2,X1,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1276]) ).
cnf(i_0_1455,plain,
( c_SEQ_OBseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk39_3(X2,X1,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1277]) ).
fof(i_0_1456,plain,
! [X4997,X4998,X4999,X5000] :
( ~ class_Fields_Ofield(X5000)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5000),X4999,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5000)),X4998),X4997)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5000),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5000)),X4998),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5000),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X5000),X4999,X4998),X4997)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5000),X4999,X4998)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mod__mult__right])]) ).
cnf(i_0_1457,plain,
( X2 = X3
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1278]) ).
cnf(i_0_1458,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_1279]) ).
fof(i_0_1459,plain,
! [X5624,X5625,X5626,X5627,X5628,X5629] :
( ( c_Groups_Oplus__class_Oplus(X5629,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5629),X5628),X5627),X5626) != c_Groups_Oplus__class_Oplus(X5629,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5629),X5625),X5627),X5624)
| c_Groups_Oplus__class_Oplus(X5629,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5629),c_Groups_Ominus__class_Ominus(X5629,X5628,X5625)),X5627),X5626) = X5624
| ~ class_Rings_Oring(X5629) )
& ( c_Groups_Oplus__class_Oplus(X5629,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5629),c_Groups_Ominus__class_Ominus(X5629,X5628,X5625)),X5627),X5626) != X5624
| c_Groups_Oplus__class_Oplus(X5629,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5629),X5628),X5627),X5626) = c_Groups_Oplus__class_Oplus(X5629,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5629),X5625),X5627),X5624)
| ~ class_Rings_Oring(X5629) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).
fof(i_0_1460,plain,
! [X5618,X5619,X5620,X5621,X5622,X5623] :
( ( c_Groups_Oplus__class_Oplus(X5623,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5623),X5622),X5621),X5620) != c_Groups_Oplus__class_Oplus(X5623,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5623),X5619),X5621),X5618)
| X5620 = c_Groups_Oplus__class_Oplus(X5623,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5623),c_Groups_Ominus__class_Ominus(X5623,X5619,X5622)),X5621),X5618)
| ~ class_Rings_Oring(X5623) )
& ( X5620 != c_Groups_Oplus__class_Oplus(X5623,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5623),c_Groups_Ominus__class_Ominus(X5623,X5619,X5622)),X5621),X5618)
| c_Groups_Oplus__class_Oplus(X5623,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5623),X5622),X5621),X5620) = c_Groups_Oplus__class_Oplus(X5623,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5623),X5619),X5621),X5618)
| ~ class_Rings_Oring(X5623) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).
cnf(i_0_1461,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Nat_OSuc(esk53_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_1280]) ).
cnf(i_0_1462,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_1269]) ).
cnf(i_0_1463,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_1270]) ).
fof(i_0_1464,plain,
! [X5443,X5444,X5445] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5445),X5444),X5443) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5445),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5444,X5443)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5445),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5444,X5443)),X5443)),
inference(variable_rename,[status(thm)],[fact_zdiv__zmult1__eq]) ).
fof(i_0_1465,plain,
! [X4150,X4151,X4152] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4152),X4151),X4150) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4152),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4151,X4150)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4152),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4151,X4150)),X4150)),
inference(variable_rename,[status(thm)],[fact_div__mult1__eq]) ).
cnf(i_0_1466,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Nat_OSuc(esk53_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_1280]) ).
fof(i_0_1467,plain,
! [X5635,X5636,X5637,X5638,X5639] :
( ~ class_Rings_Oring(X5639)
| c_Groups_Ominus__class_Ominus(X5639,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5639),X5638),X5637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5639),X5636),X5635)) = c_Groups_Oplus__class_Oplus(X5639,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5639),X5638),c_Groups_Ominus__class_Ominus(X5639,X5637,X5635)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5639),c_Groups_Ominus__class_Ominus(X5639,X5638,X5636)),X5635)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__diff__mult])]) ).
fof(i_0_1468,plain,
! [X5105,X5106] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5106)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5105)),X5106),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,X5106,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X5105)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_LIMSEQ__inverse__realpow__zero__lemma])]) ).
fof(i_0_1469,plain,
! [X5392,X5393,X5394,X5395] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5395)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5394)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5394,X5393)
| 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),X5393),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5392,X5395)),X5394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5393),X5395)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux4])]) ).
fof(i_0_1470,plain,
! [X5396,X5397,X5398,X5399] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5399)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5398,X5397)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5397,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5398),X5399),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5398),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5396,X5399)),X5397)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux1])]) ).
fof(i_0_1471,plain,
! [X5434,X5435,X5436] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5436)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5435,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5434),X5436)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5434),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5435,X5434),X5436)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5435,X5434)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq])]) ).
cnf(i_0_1472,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_1280]) ).
fof(i_0_1473,plain,
! [X4126,X4127] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4127)
| c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4126),c_RealDef_Oreal(tc_Nat_Onat,X4127)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4126,X4127)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4126,X4127)),c_RealDef_Oreal(tc_Nat_Onat,X4127))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__div__aux])]) ).
fof(i_0_1474,plain,
! [X4162,X4163,X4164,X4165] :
( ~ class_Divides_Osemiring__div(X4165)
| c_Groups_Oplus__class_Oplus(X4165,c_Groups_Oplus__class_Oplus(X4165,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4165),X4164),c_Divides_Odiv__class_Odiv(X4165,X4163,X4164)),c_Divides_Odiv__class_Omod(X4165,X4163,X4164)),X4162) = c_Groups_Oplus__class_Oplus(X4165,X4163,X4162) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality2])]) ).
fof(i_0_1475,plain,
! [X4313,X4314,X4315,X4316,X4317] :
( ~ class_Rings_Osemiring(X4317)
| c_Groups_Oplus__class_Oplus(X4317,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4317),X4316),X4315),c_Groups_Oplus__class_Oplus(X4317,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4317),X4314),X4315),X4313)) = c_Groups_Oplus__class_Oplus(X4317,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4317),c_Groups_Oplus__class_Oplus(X4317,X4316,X4314)),X4315),X4313) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).
fof(i_0_1476,plain,
! [X5871,X5872,X5873,X5874,X5875,X5876,X5877,X5878,X5879,X5880] :
( ( X5872 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(X5873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ epred1_3(X5873,X5872,X5871) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5872)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5875)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5875,X5872)
| X5871 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5872),X5874),X5875)
| hBOOL(hAPP(X5873,X5874))
| ~ epred1_3(X5873,X5872,X5871) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5872,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5872,X5877)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5877,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5871 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5872),X5876),X5877)
| hBOOL(hAPP(X5873,X5876))
| ~ epred1_3(X5873,X5872,X5871) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5879)
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,esk81_3(X5878,X5879,X5880))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5879)
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X5878,X5879,X5880),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5879)
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk80_3(X5878,X5879,X5880)),esk81_3(X5878,X5879,X5880))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5879)
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( ~ hBOOL(hAPP(X5880,esk80_3(X5878,X5879,X5880)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5879)
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,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),esk79_3(X5878,X5879,X5880))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,esk81_3(X5878,X5879,X5880))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk79_3(X5878,X5879,X5880))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X5878,X5879,X5880),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),esk79_3(X5878,X5879,X5880))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk80_3(X5878,X5879,X5880)),esk81_3(X5878,X5879,X5880))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk79_3(X5878,X5879,X5880))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( ~ hBOOL(hAPP(X5880,esk80_3(X5878,X5879,X5880)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk79_3(X5878,X5879,X5880))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_3(X5878,X5879,X5880),X5879)
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,esk81_3(X5878,X5879,X5880))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_3(X5878,X5879,X5880),X5879)
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X5878,X5879,X5880),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_3(X5878,X5879,X5880),X5879)
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk80_3(X5878,X5879,X5880)),esk81_3(X5878,X5879,X5880))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_3(X5878,X5879,X5880),X5879)
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( ~ hBOOL(hAPP(X5880,esk80_3(X5878,X5879,X5880)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_3(X5878,X5879,X5880),X5879)
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk78_3(X5878,X5879,X5880)),esk79_3(X5878,X5879,X5880))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,esk81_3(X5878,X5879,X5880))
| X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk78_3(X5878,X5879,X5880)),esk79_3(X5878,X5879,X5880))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X5878,X5879,X5880),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk78_3(X5878,X5879,X5880)),esk79_3(X5878,X5879,X5880))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk80_3(X5878,X5879,X5880)),esk81_3(X5878,X5879,X5880))
| X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk78_3(X5878,X5879,X5880)),esk79_3(X5878,X5879,X5880))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( ~ hBOOL(hAPP(X5880,esk80_3(X5878,X5879,X5880)))
| X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk78_3(X5878,X5879,X5880)),esk79_3(X5878,X5879,X5880))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5880,esk78_3(X5878,X5879,X5880)))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,esk81_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,esk78_3(X5878,X5879,X5880)))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X5878,X5879,X5880),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5880,esk78_3(X5878,X5879,X5880)))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk80_3(X5878,X5879,X5880)),esk81_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,esk78_3(X5878,X5879,X5880)))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( ~ hBOOL(hAPP(X5880,esk80_3(X5878,X5879,X5880)))
| ~ hBOOL(hAPP(X5880,esk78_3(X5878,X5879,X5880)))
| X5879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5879)
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,esk81_3(X5878,X5879,X5880))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5879)
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X5878,X5879,X5880),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5879)
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk80_3(X5878,X5879,X5880)),esk81_3(X5878,X5879,X5880))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5879)
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( ~ hBOOL(hAPP(X5880,esk80_3(X5878,X5879,X5880)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5879)
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,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),esk79_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,esk81_3(X5878,X5879,X5880))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk79_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X5878,X5879,X5880),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),esk79_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk80_3(X5878,X5879,X5880)),esk81_3(X5878,X5879,X5880))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk79_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( ~ hBOOL(hAPP(X5880,esk80_3(X5878,X5879,X5880)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk79_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_3(X5878,X5879,X5880),X5879)
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,esk81_3(X5878,X5879,X5880))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_3(X5878,X5879,X5880),X5879)
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X5878,X5879,X5880),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_3(X5878,X5879,X5880),X5879)
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk80_3(X5878,X5879,X5880)),esk81_3(X5878,X5879,X5880))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_3(X5878,X5879,X5880),X5879)
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( ~ hBOOL(hAPP(X5880,esk80_3(X5878,X5879,X5880)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_3(X5878,X5879,X5880),X5879)
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk78_3(X5878,X5879,X5880)),esk79_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,esk81_3(X5878,X5879,X5880))
| X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk78_3(X5878,X5879,X5880)),esk79_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X5878,X5879,X5880),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk78_3(X5878,X5879,X5880)),esk79_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk80_3(X5878,X5879,X5880)),esk81_3(X5878,X5879,X5880))
| X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk78_3(X5878,X5879,X5880)),esk79_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( ~ hBOOL(hAPP(X5880,esk80_3(X5878,X5879,X5880)))
| X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk78_3(X5878,X5879,X5880)),esk79_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5880,esk78_3(X5878,X5879,X5880)))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5879,esk81_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,esk78_3(X5878,X5879,X5880)))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X5878,X5879,X5880),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5880,esk78_3(X5878,X5879,X5880)))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( X5878 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5879),esk80_3(X5878,X5879,X5880)),esk81_3(X5878,X5879,X5880))
| ~ hBOOL(hAPP(X5880,esk78_3(X5878,X5879,X5880)))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) )
& ( ~ hBOOL(hAPP(X5880,esk80_3(X5878,X5879,X5880)))
| ~ hBOOL(hAPP(X5880,esk78_3(X5878,X5879,X5880)))
| ~ hBOOL(hAPP(X5880,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5880,X5879,X5878) ) ),
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_1258])])])])])]) ).
fof(i_0_1477,plain,
! [X4979,X4980,X4981,X4982,X4983,X4984] :
( ~ class_Rings_Olinordered__semiring__1__strict(X4984)
| ~ c_Orderings_Oord__class_Oless(X4984,X4983,X4982)
| ~ c_Orderings_Oord__class_Oless(X4984,X4981,X4982)
| ~ c_Orderings_Oord__class_Oless__eq(X4984,c_Groups_Ozero__class_Ozero(X4984),X4980)
| ~ c_Orderings_Oord__class_Oless__eq(X4984,c_Groups_Ozero__class_Ozero(X4984),X4979)
| c_Groups_Oplus__class_Oplus(X4984,X4980,X4979) != c_Groups_Oone__class_Oone(X4984)
| c_Orderings_Oord__class_Oless(X4984,c_Groups_Oplus__class_Oplus(X4984,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4984),X4980),X4983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4984),X4979),X4981)),X4982) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).
fof(i_0_1478,plain,
! [X4923,X4924,X4925,X4926,X4927,X4928] :
( ~ class_Rings_Olinordered__semiring__1(X4928)
| ~ c_Orderings_Oord__class_Oless__eq(X4928,X4927,X4926)
| ~ c_Orderings_Oord__class_Oless__eq(X4928,X4925,X4926)
| ~ c_Orderings_Oord__class_Oless__eq(X4928,c_Groups_Ozero__class_Ozero(X4928),X4924)
| ~ c_Orderings_Oord__class_Oless__eq(X4928,c_Groups_Ozero__class_Ozero(X4928),X4923)
| c_Groups_Oplus__class_Oplus(X4928,X4924,X4923) != c_Groups_Oone__class_Oone(X4928)
| c_Orderings_Oord__class_Oless__eq(X4928,c_Groups_Oplus__class_Oplus(X4928,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4928),X4924),X4927),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4928),X4923),X4925)),X4926) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).
fof(i_0_1479,plain,
! [X5885,X5886,X5887,X5888,X5889,X5890,X5891,X5892,X5893,X5894] :
( ( X5886 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(X5887,X5885))
| ~ epred2_3(X5887,X5886,X5885) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5886)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5889)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5889,X5886)
| X5885 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5886),X5888),X5889)
| hBOOL(hAPP(X5887,X5889))
| ~ epred2_3(X5887,X5886,X5885) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5886,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5886,X5891)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5891,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5885 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5886),X5890),X5891)
| hBOOL(hAPP(X5887,X5891))
| ~ epred2_3(X5887,X5886,X5885) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5893)
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,esk85_3(X5892,X5893,X5894))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5893)
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X5892,X5893,X5894),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5893)
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk84_3(X5892,X5893,X5894)),esk85_3(X5892,X5893,X5894))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5893)
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( ~ hBOOL(hAPP(X5894,esk85_3(X5892,X5893,X5894)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5893)
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,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),esk83_3(X5892,X5893,X5894))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,esk85_3(X5892,X5893,X5894))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk83_3(X5892,X5893,X5894))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X5892,X5893,X5894),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),esk83_3(X5892,X5893,X5894))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk84_3(X5892,X5893,X5894)),esk85_3(X5892,X5893,X5894))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk83_3(X5892,X5893,X5894))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( ~ hBOOL(hAPP(X5894,esk85_3(X5892,X5893,X5894)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk83_3(X5892,X5893,X5894))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X5892,X5893,X5894),X5893)
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,esk85_3(X5892,X5893,X5894))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X5892,X5893,X5894),X5893)
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X5892,X5893,X5894),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X5892,X5893,X5894),X5893)
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk84_3(X5892,X5893,X5894)),esk85_3(X5892,X5893,X5894))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X5892,X5893,X5894),X5893)
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( ~ hBOOL(hAPP(X5894,esk85_3(X5892,X5893,X5894)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X5892,X5893,X5894),X5893)
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk82_3(X5892,X5893,X5894)),esk83_3(X5892,X5893,X5894))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,esk85_3(X5892,X5893,X5894))
| X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk82_3(X5892,X5893,X5894)),esk83_3(X5892,X5893,X5894))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X5892,X5893,X5894),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk82_3(X5892,X5893,X5894)),esk83_3(X5892,X5893,X5894))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk84_3(X5892,X5893,X5894)),esk85_3(X5892,X5893,X5894))
| X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk82_3(X5892,X5893,X5894)),esk83_3(X5892,X5893,X5894))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( ~ hBOOL(hAPP(X5894,esk85_3(X5892,X5893,X5894)))
| X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk82_3(X5892,X5893,X5894)),esk83_3(X5892,X5893,X5894))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5894,esk83_3(X5892,X5893,X5894)))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,esk85_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,esk83_3(X5892,X5893,X5894)))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X5892,X5893,X5894),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5894,esk83_3(X5892,X5893,X5894)))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk84_3(X5892,X5893,X5894)),esk85_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,esk83_3(X5892,X5893,X5894)))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( ~ hBOOL(hAPP(X5894,esk85_3(X5892,X5893,X5894)))
| ~ hBOOL(hAPP(X5894,esk83_3(X5892,X5893,X5894)))
| X5893 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5893)
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,esk85_3(X5892,X5893,X5894))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5893)
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X5892,X5893,X5894),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5893)
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk84_3(X5892,X5893,X5894)),esk85_3(X5892,X5893,X5894))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5893)
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( ~ hBOOL(hAPP(X5894,esk85_3(X5892,X5893,X5894)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5893)
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,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),esk83_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,esk85_3(X5892,X5893,X5894))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk83_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X5892,X5893,X5894),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),esk83_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk84_3(X5892,X5893,X5894)),esk85_3(X5892,X5893,X5894))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk83_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( ~ hBOOL(hAPP(X5894,esk85_3(X5892,X5893,X5894)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk83_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X5892,X5893,X5894),X5893)
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,esk85_3(X5892,X5893,X5894))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X5892,X5893,X5894),X5893)
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X5892,X5893,X5894),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X5892,X5893,X5894),X5893)
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk84_3(X5892,X5893,X5894)),esk85_3(X5892,X5893,X5894))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X5892,X5893,X5894),X5893)
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( ~ hBOOL(hAPP(X5894,esk85_3(X5892,X5893,X5894)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X5892,X5893,X5894),X5893)
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk82_3(X5892,X5893,X5894)),esk83_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,esk85_3(X5892,X5893,X5894))
| X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk82_3(X5892,X5893,X5894)),esk83_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X5892,X5893,X5894),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk82_3(X5892,X5893,X5894)),esk83_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk84_3(X5892,X5893,X5894)),esk85_3(X5892,X5893,X5894))
| X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk82_3(X5892,X5893,X5894)),esk83_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( ~ hBOOL(hAPP(X5894,esk85_3(X5892,X5893,X5894)))
| X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk82_3(X5892,X5893,X5894)),esk83_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5894,esk83_3(X5892,X5893,X5894)))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5893,esk85_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,esk83_3(X5892,X5893,X5894)))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X5892,X5893,X5894),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5894,esk83_3(X5892,X5893,X5894)))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( X5892 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5893),esk84_3(X5892,X5893,X5894)),esk85_3(X5892,X5893,X5894))
| ~ hBOOL(hAPP(X5894,esk83_3(X5892,X5893,X5894)))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) )
& ( ~ hBOOL(hAPP(X5894,esk85_3(X5892,X5893,X5894)))
| ~ hBOOL(hAPP(X5894,esk83_3(X5892,X5893,X5894)))
| ~ hBOOL(hAPP(X5894,X5892))
| epred2_3(X5894,X5893,X5892) ) ),
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_1257])])])])])]) ).
fof(i_0_1480,plain,
! [X5400,X5401,X5402,X5403] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5403)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5402,X5401)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5401,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| 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),X5402),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5400,X5403)),X5401),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux2])]) ).
fof(i_0_1481,plain,
! [X5388,X5389,X5390,X5391] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5391)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5390)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5390,X5389)
| 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),X5389),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5388,X5391)),X5390)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux3])]) ).
fof(i_0_1482,plain,
! [X4508,X4509,X4510,X4511] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4511)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4510,X4509)
| 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),X4509),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4508,X4511)),X4510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4509),X4511)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__lemma])]) ).
fof(i_0_1483,plain,
! [X4147,X4148,X4149] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4149,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4148),X4147)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4148),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4149,X4148),X4147)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4149,X4148)),
inference(variable_rename,[status(thm)],[fact_mod__mult2__eq]) ).
fof(i_0_1484,plain,
! [X5440,X5441,X5442] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5442),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5441,X5442)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5441,X5442)),X5440) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5441,X5440),
inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality]) ).
fof(i_0_1485,plain,
! [X4118,X4119,X4120] :
( ~ class_RealVector_Oreal__normed__vector(X4120)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4119)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4120,hAPP(X4118,esk50_3(X4118,X4119,X4120))),X4119)
| c_SEQ_OBseq(X4120,X4118) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_BseqI])])]) ).
fof(i_0_1486,plain,
! [X4055,X4056,X4058,X4059] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk40_2(X4055,X4056))
| ~ c_SEQ_OBseq(X4056,X4055)
| ~ class_RealVector_Oreal__normed__vector(X4056) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4056,hAPP(X4055,X4058)),esk40_2(X4055,X4056))
| ~ c_SEQ_OBseq(X4056,X4055)
| ~ class_RealVector_Oreal__normed__vector(X4056) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4059)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4056,hAPP(X4055,esk41_3(X4055,X4056,X4059))),X4059)
| c_SEQ_OBseq(X4056,X4055)
| ~ class_RealVector_Oreal__normed__vector(X4056) ) ),
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_1487,plain,
! [X5063,X5064,X5065,X5066] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5066),X5065),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5064),X5065),X5063)) = 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,X5066,X5064)),X5065),X5063),
inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(i_0_1488,plain,
! [X5107,X5108,X5109] :
( ( c_Orderings_Oord__class_Oless(X5109,c_Groups_Ozero__class_Ozero(X5109),esk67_3(X5107,X5108,X5109))
| c_Orderings_Oord__class_Oless__eq(X5109,X5108,X5107)
| ~ class_Fields_Olinordered__field__inverse__zero(X5109) )
& ( c_Orderings_Oord__class_Oless(X5109,esk67_3(X5107,X5108,X5109),c_Groups_Oone__class_Oone(X5109))
| c_Orderings_Oord__class_Oless__eq(X5109,X5108,X5107)
| ~ class_Fields_Olinordered__field__inverse__zero(X5109) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5109,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5109),esk67_3(X5107,X5108,X5109)),X5108),X5107)
| c_Orderings_Oord__class_Oless__eq(X5109,X5108,X5107)
| ~ class_Fields_Olinordered__field__inverse__zero(X5109) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__le__mult__one__interval])])])]) ).
fof(i_0_1489,plain,
! [X4414,X4415,X4416,X4417] :
( ~ class_Divides_Osemiring__div(X4417)
| c_Divides_Odiv__class_Omod(X4417,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4417),X4416),X4415),X4414) = c_Divides_Odiv__class_Omod(X4417,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4417),c_Divides_Odiv__class_Omod(X4417,X4416,X4414)),c_Divides_Odiv__class_Omod(X4417,X4415,X4414)),X4414) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__eq])]) ).
fof(i_0_1490,plain,
! [X4874,X4875,X4876,X4877,X4878] :
( ~ class_Fields_Ofield(X4878)
| X4877 = c_Groups_Ozero__class_Ozero(X4878)
| X4876 = c_Groups_Ozero__class_Ozero(X4878)
| c_Groups_Oplus__class_Oplus(X4878,c_Rings_Oinverse__class_Odivide(X4878,X4875,X4877),c_Rings_Oinverse__class_Odivide(X4878,X4874,X4876)) = c_Rings_Oinverse__class_Odivide(X4878,c_Groups_Oplus__class_Oplus(X4878,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4878),X4875),X4876),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4878),X4874),X4877)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4878),X4877),X4876)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__eq])]) ).
cnf(i_0_1491,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_1281]) ).
fof(i_0_1492,plain,
! [X4822,X4823,X4824] :
( ( ~ c_Orderings_Oord__class_Oless(X4824,c_Groups_Ozero__class_Ozero(X4824),c_Groups_Oplus__class_Oplus(X4824,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4824),X4823),X4823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4824),X4822),X4822)))
| X4823 != c_Groups_Ozero__class_Ozero(X4824)
| X4822 != c_Groups_Ozero__class_Ozero(X4824)
| ~ class_Rings_Olinordered__ring__strict(X4824) )
& ( X4823 = c_Groups_Ozero__class_Ozero(X4824)
| c_Orderings_Oord__class_Oless(X4824,c_Groups_Ozero__class_Ozero(X4824),c_Groups_Oplus__class_Oplus(X4824,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4824),X4823),X4823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4824),X4822),X4822)))
| ~ class_Rings_Olinordered__ring__strict(X4824) )
& ( X4822 = c_Groups_Ozero__class_Ozero(X4824)
| c_Orderings_Oord__class_Oless(X4824,c_Groups_Ozero__class_Ozero(X4824),c_Groups_Oplus__class_Oplus(X4824,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4824),X4823),X4823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4824),X4822),X4822)))
| ~ class_Rings_Olinordered__ring__strict(X4824) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).
fof(i_0_1493,plain,
! [X4180,X4181,X4182,X4183,X4184] :
( ~ class_Rings_Ocomm__semiring__1(X4184)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4184),X4183),X4182)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4184),X4181),X4180)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4184),X4181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4184),X4183),X4182)),X4180)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).
fof(i_0_1494,plain,
! [X4816,X4817,X4818] :
( ( X4817 = c_Groups_Ozero__class_Ozero(X4818)
| ~ c_Orderings_Oord__class_Oless__eq(X4818,c_Groups_Oplus__class_Oplus(X4818,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4818),X4817),X4817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4818),X4816),X4816)),c_Groups_Ozero__class_Ozero(X4818))
| ~ class_Rings_Olinordered__ring__strict(X4818) )
& ( X4816 = c_Groups_Ozero__class_Ozero(X4818)
| ~ c_Orderings_Oord__class_Oless__eq(X4818,c_Groups_Oplus__class_Oplus(X4818,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4818),X4817),X4817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4818),X4816),X4816)),c_Groups_Ozero__class_Ozero(X4818))
| ~ class_Rings_Olinordered__ring__strict(X4818) )
& ( X4817 != c_Groups_Ozero__class_Ozero(X4818)
| X4816 != c_Groups_Ozero__class_Ozero(X4818)
| c_Orderings_Oord__class_Oless__eq(X4818,c_Groups_Oplus__class_Oplus(X4818,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4818),X4817),X4817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4818),X4816),X4816)),c_Groups_Ozero__class_Ozero(X4818))
| ~ class_Rings_Olinordered__ring__strict(X4818) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).
fof(i_0_1495,plain,
! [X4825,X4826,X4827] :
( ~ class_Rings_Olinordered__ring(X4827)
| ~ c_Orderings_Oord__class_Oless(X4827,c_Groups_Oplus__class_Oplus(X4827,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4827),X4826),X4826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4827),X4825),X4825)),c_Groups_Ozero__class_Ozero(X4827)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1282])]) ).
cnf(i_0_1496,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_1283]) ).
cnf(i_0_1497,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1284]) ).
cnf(i_0_1498,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_1285]) ).
fof(i_0_1499,plain,
! [X4217,X4218,X4219,X4220,X4221] :
( ( X4220 = X4219
| X4218 = X4217
| c_Groups_Oplus__class_Oplus(X4221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4219),X4217)) != c_Groups_Oplus__class_Oplus(X4221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4219),X4218))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4221) )
& ( X4220 != X4219
| c_Groups_Oplus__class_Oplus(X4221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4219),X4217)) = c_Groups_Oplus__class_Oplus(X4221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4219),X4218))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4221) )
& ( X4218 != X4217
| c_Groups_Oplus__class_Oplus(X4221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4219),X4217)) = c_Groups_Oplus__class_Oplus(X4221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4219),X4218))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4221) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).
fof(i_0_1500,plain,
! [X4230,X4231,X4232,X4233,X4234] :
( ( c_Groups_Oplus__class_Oplus(X4234,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4234),X4233),X4232),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4234),X4231),X4230)) != c_Groups_Oplus__class_Oplus(X4234,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4234),X4233),X4230),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4234),X4231),X4232))
| X4233 = X4231
| X4232 = X4230
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4234) )
& ( X4233 != X4231
| c_Groups_Oplus__class_Oplus(X4234,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4234),X4233),X4232),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4234),X4231),X4230)) = c_Groups_Oplus__class_Oplus(X4234,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4234),X4233),X4230),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4234),X4231),X4232))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4234) )
& ( X4232 != X4230
| c_Groups_Oplus__class_Oplus(X4234,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4234),X4233),X4232),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4234),X4231),X4230)) = c_Groups_Oplus__class_Oplus(X4234,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4234),X4233),X4230),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4234),X4231),X4232))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4234) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).
cnf(i_0_1501,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1278]) ).
cnf(i_0_1502,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_1286]) ).
cnf(i_0_1503,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_1287]) ).
fof(i_0_1504,plain,
! [X5269,X5270,X5271] :
( ~ class_Rings_Oring__1(X5271)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5271),c_Groups_Ouminus__class_Ouminus(X5271,X5270)),X5269) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5271),hAPP(hAPP(c_Power_Opower__class_Opower(X5271),c_Groups_Ouminus__class_Ouminus(X5271,c_Groups_Oone__class_Oone(X5271))),X5269)),hAPP(hAPP(c_Power_Opower__class_Opower(X5271),X5270),X5269)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).
fof(i_0_1505,plain,
! [X5373,X5374,X5375] :
( ~ 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),X5375),X5374),X5373),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),X5373)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5375)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5374,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_1506,plain,
! [X5376,X5377,X5378] :
( ~ 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),X5378),X5377),X5376))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5376,X5378)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5378)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5377) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).
fof(i_0_1507,plain,
! [X4969,X4970,X4971,X4972,X4973,X4974,X4975,X4976] :
( ( X4969 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X4971,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X4971,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4970,X4969))) )
& ( X4969 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4973,X4969)
| X4970 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4969),X4972),X4973)
| hBOOL(hAPP(X4971,X4972))
| ~ hBOOL(hAPP(X4971,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4970,X4969))) )
& ( X4974 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4974 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X4976,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4975,X4974))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk58_3(X4974,X4975,X4976),X4974)
| X4974 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X4976,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4975,X4974))) )
& ( X4975 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4974),esk57_3(X4974,X4975,X4976)),esk58_3(X4974,X4975,X4976))
| X4974 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X4976,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4975,X4974))) )
& ( ~ hBOOL(hAPP(X4976,esk57_3(X4974,X4975,X4976)))
| X4974 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X4976,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4975,X4974))) )
& ( X4974 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X4976,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4976,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4975,X4974))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk58_3(X4974,X4975,X4976),X4974)
| ~ hBOOL(hAPP(X4976,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4976,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4975,X4974))) )
& ( X4975 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4974),esk57_3(X4974,X4975,X4976)),esk58_3(X4974,X4975,X4976))
| ~ hBOOL(hAPP(X4976,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4976,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4975,X4974))) )
& ( ~ hBOOL(hAPP(X4976,esk57_3(X4974,X4975,X4976)))
| ~ hBOOL(hAPP(X4976,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4976,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4975,X4974))) ) ),
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_1508,plain,
! [X4866,X4867,X4868,X4869] :
( ( ~ c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4867)
| c_Orderings_Oord__class_Oless(X4869,X4868,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4869),X4866),X4867))
| ~ c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) )
& ( ~ c_Orderings_Oord__class_Oless(X4869,X4867,c_Groups_Ozero__class_Ozero(X4869))
| c_Orderings_Oord__class_Oless(X4869,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4869),X4866),X4867),X4868)
| c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4867)
| ~ c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) )
& ( c_Orderings_Oord__class_Oless(X4869,X4867,c_Groups_Ozero__class_Ozero(X4869))
| c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4866)
| c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4867)
| ~ c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) )
& ( ~ c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4867)
| c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4867)
| c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) )
& ( ~ c_Orderings_Oord__class_Oless(X4869,X4867,c_Groups_Ozero__class_Ozero(X4869))
| c_Orderings_Oord__class_Oless(X4869,X4867,c_Groups_Ozero__class_Ozero(X4869))
| c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4867)
| c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) )
& ( ~ c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4866)
| c_Orderings_Oord__class_Oless(X4869,X4867,c_Groups_Ozero__class_Ozero(X4869))
| c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4867)
| c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) )
& ( ~ c_Orderings_Oord__class_Oless(X4869,X4867,c_Groups_Ozero__class_Ozero(X4869))
| ~ c_Orderings_Oord__class_Oless(X4869,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4869),X4866),X4867),X4868)
| c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4867)
| c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) )
& ( ~ c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4866)
| ~ c_Orderings_Oord__class_Oless(X4869,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4869),X4866),X4867),X4868)
| c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4867)
| c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) )
& ( ~ c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4867)
| ~ c_Orderings_Oord__class_Oless(X4869,X4868,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4869),X4866),X4867))
| c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) )
& ( ~ c_Orderings_Oord__class_Oless(X4869,X4867,c_Groups_Ozero__class_Ozero(X4869))
| c_Orderings_Oord__class_Oless(X4869,X4867,c_Groups_Ozero__class_Ozero(X4869))
| ~ c_Orderings_Oord__class_Oless(X4869,X4868,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4869),X4866),X4867))
| c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) )
& ( ~ c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4866)
| c_Orderings_Oord__class_Oless(X4869,X4867,c_Groups_Ozero__class_Ozero(X4869))
| ~ c_Orderings_Oord__class_Oless(X4869,X4868,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4869),X4866),X4867))
| c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) )
& ( ~ c_Orderings_Oord__class_Oless(X4869,X4867,c_Groups_Ozero__class_Ozero(X4869))
| ~ c_Orderings_Oord__class_Oless(X4869,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4869),X4866),X4867),X4868)
| ~ c_Orderings_Oord__class_Oless(X4869,X4868,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4869),X4866),X4867))
| c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) )
& ( ~ c_Orderings_Oord__class_Oless(X4869,c_Groups_Ozero__class_Ozero(X4869),X4866)
| ~ c_Orderings_Oord__class_Oless(X4869,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4869),X4866),X4867),X4868)
| ~ c_Orderings_Oord__class_Oless(X4869,X4868,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4869),X4866),X4867))
| c_Orderings_Oord__class_Oless(X4869,c_Rings_Oinverse__class_Odivide(X4869,X4868,X4867),X4866)
| ~ class_Fields_Olinordered__field__inverse__zero(X4869) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1288])])]) ).
fof(i_0_1509,plain,
! [X4961,X4962,X4963,X4964] :
( ( ~ c_Orderings_Oord__class_Oless(X4964,c_Groups_Ozero__class_Ozero(X4964),X4962)
| c_Orderings_Oord__class_Oless__eq(X4964,X4963,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4964),X4961),X4962))
| ~ c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) )
& ( ~ c_Orderings_Oord__class_Oless(X4964,X4962,c_Groups_Ozero__class_Ozero(X4964))
| c_Orderings_Oord__class_Oless__eq(X4964,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4964),X4961),X4962),X4963)
| c_Orderings_Oord__class_Oless(X4964,c_Groups_Ozero__class_Ozero(X4964),X4962)
| ~ c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) )
& ( c_Orderings_Oord__class_Oless(X4964,X4962,c_Groups_Ozero__class_Ozero(X4964))
| c_Orderings_Oord__class_Oless__eq(X4964,c_Groups_Ozero__class_Ozero(X4964),X4961)
| c_Orderings_Oord__class_Oless(X4964,c_Groups_Ozero__class_Ozero(X4964),X4962)
| ~ c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) )
& ( ~ c_Orderings_Oord__class_Oless(X4964,c_Groups_Ozero__class_Ozero(X4964),X4962)
| c_Orderings_Oord__class_Oless(X4964,c_Groups_Ozero__class_Ozero(X4964),X4962)
| c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) )
& ( ~ c_Orderings_Oord__class_Oless(X4964,X4962,c_Groups_Ozero__class_Ozero(X4964))
| c_Orderings_Oord__class_Oless(X4964,X4962,c_Groups_Ozero__class_Ozero(X4964))
| c_Orderings_Oord__class_Oless(X4964,c_Groups_Ozero__class_Ozero(X4964),X4962)
| c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4964,c_Groups_Ozero__class_Ozero(X4964),X4961)
| c_Orderings_Oord__class_Oless(X4964,X4962,c_Groups_Ozero__class_Ozero(X4964))
| c_Orderings_Oord__class_Oless(X4964,c_Groups_Ozero__class_Ozero(X4964),X4962)
| c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) )
& ( ~ c_Orderings_Oord__class_Oless(X4964,X4962,c_Groups_Ozero__class_Ozero(X4964))
| ~ c_Orderings_Oord__class_Oless__eq(X4964,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4964),X4961),X4962),X4963)
| c_Orderings_Oord__class_Oless(X4964,c_Groups_Ozero__class_Ozero(X4964),X4962)
| c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4964,c_Groups_Ozero__class_Ozero(X4964),X4961)
| ~ c_Orderings_Oord__class_Oless__eq(X4964,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4964),X4961),X4962),X4963)
| c_Orderings_Oord__class_Oless(X4964,c_Groups_Ozero__class_Ozero(X4964),X4962)
| c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) )
& ( ~ c_Orderings_Oord__class_Oless(X4964,c_Groups_Ozero__class_Ozero(X4964),X4962)
| ~ c_Orderings_Oord__class_Oless__eq(X4964,X4963,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4964),X4961),X4962))
| c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) )
& ( ~ c_Orderings_Oord__class_Oless(X4964,X4962,c_Groups_Ozero__class_Ozero(X4964))
| c_Orderings_Oord__class_Oless(X4964,X4962,c_Groups_Ozero__class_Ozero(X4964))
| ~ c_Orderings_Oord__class_Oless__eq(X4964,X4963,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4964),X4961),X4962))
| c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4964,c_Groups_Ozero__class_Ozero(X4964),X4961)
| c_Orderings_Oord__class_Oless(X4964,X4962,c_Groups_Ozero__class_Ozero(X4964))
| ~ c_Orderings_Oord__class_Oless__eq(X4964,X4963,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4964),X4961),X4962))
| c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) )
& ( ~ c_Orderings_Oord__class_Oless(X4964,X4962,c_Groups_Ozero__class_Ozero(X4964))
| ~ c_Orderings_Oord__class_Oless__eq(X4964,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4964),X4961),X4962),X4963)
| ~ c_Orderings_Oord__class_Oless__eq(X4964,X4963,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4964),X4961),X4962))
| c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4964,c_Groups_Ozero__class_Ozero(X4964),X4961)
| ~ c_Orderings_Oord__class_Oless__eq(X4964,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4964),X4961),X4962),X4963)
| ~ c_Orderings_Oord__class_Oless__eq(X4964,X4963,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4964),X4961),X4962))
| c_Orderings_Oord__class_Oless__eq(X4964,c_Rings_Oinverse__class_Odivide(X4964,X4963,X4962),X4961)
| ~ class_Fields_Olinordered__field__inverse__zero(X4964) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1289])])]) ).
fof(i_0_1510,plain,
! [X4870,X4871,X4872,X4873] :
( ( ~ c_Orderings_Oord__class_Oless(X4873,c_Groups_Ozero__class_Ozero(X4873),X4870)
| c_Orderings_Oord__class_Oless(X4873,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4873),X4872),X4870),X4871)
| ~ c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) )
& ( ~ c_Orderings_Oord__class_Oless(X4873,X4870,c_Groups_Ozero__class_Ozero(X4873))
| c_Orderings_Oord__class_Oless(X4873,X4871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4873),X4872),X4870))
| c_Orderings_Oord__class_Oless(X4873,c_Groups_Ozero__class_Ozero(X4873),X4870)
| ~ c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) )
& ( c_Orderings_Oord__class_Oless(X4873,X4870,c_Groups_Ozero__class_Ozero(X4873))
| c_Orderings_Oord__class_Oless(X4873,X4872,c_Groups_Ozero__class_Ozero(X4873))
| c_Orderings_Oord__class_Oless(X4873,c_Groups_Ozero__class_Ozero(X4873),X4870)
| ~ c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) )
& ( ~ c_Orderings_Oord__class_Oless(X4873,c_Groups_Ozero__class_Ozero(X4873),X4870)
| c_Orderings_Oord__class_Oless(X4873,c_Groups_Ozero__class_Ozero(X4873),X4870)
| c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) )
& ( ~ c_Orderings_Oord__class_Oless(X4873,X4870,c_Groups_Ozero__class_Ozero(X4873))
| c_Orderings_Oord__class_Oless(X4873,X4870,c_Groups_Ozero__class_Ozero(X4873))
| c_Orderings_Oord__class_Oless(X4873,c_Groups_Ozero__class_Ozero(X4873),X4870)
| c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) )
& ( ~ c_Orderings_Oord__class_Oless(X4873,X4872,c_Groups_Ozero__class_Ozero(X4873))
| c_Orderings_Oord__class_Oless(X4873,X4870,c_Groups_Ozero__class_Ozero(X4873))
| c_Orderings_Oord__class_Oless(X4873,c_Groups_Ozero__class_Ozero(X4873),X4870)
| c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) )
& ( ~ c_Orderings_Oord__class_Oless(X4873,X4870,c_Groups_Ozero__class_Ozero(X4873))
| ~ c_Orderings_Oord__class_Oless(X4873,X4871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4873),X4872),X4870))
| c_Orderings_Oord__class_Oless(X4873,c_Groups_Ozero__class_Ozero(X4873),X4870)
| c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) )
& ( ~ c_Orderings_Oord__class_Oless(X4873,X4872,c_Groups_Ozero__class_Ozero(X4873))
| ~ c_Orderings_Oord__class_Oless(X4873,X4871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4873),X4872),X4870))
| c_Orderings_Oord__class_Oless(X4873,c_Groups_Ozero__class_Ozero(X4873),X4870)
| c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) )
& ( ~ c_Orderings_Oord__class_Oless(X4873,c_Groups_Ozero__class_Ozero(X4873),X4870)
| ~ c_Orderings_Oord__class_Oless(X4873,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4873),X4872),X4870),X4871)
| c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) )
& ( ~ c_Orderings_Oord__class_Oless(X4873,X4870,c_Groups_Ozero__class_Ozero(X4873))
| c_Orderings_Oord__class_Oless(X4873,X4870,c_Groups_Ozero__class_Ozero(X4873))
| ~ c_Orderings_Oord__class_Oless(X4873,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4873),X4872),X4870),X4871)
| c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) )
& ( ~ c_Orderings_Oord__class_Oless(X4873,X4872,c_Groups_Ozero__class_Ozero(X4873))
| c_Orderings_Oord__class_Oless(X4873,X4870,c_Groups_Ozero__class_Ozero(X4873))
| ~ c_Orderings_Oord__class_Oless(X4873,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4873),X4872),X4870),X4871)
| c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) )
& ( ~ c_Orderings_Oord__class_Oless(X4873,X4870,c_Groups_Ozero__class_Ozero(X4873))
| ~ c_Orderings_Oord__class_Oless(X4873,X4871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4873),X4872),X4870))
| ~ c_Orderings_Oord__class_Oless(X4873,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4873),X4872),X4870),X4871)
| c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) )
& ( ~ c_Orderings_Oord__class_Oless(X4873,X4872,c_Groups_Ozero__class_Ozero(X4873))
| ~ c_Orderings_Oord__class_Oless(X4873,X4871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4873),X4872),X4870))
| ~ c_Orderings_Oord__class_Oless(X4873,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4873),X4872),X4870),X4871)
| c_Orderings_Oord__class_Oless(X4873,X4872,c_Rings_Oinverse__class_Odivide(X4873,X4871,X4870))
| ~ class_Fields_Olinordered__field__inverse__zero(X4873) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1290])])]) ).
fof(i_0_1511,plain,
! [X4965,X4966,X4967,X4968] :
( ( ~ c_Orderings_Oord__class_Oless(X4968,c_Groups_Ozero__class_Ozero(X4968),X4965)
| c_Orderings_Oord__class_Oless__eq(X4968,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4968),X4967),X4965),X4966)
| ~ c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) )
& ( ~ c_Orderings_Oord__class_Oless(X4968,X4965,c_Groups_Ozero__class_Ozero(X4968))
| c_Orderings_Oord__class_Oless__eq(X4968,X4966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4968),X4967),X4965))
| c_Orderings_Oord__class_Oless(X4968,c_Groups_Ozero__class_Ozero(X4968),X4965)
| ~ c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) )
& ( c_Orderings_Oord__class_Oless(X4968,X4965,c_Groups_Ozero__class_Ozero(X4968))
| c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Groups_Ozero__class_Ozero(X4968))
| c_Orderings_Oord__class_Oless(X4968,c_Groups_Ozero__class_Ozero(X4968),X4965)
| ~ c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) )
& ( ~ c_Orderings_Oord__class_Oless(X4968,c_Groups_Ozero__class_Ozero(X4968),X4965)
| c_Orderings_Oord__class_Oless(X4968,c_Groups_Ozero__class_Ozero(X4968),X4965)
| c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) )
& ( ~ c_Orderings_Oord__class_Oless(X4968,X4965,c_Groups_Ozero__class_Ozero(X4968))
| c_Orderings_Oord__class_Oless(X4968,X4965,c_Groups_Ozero__class_Ozero(X4968))
| c_Orderings_Oord__class_Oless(X4968,c_Groups_Ozero__class_Ozero(X4968),X4965)
| c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Groups_Ozero__class_Ozero(X4968))
| c_Orderings_Oord__class_Oless(X4968,X4965,c_Groups_Ozero__class_Ozero(X4968))
| c_Orderings_Oord__class_Oless(X4968,c_Groups_Ozero__class_Ozero(X4968),X4965)
| c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) )
& ( ~ c_Orderings_Oord__class_Oless(X4968,X4965,c_Groups_Ozero__class_Ozero(X4968))
| ~ c_Orderings_Oord__class_Oless__eq(X4968,X4966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4968),X4967),X4965))
| c_Orderings_Oord__class_Oless(X4968,c_Groups_Ozero__class_Ozero(X4968),X4965)
| c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Groups_Ozero__class_Ozero(X4968))
| ~ c_Orderings_Oord__class_Oless__eq(X4968,X4966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4968),X4967),X4965))
| c_Orderings_Oord__class_Oless(X4968,c_Groups_Ozero__class_Ozero(X4968),X4965)
| c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) )
& ( ~ c_Orderings_Oord__class_Oless(X4968,c_Groups_Ozero__class_Ozero(X4968),X4965)
| ~ c_Orderings_Oord__class_Oless__eq(X4968,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4968),X4967),X4965),X4966)
| c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) )
& ( ~ c_Orderings_Oord__class_Oless(X4968,X4965,c_Groups_Ozero__class_Ozero(X4968))
| c_Orderings_Oord__class_Oless(X4968,X4965,c_Groups_Ozero__class_Ozero(X4968))
| ~ c_Orderings_Oord__class_Oless__eq(X4968,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4968),X4967),X4965),X4966)
| c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Groups_Ozero__class_Ozero(X4968))
| c_Orderings_Oord__class_Oless(X4968,X4965,c_Groups_Ozero__class_Ozero(X4968))
| ~ c_Orderings_Oord__class_Oless__eq(X4968,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4968),X4967),X4965),X4966)
| c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) )
& ( ~ c_Orderings_Oord__class_Oless(X4968,X4965,c_Groups_Ozero__class_Ozero(X4968))
| ~ c_Orderings_Oord__class_Oless__eq(X4968,X4966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4968),X4967),X4965))
| ~ c_Orderings_Oord__class_Oless__eq(X4968,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4968),X4967),X4965),X4966)
| c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Groups_Ozero__class_Ozero(X4968))
| ~ c_Orderings_Oord__class_Oless__eq(X4968,X4966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4968),X4967),X4965))
| ~ c_Orderings_Oord__class_Oless__eq(X4968,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4968),X4967),X4965),X4966)
| c_Orderings_Oord__class_Oless__eq(X4968,X4967,c_Rings_Oinverse__class_Odivide(X4968,X4966,X4965))
| ~ class_Fields_Olinordered__field__inverse__zero(X4968) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1291])])]) ).
fof(i_0_1512,plain,
! [X5649,X5650,X5651,X5652] :
( ~ class_Divides_Oring__div(X5652)
| c_Divides_Odiv__class_Omod(X5652,c_Groups_Ominus__class_Ominus(X5652,X5651,X5650),X5649) = c_Divides_Odiv__class_Omod(X5652,c_Groups_Ominus__class_Ominus(X5652,c_Divides_Odiv__class_Omod(X5652,X5651,X5649),c_Divides_Odiv__class_Omod(X5652,X5650,X5649)),X5649) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__eq])]) ).
fof(i_0_1513,plain,
! [X4460,X4461,X4462,X4463] :
( ~ class_Divides_Osemiring__div(X4463)
| c_Divides_Odiv__class_Omod(X4463,c_Groups_Oplus__class_Oplus(X4463,X4462,X4461),X4460) = c_Divides_Odiv__class_Omod(X4463,c_Groups_Oplus__class_Oplus(X4463,c_Divides_Odiv__class_Omod(X4463,X4462,X4460),c_Divides_Odiv__class_Omod(X4463,X4461,X4460)),X4460) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__eq])]) ).
fof(i_0_1514,plain,
! [X4512,X4513,X4514,X4515,X4516,X4517,X4518,X4519] :
( ( X4512 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X4514,X4513))
| ~ hBOOL(hAPP(X4514,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4513,X4512))) )
& ( X4512 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4516,X4512)
| X4513 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4512),X4515),X4516)
| hBOOL(hAPP(X4514,X4516))
| ~ hBOOL(hAPP(X4514,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4513,X4512))) )
& ( X4517 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4517 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X4519,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4518,X4517))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk56_3(X4517,X4518,X4519),X4517)
| X4517 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X4519,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4518,X4517))) )
& ( X4518 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4517),esk55_3(X4517,X4518,X4519)),esk56_3(X4517,X4518,X4519))
| X4517 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X4519,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4518,X4517))) )
& ( ~ hBOOL(hAPP(X4519,esk56_3(X4517,X4518,X4519)))
| X4517 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X4519,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4518,X4517))) )
& ( X4517 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X4519,X4518))
| hBOOL(hAPP(X4519,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4518,X4517))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk56_3(X4517,X4518,X4519),X4517)
| ~ hBOOL(hAPP(X4519,X4518))
| hBOOL(hAPP(X4519,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4518,X4517))) )
& ( X4518 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4517),esk55_3(X4517,X4518,X4519)),esk56_3(X4517,X4518,X4519))
| ~ hBOOL(hAPP(X4519,X4518))
| hBOOL(hAPP(X4519,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4518,X4517))) )
& ( ~ hBOOL(hAPP(X4519,esk56_3(X4517,X4518,X4519)))
| ~ hBOOL(hAPP(X4519,X4518))
| hBOOL(hAPP(X4519,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4518,X4517))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mod])])])])])]) ).
fof(i_0_1515,plain,
! [X4402,X4403,X4404,X4405] :
( ~ class_Divides_Osemiring__div(X4405)
| c_Divides_Odiv__class_Omod(X4405,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4405),c_Divides_Odiv__class_Omod(X4405,X4404,X4403)),X4402),X4403) = c_Divides_Odiv__class_Omod(X4405,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4405),X4404),X4402),X4403) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J])]) ).
fof(i_0_1516,plain,
! [X4418,X4419,X4420,X4421] :
( ~ class_Divides_Osemiring__div(X4421)
| c_Divides_Odiv__class_Omod(X4421,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4421),X4420),X4419),X4418) = c_Divides_Odiv__class_Omod(X4421,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4421),c_Divides_Odiv__class_Omod(X4421,X4420,X4418)),X4419),X4418) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq])]) ).
fof(i_0_1517,plain,
! [X2995,X2996,X2997] :
( ~ class_Fields_Olinordered__field(X2997)
| ~ c_Orderings_Oord__class_Oless(X2997,X2996,X2995)
| c_Orderings_Oord__class_Oless(X2997,c_Rings_Oinverse__class_Odivide(X2997,c_Groups_Oplus__class_Oplus(X2997,X2996,X2995),c_Groups_Oplus__class_Oplus(X2997,c_Groups_Oone__class_Oone(X2997),c_Groups_Oone__class_Oone(X2997))),X2995) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])]) ).
fof(i_0_1518,plain,
! [X2992,X2993,X2994] :
( ~ class_Fields_Olinordered__field(X2994)
| ~ c_Orderings_Oord__class_Oless(X2994,X2993,X2992)
| c_Orderings_Oord__class_Oless(X2994,X2993,c_Rings_Oinverse__class_Odivide(X2994,c_Groups_Oplus__class_Oplus(X2994,X2993,X2992),c_Groups_Oplus__class_Oplus(X2994,c_Groups_Oone__class_Oone(X2994),c_Groups_Oone__class_Oone(X2994)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__half__sum])]) ).
fof(i_0_1519,plain,
! [X4175,X4176,X4177,X4178,X4179] :
( ~ class_Rings_Ocomm__semiring__1(X4179)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4178),X4177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4176),X4175)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4178),X4176)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4177),X4175)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).
fof(i_0_1520,plain,
! [X4185,X4186,X4187,X4188,X4189] :
( ~ class_Rings_Ocomm__semiring__1(X4189)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4189),X4188),X4187)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4189),X4186),X4185)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4189),X4188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4189),X4187),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4189),X4186),X4185))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).
fof(i_0_1521,plain,
! [X4838,X4839,X4840,X4841] :
( ~ class_Fields_Olinordered__field(X4841)
| ~ c_Orderings_Oord__class_Oless(X4841,X4840,X4839)
| ~ c_Orderings_Oord__class_Oless(X4841,c_Groups_Ozero__class_Ozero(X4841),X4838)
| ~ c_Orderings_Oord__class_Oless(X4841,c_Groups_Ozero__class_Ozero(X4841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4841),X4839),X4840))
| c_Orderings_Oord__class_Oless(X4841,c_Rings_Oinverse__class_Odivide(X4841,X4838,X4839),c_Rings_Oinverse__class_Odivide(X4841,X4838,X4840)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono])]) ).
fof(i_0_1522,plain,
! [X4933,X4934,X4935,X4936] :
( ~ class_Fields_Olinordered__field(X4936)
| ~ c_Orderings_Oord__class_Oless__eq(X4936,X4935,X4934)
| ~ c_Orderings_Oord__class_Oless__eq(X4936,c_Groups_Ozero__class_Ozero(X4936),X4933)
| ~ c_Orderings_Oord__class_Oless(X4936,c_Groups_Ozero__class_Ozero(X4936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4936),X4934),X4935))
| c_Orderings_Oord__class_Oless__eq(X4936,c_Rings_Oinverse__class_Odivide(X4936,X4933,X4934),c_Rings_Oinverse__class_Odivide(X4936,X4933,X4935)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono])]) ).
fof(i_0_1523,plain,
! [X4834,X4835,X4836,X4837] :
( ~ class_Fields_Olinordered__field(X4837)
| ~ c_Orderings_Oord__class_Oless(X4837,X4836,X4835)
| ~ c_Orderings_Oord__class_Oless(X4837,X4834,c_Groups_Ozero__class_Ozero(X4837))
| ~ c_Orderings_Oord__class_Oless(X4837,c_Groups_Ozero__class_Ozero(X4837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4837),X4836),X4835))
| c_Orderings_Oord__class_Oless(X4837,c_Rings_Oinverse__class_Odivide(X4837,X4834,X4836),c_Rings_Oinverse__class_Odivide(X4837,X4834,X4835)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg])]) ).
fof(i_0_1524,plain,
! [X4929,X4930,X4931,X4932] :
( ~ class_Fields_Olinordered__field__inverse__zero(X4932)
| ~ c_Orderings_Oord__class_Oless__eq(X4932,X4931,X4930)
| ~ c_Orderings_Oord__class_Oless__eq(X4932,X4929,c_Groups_Ozero__class_Ozero(X4932))
| ~ c_Orderings_Oord__class_Oless(X4932,c_Groups_Ozero__class_Ozero(X4932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4932),X4931),X4930))
| c_Orderings_Oord__class_Oless__eq(X4932,c_Rings_Oinverse__class_Odivide(X4932,X4929,X4931),c_Rings_Oinverse__class_Odivide(X4932,X4929,X4930)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg])]) ).
cnf(i_0_1525,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_1292]) ).
cnf(i_0_1526,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_1293]) ).
fof(i_0_1527,plain,
! [X5318,X5319,X5320] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5320,X5319)),X5318),X5319) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5320),X5318),X5319),
inference(variable_rename,[status(thm)],[fact_zpower__zmod]) ).
fof(i_0_1528,plain,
! [X4159,X4160,X4161] :
( ~ class_Divides_Osemiring__div(X4161)
| c_Groups_Oplus__class_Oplus(X4161,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4161),c_Divides_Odiv__class_Odiv(X4161,X4160,X4159)),X4159),c_Divides_Odiv__class_Omod(X4161,X4160,X4159)) = X4160 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality])]) ).
fof(i_0_1529,plain,
! [X4153,X4154,X4155] :
( ~ class_Divides_Osemiring__div(X4155)
| c_Groups_Oplus__class_Oplus(X4155,c_Divides_Odiv__class_Omod(X4155,X4154,X4153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4155),c_Divides_Odiv__class_Odiv(X4155,X4154,X4153)),X4153)) = X4154 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H])]) ).
fof(i_0_1530,plain,
! [X3107,X3108] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3108),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3108,X3107)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3107))),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__sub]) ).
cnf(i_0_1531,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_1294]) ).
fof(i_0_1532,plain,
! [X5026,X5027,X5028,X5029] :
( ~ class_Rings_Ocomm__semiring__0(X5029)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5029)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5029),X5028,X5027)),X5026) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5029)),X5028),X5026),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5029)),X5027),X5026)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__add__left])]) ).
cnf(i_0_1533,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_1295]) ).
cnf(i_0_1534,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_1296]) ).
fof(i_0_1535,plain,
! [X5643,X5644,X5645,X5646,X5647,X5648] :
( ~ class_Divides_Oring__div(X5648)
| c_Divides_Odiv__class_Omod(X5648,X5647,X5646) != c_Divides_Odiv__class_Omod(X5648,X5645,X5646)
| c_Divides_Odiv__class_Omod(X5648,X5644,X5646) != c_Divides_Odiv__class_Omod(X5648,X5643,X5646)
| c_Divides_Odiv__class_Omod(X5648,c_Groups_Ominus__class_Ominus(X5648,X5647,X5644),X5646) = c_Divides_Odiv__class_Omod(X5648,c_Groups_Ominus__class_Ominus(X5648,X5645,X5643),X5646) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__cong])]) ).
fof(i_0_1536,plain,
! [X4472,X4473,X4474,X4475,X4476,X4477] :
( ~ class_Divides_Osemiring__div(X4477)
| c_Divides_Odiv__class_Omod(X4477,X4476,X4475) != c_Divides_Odiv__class_Omod(X4477,X4474,X4475)
| c_Divides_Odiv__class_Omod(X4477,X4473,X4475) != c_Divides_Odiv__class_Omod(X4477,X4472,X4475)
| c_Divides_Odiv__class_Omod(X4477,c_Groups_Oplus__class_Oplus(X4477,X4476,X4473),X4475) = c_Divides_Odiv__class_Omod(X4477,c_Groups_Oplus__class_Oplus(X4477,X4474,X4472),X4475) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__cong])]) ).
fof(i_0_1537,plain,
! [X4396,X4397,X4398,X4399,X4400,X4401] :
( ~ class_Divides_Osemiring__div(X4401)
| c_Divides_Odiv__class_Omod(X4401,X4400,X4399) != c_Divides_Odiv__class_Omod(X4401,X4398,X4399)
| c_Divides_Odiv__class_Omod(X4401,X4397,X4399) != c_Divides_Odiv__class_Omod(X4401,X4396,X4399)
| c_Divides_Odiv__class_Omod(X4401,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4401),X4400),X4397),X4399) = c_Divides_Odiv__class_Omod(X4401,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4401),X4398),X4396),X4399) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__cong])]) ).
fof(i_0_1538,plain,
! [X5288,X5289,X5290] :
( ~ class_Rings_Olinordered__semidom(X5290)
| ~ c_Orderings_Oord__class_Oless(X5290,c_Groups_Ozero__class_Ozero(X5290),X5289)
| ~ c_Orderings_Oord__class_Oless(X5290,X5289,c_Groups_Oone__class_Oone(X5290))
| c_Orderings_Oord__class_Oless(X5290,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5290),X5289),hAPP(hAPP(c_Power_Opower__class_Opower(X5290),X5289),X5288)),hAPP(hAPP(c_Power_Opower__class_Opower(X5290),X5289),X5288)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).
fof(i_0_1539,plain,
! [X5474] :
( ( ~ 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),X5474),X5474),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5474,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5474,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),X5474),X5474),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_1540,plain,
! [X2984,X2985,X2986,X2987,X2988] :
( ~ class_RealVector_Oreal__normed__vector(X2988)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2988,X2987),X2986)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2988,X2985),X2984)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2988,c_Groups_Oplus__class_Oplus(X2988,X2987,X2985)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2986,X2984)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__add__less])]) ).
fof(i_0_1541,plain,
! [X3082,X3083,X3084,X3085,X3086] :
( ~ class_Fields_Olinordered__field(X3086)
| ~ c_Orderings_Oord__class_Oless(X3086,c_Groups_Ozero__class_Ozero(X3086),X3085)
| ~ c_Orderings_Oord__class_Oless__eq(X3086,X3085,X3084)
| ~ c_Orderings_Oord__class_Oless(X3086,c_Groups_Ozero__class_Ozero(X3086),X3083)
| ~ c_Orderings_Oord__class_Oless(X3086,X3083,X3082)
| c_Orderings_Oord__class_Oless(X3086,c_Rings_Oinverse__class_Odivide(X3086,X3085,X3082),c_Rings_Oinverse__class_Odivide(X3086,X3084,X3083)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less2])]) ).
fof(i_0_1542,plain,
! [X3077,X3078,X3079,X3080,X3081] :
( ~ class_Fields_Olinordered__field(X3081)
| ~ c_Orderings_Oord__class_Oless__eq(X3081,c_Groups_Ozero__class_Ozero(X3081),X3080)
| ~ c_Orderings_Oord__class_Oless(X3081,X3080,X3079)
| ~ c_Orderings_Oord__class_Oless(X3081,c_Groups_Ozero__class_Ozero(X3081),X3078)
| ~ c_Orderings_Oord__class_Oless__eq(X3081,X3078,X3077)
| c_Orderings_Oord__class_Oless(X3081,c_Rings_Oinverse__class_Odivide(X3081,X3080,X3077),c_Rings_Oinverse__class_Odivide(X3081,X3079,X3078)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less])]) ).
fof(i_0_1543,plain,
! [X3072,X3073,X3074,X3075,X3076] :
( ~ class_Fields_Olinordered__field(X3076)
| ~ c_Orderings_Oord__class_Oless__eq(X3076,c_Groups_Ozero__class_Ozero(X3076),X3075)
| ~ c_Orderings_Oord__class_Oless__eq(X3076,X3075,X3074)
| ~ c_Orderings_Oord__class_Oless(X3076,c_Groups_Ozero__class_Ozero(X3076),X3073)
| ~ c_Orderings_Oord__class_Oless__eq(X3076,X3073,X3072)
| c_Orderings_Oord__class_Oless__eq(X3076,c_Rings_Oinverse__class_Odivide(X3076,X3075,X3072),c_Rings_Oinverse__class_Odivide(X3076,X3074,X3073)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__le])]) ).
fof(i_0_1544,plain,
! [X4280,X4281,X4282,X4283,X4284] :
( ~ class_Fields_Ofield__inverse__zero(X4284)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4284),c_Rings_Oinverse__class_Odivide(X4284,X4283,X4282)),c_Rings_Oinverse__class_Odivide(X4284,X4281,X4280)) = c_Rings_Oinverse__class_Odivide(X4284,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4284),X4283),X4281),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4284),X4282),X4280)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq])]) ).
fof(i_0_1545,plain,
! [X4285,X4286,X4287,X4288] :
( ~ class_Rings_Ocomm__semiring__0(X4288)
| hAPP(c_Polynomial_Opoly(X4288,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4288)),X4287),X4286)),X4285) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4288),hAPP(c_Polynomial_Opoly(X4288,X4287),X4285)),hAPP(c_Polynomial_Opoly(X4288,X4286),X4285)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mult])]) ).
fof(i_0_1546,plain,
! [X5773,X5774,X5775] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5774,X5775),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5773,X5775))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5774,X5773)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5775,X5773)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5775,X5774) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5774,X5773)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5774,X5775),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5773,X5775))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5775,X5773)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5775,X5774) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).
fof(i_0_1547,plain,
! [X5696,X5697,X5698] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5697,X5698),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5696,X5698))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5697,X5696)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5698,X5696)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5698,X5697) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5697,X5696)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5697,X5698),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5696,X5698))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5698,X5696)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5698,X5697) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).
fof(i_0_1548,plain,
! [X4803,X4804,X4805,X4806,X4807] :
( ~ class_Rings_Olinordered__semiring__strict(X4807)
| ~ c_Orderings_Oord__class_Oless(X4807,X4806,X4805)
| ~ c_Orderings_Oord__class_Oless(X4807,X4804,X4803)
| ~ c_Orderings_Oord__class_Oless(X4807,c_Groups_Ozero__class_Ozero(X4807),X4805)
| ~ c_Orderings_Oord__class_Oless__eq(X4807,c_Groups_Ozero__class_Ozero(X4807),X4804)
| c_Orderings_Oord__class_Oless(X4807,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4807),X4806),X4804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4807),X4805),X4803)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).
fof(i_0_1549,plain,
! [X4798,X4799,X4800,X4801,X4802] :
( ~ class_Rings_Olinordered__semiring__strict(X4802)
| ~ c_Orderings_Oord__class_Oless(X4802,X4801,X4800)
| ~ c_Orderings_Oord__class_Oless(X4802,X4799,X4798)
| ~ c_Orderings_Oord__class_Oless__eq(X4802,c_Groups_Ozero__class_Ozero(X4802),X4801)
| ~ c_Orderings_Oord__class_Oless__eq(X4802,c_Groups_Ozero__class_Ozero(X4802),X4799)
| c_Orderings_Oord__class_Oless(X4802,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4802),X4801),X4799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4802),X4800),X4798)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).
fof(i_0_1550,plain,
! [X4788,X4789,X4790,X4791,X4792] :
( ~ class_Rings_Olinordered__semiring__strict(X4792)
| ~ c_Orderings_Oord__class_Oless__eq(X4792,X4791,X4790)
| ~ c_Orderings_Oord__class_Oless(X4792,X4789,X4788)
| ~ c_Orderings_Oord__class_Oless(X4792,c_Groups_Ozero__class_Ozero(X4792),X4791)
| ~ c_Orderings_Oord__class_Oless__eq(X4792,c_Groups_Ozero__class_Ozero(X4792),X4789)
| c_Orderings_Oord__class_Oless(X4792,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4792),X4791),X4789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4792),X4790),X4788)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).
fof(i_0_1551,plain,
! [X4793,X4794,X4795,X4796,X4797] :
( ~ class_Rings_Olinordered__semiring__strict(X4797)
| ~ c_Orderings_Oord__class_Oless(X4797,X4796,X4795)
| ~ c_Orderings_Oord__class_Oless__eq(X4797,X4794,X4793)
| ~ c_Orderings_Oord__class_Oless__eq(X4797,c_Groups_Ozero__class_Ozero(X4797),X4796)
| ~ c_Orderings_Oord__class_Oless(X4797,c_Groups_Ozero__class_Ozero(X4797),X4794)
| c_Orderings_Oord__class_Oless(X4797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4797),X4796),X4794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4797),X4795),X4793)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).
fof(i_0_1552,plain,
! [X4577,X4578,X4579,X4580,X4581] :
( ~ class_Rings_Oordered__semiring(X4581)
| ~ c_Orderings_Oord__class_Oless__eq(X4581,X4580,X4579)
| ~ c_Orderings_Oord__class_Oless__eq(X4581,X4578,X4577)
| ~ c_Orderings_Oord__class_Oless__eq(X4581,c_Groups_Ozero__class_Ozero(X4581),X4580)
| ~ c_Orderings_Oord__class_Oless__eq(X4581,c_Groups_Ozero__class_Ozero(X4581),X4578)
| c_Orderings_Oord__class_Oless__eq(X4581,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4581),X4580),X4578),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4581),X4579),X4577)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).
fof(i_0_1553,plain,
! [X4582,X4583,X4584,X4585,X4586] :
( ~ class_Rings_Oordered__semiring(X4586)
| ~ c_Orderings_Oord__class_Oless__eq(X4586,X4585,X4584)
| ~ c_Orderings_Oord__class_Oless__eq(X4586,X4583,X4582)
| ~ c_Orderings_Oord__class_Oless__eq(X4586,c_Groups_Ozero__class_Ozero(X4586),X4584)
| ~ c_Orderings_Oord__class_Oless__eq(X4586,c_Groups_Ozero__class_Ozero(X4586),X4583)
| c_Orderings_Oord__class_Oless__eq(X4586,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4586),X4585),X4583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4586),X4584),X4582)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).
fof(i_0_1554,plain,
! [X4170,X4171,X4172,X4173,X4174] :
( ~ class_RealVector_Oreal__normed__algebra(X4174)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4174,X4173),X4172)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4174,X4171),X4170)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4174,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4174),X4173),X4171)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4172),X4170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__less])]) ).
fof(i_0_1555,plain,
! [X5404,X5405,X5406,X5407] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5406)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5406)
| X5406 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5407,X5406) = X5404
| X5407 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5406),X5405),X5404) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5406,X5404)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5404,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5406)
| X5406 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5407,X5406) = X5404
| X5407 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5406),X5405),X5404) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5406)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5404)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5404,X5406)
| X5406 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5407,X5406) = X5404
| X5407 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5406),X5405),X5404) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5406,X5404)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5404,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),X5404)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5404,X5406)
| X5406 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5407,X5406) = X5404
| X5407 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5406),X5405),X5404) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1297])])]) ).
fof(i_0_1556,plain,
! [X5324,X5325,X5326,X5327] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5326)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5326)
| X5326 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5327,X5326) = X5325
| X5327 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5326),X5325),X5324) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5326,X5324)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5324,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5326)
| X5326 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5327,X5326) = X5325
| X5327 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5326),X5325),X5324) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5326)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5324)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5324,X5326)
| X5326 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5327,X5326) = X5325
| X5327 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5326),X5325),X5324) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5326,X5324)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5324,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),X5324)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5324,X5326)
| X5326 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5327,X5326) = X5325
| X5327 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5326),X5325),X5324) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1298])])]) ).
fof(i_0_1557,plain,
! [X5186,X5187,X5188,X5189] :
( ~ class_Groups_Ocomm__monoid__mult(X5189)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5189),X5188),X5187)),X5186) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5189),hAPP(hAPP(c_Power_Opower__class_Opower(X5189),X5188),X5186)),hAPP(hAPP(c_Power_Opower__class_Opower(X5189),X5187),X5186)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).
fof(i_0_1558,plain,
! [X5111,X5112,X5113,X5114] :
( ~ class_Rings_Ocomm__semiring__1(X5114)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5114),X5113),X5112)),X5111) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5114),hAPP(hAPP(c_Power_Opower__class_Opower(X5114),X5113),X5111)),hAPP(hAPP(c_Power_Opower__class_Opower(X5114),X5112),X5111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).
fof(i_0_1559,plain,
! [X4819,X4820,X4821] :
( ~ class_Rings_Olinordered__ring(X4821)
| c_Orderings_Oord__class_Oless__eq(X4821,c_Groups_Ozero__class_Ozero(X4821),c_Groups_Oplus__class_Oplus(X4821,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4821),X4820),X4820),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4821),X4819),X4819))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).
cnf(i_0_1560,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_1299]) ).
cnf(i_0_1561,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_1287]) ).
cnf(i_0_1562,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_1287]) ).
cnf(i_0_1563,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_1300]) ).
fof(i_0_1564,plain,
! [X2978] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2978),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2978)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk9_0),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk9_0)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096])])])])]) ).
fof(i_0_1565,plain,
! [X5261,X5262,X5263] :
( ~ class_Rings_Olinordered__semidom(X5263)
| ~ c_Orderings_Oord__class_Oless(X5263,c_Groups_Oone__class_Oone(X5263),X5262)
| c_Orderings_Oord__class_Oless(X5263,hAPP(hAPP(c_Power_Opower__class_Opower(X5263),X5262),X5261),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5263),X5262),hAPP(hAPP(c_Power_Opower__class_Opower(X5263),X5262),X5261))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).
fof(i_0_1566,plain,
! [X4784,X4785,X4786,X4787] :
( ~ class_Rings_Olinordered__semiring(X4787)
| ~ c_Orderings_Oord__class_Oless(X4787,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4787),X4786),X4785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4787),X4784),X4785))
| ~ c_Orderings_Oord__class_Oless__eq(X4787,c_Groups_Ozero__class_Ozero(X4787),X4785)
| c_Orderings_Oord__class_Oless(X4787,X4786,X4784) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).
fof(i_0_1567,plain,
! [X4780,X4781,X4782,X4783] :
( ~ class_Rings_Olinordered__semiring__strict(X4783)
| ~ c_Orderings_Oord__class_Oless(X4783,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4783),X4782),X4781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4783),X4780),X4781))
| ~ c_Orderings_Oord__class_Oless__eq(X4783,c_Groups_Ozero__class_Ozero(X4783),X4781)
| c_Orderings_Oord__class_Oless(X4783,X4782,X4780) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).
fof(i_0_1568,plain,
! [X5246,X5247,X5248,X5249] :
( ~ class_Rings_Olinordered__semidom(X5249)
| ~ c_Orderings_Oord__class_Oless(X5249,hAPP(hAPP(c_Power_Opower__class_Opower(X5249),X5248),X5247),hAPP(hAPP(c_Power_Opower__class_Opower(X5249),X5246),X5247))
| ~ c_Orderings_Oord__class_Oless__eq(X5249,c_Groups_Ozero__class_Ozero(X5249),X5246)
| c_Orderings_Oord__class_Oless(X5249,X5248,X5246) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).
fof(i_0_1569,plain,
! [X4776,X4777,X4778,X4779] :
( ~ class_Rings_Olinordered__semiring(X4779)
| ~ c_Orderings_Oord__class_Oless(X4779,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4779),X4778),X4777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4779),X4778),X4776))
| ~ c_Orderings_Oord__class_Oless__eq(X4779,c_Groups_Ozero__class_Ozero(X4779),X4778)
| c_Orderings_Oord__class_Oless(X4779,X4777,X4776) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).
fof(i_0_1570,plain,
! [X4772,X4773,X4774,X4775] :
( ~ class_Rings_Olinordered__semiring__strict(X4775)
| ~ c_Orderings_Oord__class_Oless(X4775,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4775),X4774),X4773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4775),X4774),X4772))
| ~ c_Orderings_Oord__class_Oless__eq(X4775,c_Groups_Ozero__class_Ozero(X4775),X4774)
| c_Orderings_Oord__class_Oless(X4775,X4773,X4772) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).
fof(i_0_1571,plain,
! [X4603,X4604,X4605,X4606] :
( ( ~ c_Orderings_Oord__class_Oless(X4606,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4606),X4605),X4604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4606),X4605),X4603))
| c_Orderings_Oord__class_Oless(X4606,X4604,X4603)
| ~ c_Orderings_Oord__class_Oless(X4606,c_Groups_Ozero__class_Ozero(X4606),X4605)
| ~ class_Rings_Olinordered__ring__strict(X4606) )
& ( ~ c_Orderings_Oord__class_Oless(X4606,X4604,X4603)
| c_Orderings_Oord__class_Oless(X4606,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4606),X4605),X4604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4606),X4605),X4603))
| ~ c_Orderings_Oord__class_Oless(X4606,c_Groups_Ozero__class_Ozero(X4606),X4605)
| ~ class_Rings_Olinordered__ring__strict(X4606) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).
fof(i_0_1572,plain,
! [X4768,X4769,X4770,X4771] :
( ~ class_Rings_Olinordered__semiring__strict(X4771)
| ~ c_Orderings_Oord__class_Oless__eq(X4771,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4771),X4770),X4769),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4771),X4768),X4769))
| ~ c_Orderings_Oord__class_Oless(X4771,c_Groups_Ozero__class_Ozero(X4771),X4769)
| c_Orderings_Oord__class_Oless__eq(X4771,X4770,X4768) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).
fof(i_0_1573,plain,
! [X4764,X4765,X4766,X4767] :
( ~ class_Rings_Olinordered__semiring__strict(X4767)
| ~ c_Orderings_Oord__class_Oless__eq(X4767,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4767),X4766),X4765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4767),X4766),X4764))
| ~ c_Orderings_Oord__class_Oless(X4767,c_Groups_Ozero__class_Ozero(X4767),X4766)
| c_Orderings_Oord__class_Oless__eq(X4767,X4765,X4764) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).
fof(i_0_1574,plain,
! [X4812,X4813,X4814,X4815] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4815,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4815),X4814),X4813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4815),X4814),X4812))
| c_Orderings_Oord__class_Oless__eq(X4815,X4813,X4812)
| ~ c_Orderings_Oord__class_Oless(X4815,c_Groups_Ozero__class_Ozero(X4815),X4814)
| ~ class_Rings_Olinordered__ring__strict(X4815) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4815,X4813,X4812)
| c_Orderings_Oord__class_Oless__eq(X4815,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4815),X4814),X4813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4815),X4814),X4812))
| ~ c_Orderings_Oord__class_Oless(X4815,c_Groups_Ozero__class_Ozero(X4815),X4814)
| ~ class_Rings_Olinordered__ring__strict(X4815) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).
fof(i_0_1575,plain,
! [X4622,X4623,X4624,X4625] :
( ( ~ c_Orderings_Oord__class_Oless(X4625,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),X4624),X4623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),X4624),X4622))
| c_Orderings_Oord__class_Oless(X4625,X4622,X4623)
| ~ c_Orderings_Oord__class_Oless(X4625,X4624,c_Groups_Ozero__class_Ozero(X4625))
| ~ class_Rings_Olinordered__ring__strict(X4625) )
& ( ~ c_Orderings_Oord__class_Oless(X4625,X4622,X4623)
| c_Orderings_Oord__class_Oless(X4625,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),X4624),X4623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),X4624),X4622))
| ~ c_Orderings_Oord__class_Oless(X4625,X4624,c_Groups_Ozero__class_Ozero(X4625))
| ~ class_Rings_Olinordered__ring__strict(X4625) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).
fof(i_0_1576,plain,
! [X4808,X4809,X4810,X4811] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4811,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4811),X4810),X4809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4811),X4810),X4808))
| c_Orderings_Oord__class_Oless__eq(X4811,X4808,X4809)
| ~ c_Orderings_Oord__class_Oless(X4811,X4810,c_Groups_Ozero__class_Ozero(X4811))
| ~ class_Rings_Olinordered__ring__strict(X4811) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4811,X4808,X4809)
| c_Orderings_Oord__class_Oless__eq(X4811,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4811),X4810),X4809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4811),X4810),X4808))
| ~ c_Orderings_Oord__class_Oless(X4811,X4810,c_Groups_Ozero__class_Ozero(X4811))
| ~ class_Rings_Olinordered__ring__strict(X4811) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).
fof(i_0_1577,plain,
! [X5280,X5281,X5282,X5283] :
( ( ~ c_Orderings_Oord__class_Oless(X5283,hAPP(hAPP(c_Power_Opower__class_Opower(X5283),X5282),X5281),hAPP(hAPP(c_Power_Opower__class_Opower(X5283),X5282),X5280))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5281,X5280)
| ~ c_Orderings_Oord__class_Oless(X5283,c_Groups_Oone__class_Oone(X5283),X5282)
| ~ class_Rings_Olinordered__semidom(X5283) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5281,X5280)
| c_Orderings_Oord__class_Oless(X5283,hAPP(hAPP(c_Power_Opower__class_Opower(X5283),X5282),X5281),hAPP(hAPP(c_Power_Opower__class_Opower(X5283),X5282),X5280))
| ~ c_Orderings_Oord__class_Oless(X5283,c_Groups_Oone__class_Oone(X5283),X5282)
| ~ class_Rings_Olinordered__semidom(X5283) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).
fof(i_0_1578,plain,
! [X5276,X5277,X5278,X5279] :
( ~ class_Rings_Olinordered__semidom(X5279)
| ~ c_Orderings_Oord__class_Oless(X5279,c_Groups_Oone__class_Oone(X5279),X5278)
| ~ c_Orderings_Oord__class_Oless(X5279,hAPP(hAPP(c_Power_Opower__class_Opower(X5279),X5278),X5277),hAPP(hAPP(c_Power_Opower__class_Opower(X5279),X5278),X5276))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5277,X5276) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).
fof(i_0_1579,plain,
! [X5310,X5311,X5312,X5313] :
( ~ class_Rings_Olinordered__semidom(X5313)
| ~ c_Orderings_Oord__class_Oless(X5313,c_Groups_Oone__class_Oone(X5313),X5312)
| ~ c_Orderings_Oord__class_Oless__eq(X5313,hAPP(hAPP(c_Power_Opower__class_Opower(X5313),X5312),X5311),hAPP(hAPP(c_Power_Opower__class_Opower(X5313),X5312),X5310))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5311,X5310) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).
fof(i_0_1580,plain,
! [X5306,X5307,X5308,X5309] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5309,hAPP(hAPP(c_Power_Opower__class_Opower(X5309),X5308),X5307),hAPP(hAPP(c_Power_Opower__class_Opower(X5309),X5308),X5306))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5307,X5306)
| ~ c_Orderings_Oord__class_Oless(X5309,c_Groups_Oone__class_Oone(X5309),X5308)
| ~ class_Rings_Olinordered__semidom(X5309) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5307,X5306)
| c_Orderings_Oord__class_Oless__eq(X5309,hAPP(hAPP(c_Power_Opower__class_Opower(X5309),X5308),X5307),hAPP(hAPP(c_Power_Opower__class_Opower(X5309),X5308),X5306))
| ~ c_Orderings_Oord__class_Oless(X5309,c_Groups_Oone__class_Oone(X5309),X5308)
| ~ class_Rings_Olinordered__semidom(X5309) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).
fof(i_0_1581,plain,
! [X5136,X5137,X5138,X5139] :
( ~ class_Rings_Ocomm__semiring__1(X5139)
| hAPP(c_Polynomial_Opoly(X5139,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5139)),X5138),X5137)),X5136) = hAPP(hAPP(c_Power_Opower__class_Opower(X5139),hAPP(c_Polynomial_Opoly(X5139,X5138),X5136)),X5137) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__power])]) ).
fof(i_0_1582,plain,
! [X5089,X5090,X5092] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk63_2(X5089,X5090))
| ~ class_RealVector_Oreal__normed__field(X5090) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5090,c_Rings_Oinverse__class_Odivide(X5090,X5092,X5089)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5090,X5092)),esk63_2(X5089,X5090)))
| ~ class_RealVector_Oreal__normed__field(X5090) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Ononneg__bounded])])])])]) ).
fof(i_0_1583,plain,
! [X5071,X5072,X5074] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk59_2(X5071,X5072))
| ~ class_RealVector_Oreal__normed__field(X5072) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5072,c_Rings_Oinverse__class_Odivide(X5072,X5074,X5071)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5072,X5074)),esk59_2(X5071,X5072)))
| ~ class_RealVector_Oreal__normed__field(X5072) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Opos__bounded])])])])]) ).
fof(i_0_1584,plain,
! [X5058,X5059] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5059)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5058)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X5059)),c_RComplete_Onatfloor(X5058)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5059),X5058))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mult__natfloor])]) ).
fof(i_0_1585,plain,
! [X4003,X4004,X4005,X4006,X4007] :
( ~ class_Rings_Ocomm__semiring__1(X4007)
| c_Groups_Oplus__class_Oplus(X4007,c_Groups_Oplus__class_Oplus(X4007,X4006,X4005),c_Groups_Oplus__class_Oplus(X4007,X4004,X4003)) = c_Groups_Oplus__class_Oplus(X4007,c_Groups_Oplus__class_Oplus(X4007,X4006,X4004),c_Groups_Oplus__class_Oplus(X4007,X4005,X4003)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_1586,plain,
! [X4468,X4469,X4470,X4471] :
( ~ class_Divides_Osemiring__div(X4471)
| c_Divides_Odiv__class_Omod(X4471,c_Groups_Oplus__class_Oplus(X4471,c_Divides_Odiv__class_Omod(X4471,X4470,X4469),X4468),X4469) = c_Divides_Odiv__class_Omod(X4471,c_Groups_Oplus__class_Oplus(X4471,X4470,X4468),X4469) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J])]) ).
fof(i_0_1587,plain,
! [X4464,X4465,X4466,X4467] :
( ~ class_Divides_Osemiring__div(X4467)
| c_Divides_Odiv__class_Omod(X4467,c_Groups_Oplus__class_Oplus(X4467,X4466,c_Divides_Odiv__class_Omod(X4467,X4465,X4464)),X4464) = c_Divides_Odiv__class_Omod(X4467,c_Groups_Oplus__class_Oplus(X4467,X4466,X4465),X4464) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J])]) ).
fof(i_0_1588,plain,
! [X5653,X5654,X5655,X5656] :
( ~ class_Divides_Oring__div(X5656)
| c_Divides_Odiv__class_Omod(X5656,c_Groups_Ominus__class_Ominus(X5656,X5655,X5654),X5653) = c_Divides_Odiv__class_Omod(X5656,c_Groups_Ominus__class_Ominus(X5656,c_Divides_Odiv__class_Omod(X5656,X5655,X5653),X5654),X5653) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq])]) ).
fof(i_0_1589,plain,
! [X4456,X4457,X4458,X4459] :
( ~ class_Divides_Osemiring__div(X4459)
| c_Divides_Odiv__class_Omod(X4459,c_Groups_Oplus__class_Oplus(X4459,X4458,X4457),X4456) = c_Divides_Odiv__class_Omod(X4459,c_Groups_Oplus__class_Oplus(X4459,c_Divides_Odiv__class_Omod(X4459,X4458,X4456),X4457),X4456) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq])]) ).
fof(i_0_1590,plain,
! [X5657,X5658,X5659,X5660] :
( ~ class_Divides_Oring__div(X5660)
| c_Divides_Odiv__class_Omod(X5660,c_Groups_Ominus__class_Ominus(X5660,X5659,X5658),X5657) = c_Divides_Odiv__class_Omod(X5660,c_Groups_Ominus__class_Ominus(X5660,X5659,c_Divides_Odiv__class_Omod(X5660,X5658,X5657)),X5657) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq])]) ).
fof(i_0_1591,plain,
! [X4452,X4453,X4454,X4455] :
( ~ class_Divides_Osemiring__div(X4455)
| c_Divides_Odiv__class_Omod(X4455,c_Groups_Oplus__class_Oplus(X4455,X4454,X4453),X4452) = c_Divides_Odiv__class_Omod(X4455,c_Groups_Oplus__class_Oplus(X4455,X4454,c_Divides_Odiv__class_Omod(X4455,X4453,X4452)),X4452) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])]) ).
fof(i_0_1592,plain,
! [X5294,X5295,X5296,X5297] :
( ~ class_Rings_Olinordered__semidom(X5297)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5296,X5295)
| ~ c_Orderings_Oord__class_Oless(X5297,c_Groups_Ozero__class_Ozero(X5297),X5294)
| ~ c_Orderings_Oord__class_Oless(X5297,X5294,c_Groups_Oone__class_Oone(X5297))
| c_Orderings_Oord__class_Oless(X5297,hAPP(hAPP(c_Power_Opower__class_Opower(X5297),X5294),X5295),hAPP(hAPP(c_Power_Opower__class_Opower(X5297),X5294),X5296)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).
fof(i_0_1593,plain,
! [X5302,X5303,X5304,X5305] :
( ~ class_Rings_Olinordered__semidom(X5305)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5304,X5303)
| ~ c_Orderings_Oord__class_Oless__eq(X5305,c_Groups_Ozero__class_Ozero(X5305),X5302)
| ~ c_Orderings_Oord__class_Oless__eq(X5305,X5302,c_Groups_Oone__class_Oone(X5305))
| c_Orderings_Oord__class_Oless__eq(X5305,hAPP(hAPP(c_Power_Opower__class_Opower(X5305),X5302),X5303),hAPP(hAPP(c_Power_Opower__class_Opower(X5305),X5302),X5304)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).
fof(i_0_1594,plain,
! [X4895,X4896,X4897,X4898] :
( ~ class_Divides_Osemiring__div(X4898)
| X4897 = c_Groups_Ozero__class_Ozero(X4898)
| c_Divides_Odiv__class_Odiv(X4898,c_Groups_Oplus__class_Oplus(X4898,X4896,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4898),X4897),X4895)),X4897) = c_Groups_Oplus__class_Oplus(X4898,X4895,c_Divides_Odiv__class_Odiv(X4898,X4896,X4897)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2])]) ).
fof(i_0_1595,plain,
! [X4899,X4900,X4901,X4902] :
( ~ class_Divides_Osemiring__div(X4902)
| X4901 = c_Groups_Ozero__class_Ozero(X4902)
| c_Divides_Odiv__class_Odiv(X4902,c_Groups_Oplus__class_Oplus(X4902,X4900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4902),X4899),X4901)),X4901) = c_Groups_Oplus__class_Oplus(X4902,X4899,c_Divides_Odiv__class_Odiv(X4902,X4900,X4901)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1])]) ).
fof(i_0_1596,plain,
! [X4879,X4880,X4881,X4882] :
( ~ class_Fields_Ofield(X4882)
| X4881 = c_Groups_Ozero__class_Ozero(X4882)
| c_Groups_Oplus__class_Oplus(X4882,c_Rings_Oinverse__class_Odivide(X4882,X4880,X4881),X4879) = c_Rings_Oinverse__class_Odivide(X4882,c_Groups_Oplus__class_Oplus(X4882,X4880,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4882),X4881),X4879)),X4881) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff])]) ).
fof(i_0_1597,plain,
! [X4883,X4884,X4885,X4886] :
( ~ class_Fields_Ofield__inverse__zero(X4886)
| X4885 = c_Groups_Ozero__class_Ozero(X4886)
| c_Groups_Oplus__class_Oplus(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4884,X4885),X4883) = c_Rings_Oinverse__class_Odivide(X4886,c_Groups_Oplus__class_Oplus(X4886,X4884,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4886),X4883),X4885)),X4885) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__num])]) ).
fof(i_0_1598,plain,
! [X4887,X4888,X4889,X4890] :
( ~ class_Fields_Ofield(X4890)
| X4889 = c_Groups_Ozero__class_Ozero(X4890)
| c_Groups_Oplus__class_Oplus(X4890,X4888,c_Rings_Oinverse__class_Odivide(X4890,X4887,X4889)) = c_Rings_Oinverse__class_Odivide(X4890,c_Groups_Oplus__class_Oplus(X4890,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4890),X4889),X4888),X4887),X4889) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])]) ).
fof(i_0_1599,plain,
! [X4891,X4892,X4893,X4894] :
( ~ class_Fields_Ofield__inverse__zero(X4894)
| X4893 = c_Groups_Ozero__class_Ozero(X4894)
| c_Groups_Oplus__class_Oplus(X4894,X4892,c_Rings_Oinverse__class_Odivide(X4894,X4891,X4893)) = c_Rings_Oinverse__class_Odivide(X4894,c_Groups_Oplus__class_Oplus(X4894,X4891,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4894),X4892),X4893)),X4893) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__num__frac])]) ).
fof(i_0_1600,plain,
! [X5152,X5153,X5154,X5155] :
( ~ class_Rings_Olinordered__semidom(X5155)
| ~ c_Orderings_Oord__class_Oless(X5155,X5154,X5153)
| ~ c_Orderings_Oord__class_Oless__eq(X5155,c_Groups_Ozero__class_Ozero(X5155),X5154)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5152)
| c_Orderings_Oord__class_Oless(X5155,hAPP(hAPP(c_Power_Opower__class_Opower(X5155),X5154),X5152),hAPP(hAPP(c_Power_Opower__class_Opower(X5155),X5153),X5152)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).
fof(i_0_1601,plain,
! [X5227,X5228,X5229,X5230] :
( ~ class_Fields_Ofield(X5230)
| X5229 = c_Groups_Ozero__class_Ozero(X5230)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5230),c_Rings_Oinverse__class_Odivide(X5230,X5228,X5229)),X5227) = c_Rings_Oinverse__class_Odivide(X5230,hAPP(hAPP(c_Power_Opower__class_Opower(X5230),X5228),X5227),hAPP(hAPP(c_Power_Opower__class_Opower(X5230),X5229),X5227)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide])]) ).
cnf(i_0_1602,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_1281]) ).
fof(i_0_1603,plain,
! [X4599,X4600,X4601,X4602] :
( ( c_Orderings_Oord__class_Oless(X4602,X4601,c_Groups_Ozero__class_Ozero(X4602))
| c_Orderings_Oord__class_Oless(X4602,c_Groups_Ozero__class_Ozero(X4602),X4601)
| ~ c_Orderings_Oord__class_Oless(X4602,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4602),X4601),X4600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4602),X4601),X4599))
| ~ class_Rings_Olinordered__ring__strict(X4602) )
& ( c_Orderings_Oord__class_Oless(X4602,X4599,X4600)
| c_Orderings_Oord__class_Oless(X4602,c_Groups_Ozero__class_Ozero(X4602),X4601)
| ~ c_Orderings_Oord__class_Oless(X4602,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4602),X4601),X4600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4602),X4601),X4599))
| ~ class_Rings_Olinordered__ring__strict(X4602) )
& ( c_Orderings_Oord__class_Oless(X4602,X4601,c_Groups_Ozero__class_Ozero(X4602))
| c_Orderings_Oord__class_Oless(X4602,X4600,X4599)
| ~ c_Orderings_Oord__class_Oless(X4602,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4602),X4601),X4600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4602),X4601),X4599))
| ~ class_Rings_Olinordered__ring__strict(X4602) )
& ( c_Orderings_Oord__class_Oless(X4602,X4599,X4600)
| c_Orderings_Oord__class_Oless(X4602,X4600,X4599)
| ~ c_Orderings_Oord__class_Oless(X4602,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4602),X4601),X4600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4602),X4601),X4599))
| ~ class_Rings_Olinordered__ring__strict(X4602) )
& ( ~ c_Orderings_Oord__class_Oless(X4602,c_Groups_Ozero__class_Ozero(X4602),X4601)
| ~ c_Orderings_Oord__class_Oless(X4602,X4600,X4599)
| c_Orderings_Oord__class_Oless(X4602,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4602),X4601),X4600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4602),X4601),X4599))
| ~ class_Rings_Olinordered__ring__strict(X4602) )
& ( ~ c_Orderings_Oord__class_Oless(X4602,X4601,c_Groups_Ozero__class_Ozero(X4602))
| ~ c_Orderings_Oord__class_Oless(X4602,X4599,X4600)
| c_Orderings_Oord__class_Oless(X4602,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4602),X4601),X4600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4602),X4601),X4599))
| ~ class_Rings_Olinordered__ring__strict(X4602) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).
fof(i_0_1604,plain,
! [X4595,X4596,X4597,X4598] :
( ( c_Orderings_Oord__class_Oless(X4598,X4596,c_Groups_Ozero__class_Ozero(X4598))
| c_Orderings_Oord__class_Oless(X4598,c_Groups_Ozero__class_Ozero(X4598),X4596)
| ~ c_Orderings_Oord__class_Oless(X4598,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4597),X4596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4595),X4596))
| ~ class_Rings_Olinordered__ring__strict(X4598) )
& ( c_Orderings_Oord__class_Oless(X4598,X4595,X4597)
| c_Orderings_Oord__class_Oless(X4598,c_Groups_Ozero__class_Ozero(X4598),X4596)
| ~ c_Orderings_Oord__class_Oless(X4598,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4597),X4596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4595),X4596))
| ~ class_Rings_Olinordered__ring__strict(X4598) )
& ( c_Orderings_Oord__class_Oless(X4598,X4596,c_Groups_Ozero__class_Ozero(X4598))
| c_Orderings_Oord__class_Oless(X4598,X4597,X4595)
| ~ c_Orderings_Oord__class_Oless(X4598,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4597),X4596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4595),X4596))
| ~ class_Rings_Olinordered__ring__strict(X4598) )
& ( c_Orderings_Oord__class_Oless(X4598,X4595,X4597)
| c_Orderings_Oord__class_Oless(X4598,X4597,X4595)
| ~ c_Orderings_Oord__class_Oless(X4598,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4597),X4596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4595),X4596))
| ~ class_Rings_Olinordered__ring__strict(X4598) )
& ( ~ c_Orderings_Oord__class_Oless(X4598,c_Groups_Ozero__class_Ozero(X4598),X4596)
| ~ c_Orderings_Oord__class_Oless(X4598,X4597,X4595)
| c_Orderings_Oord__class_Oless(X4598,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4597),X4596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4595),X4596))
| ~ class_Rings_Olinordered__ring__strict(X4598) )
& ( ~ c_Orderings_Oord__class_Oless(X4598,X4596,c_Groups_Ozero__class_Ozero(X4598))
| ~ c_Orderings_Oord__class_Oless(X4598,X4595,X4597)
| c_Orderings_Oord__class_Oless(X4598,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4597),X4596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4595),X4596))
| ~ class_Rings_Olinordered__ring__strict(X4598) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).
fof(i_0_1605,plain,
! [X5097,X5098,X5100] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk65_2(X5097,X5098))
| ~ class_RealVector_Oreal__normed__algebra(X5098) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5098,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5098),X5100),X5097)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5098,X5100)),esk65_2(X5097,X5098)))
| ~ class_RealVector_Oreal__normed__algebra(X5098) ) ),
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_1606,plain,
! [X5081,X5082,X5084] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk61_2(X5081,X5082))
| ~ class_RealVector_Oreal__normed__algebra(X5082) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5082,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5082),X5084),X5081)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5082,X5084)),esk61_2(X5081,X5082)))
| ~ class_RealVector_Oreal__normed__algebra(X5082) ) ),
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_1607,plain,
! [X4355,X4356,X4357] :
( ~ class_RealVector_Oreal__normed__algebra(X4357)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4357,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4357),X4356),X4355)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4357,X4356)),c_RealVector_Onorm__class_Onorm(X4357,X4355))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])]) ).
fof(i_0_1608,plain,
! [X5101,X5102,X5104] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk66_2(X5101,X5102))
| ~ class_RealVector_Oreal__normed__algebra(X5102) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5102,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5102),X5101),X5104)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5102,X5104)),esk66_2(X5101,X5102)))
| ~ class_RealVector_Oreal__normed__algebra(X5102) ) ),
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_1609,plain,
! [X5085,X5086,X5088] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk62_2(X5085,X5086))
| ~ class_RealVector_Oreal__normed__algebra(X5086) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5086,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5086),X5085),X5088)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5086,X5088)),esk62_2(X5085,X5086)))
| ~ class_RealVector_Oreal__normed__algebra(X5086) ) ),
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_1610,plain,
! [X4422,X4423,X4424,X4425] :
( ~ class_Divides_Osemiring__div(X4425)
| c_Divides_Odiv__class_Omod(X4425,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4425),X4424),X4423),X4422) = c_Divides_Odiv__class_Omod(X4425,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4425),X4424),c_Divides_Odiv__class_Omod(X4425,X4423,X4422)),X4422) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])]) ).
cnf(i_0_1611,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2),
inference(split_conjunct,[status(thm)],[i_0_1301]) ).
fof(i_0_1612,plain,
! [X4406,X4407,X4408,X4409] :
( ~ class_Divides_Osemiring__div(X4409)
| c_Divides_Odiv__class_Omod(X4409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4409),X4408),X4407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4409),X4406),X4407)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4409),c_Divides_Odiv__class_Omod(X4409,X4408,X4406)),X4407) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2])]) ).
fof(i_0_1613,plain,
! [X4226,X4227,X4228,X4229] :
( ~ class_Rings_Ocomm__semiring__1(X4229)
| c_Groups_Oplus__class_Oplus(X4229,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4229),X4228),X4227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4229),X4226),X4227)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4229),c_Groups_Oplus__class_Oplus(X4229,X4228,X4226)),X4227) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).
fof(i_0_1614,plain,
! [X5195,X5196,X5197,X5198] :
( ~ class_Fields_Ofield__inverse__zero(X5198)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5198),c_Rings_Oinverse__class_Odivide(X5198,X5197,X5196)),X5195) = c_Rings_Oinverse__class_Odivide(X5198,hAPP(hAPP(c_Power_Opower__class_Opower(X5198),X5197),X5195),hAPP(hAPP(c_Power_Opower__class_Opower(X5198),X5196),X5195)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])]) ).
fof(i_0_1615,plain,
! [X4309,X4310,X4311,X4312] :
( ~ class_Rings_Ocomm__semiring(X4312)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4312),c_Groups_Oplus__class_Oplus(X4312,X4311,X4310)),X4309) = c_Groups_Oplus__class_Oplus(X4312,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4312),X4311),X4309),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4312),X4310),X4309)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).
fof(i_0_1616,plain,
! [X4330,X4331,X4332,X4333] :
( ~ class_RealVector_Oreal__normed__algebra(X4333)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4333),c_Groups_Oplus__class_Oplus(X4333,X4332,X4331)),X4330) = c_Groups_Oplus__class_Oplus(X4333,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4333),X4332),X4330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4333),X4331),X4330)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd])]) ).
fof(i_0_1617,plain,
! [X4326,X4327,X4328,X4329] :
( ~ class_RealVector_Oreal__normed__algebra(X4329)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4329),c_Groups_Oplus__class_Oplus(X4329,X4328,X4327)),X4326) = c_Groups_Oplus__class_Oplus(X4329,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4329),X4328),X4326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4329),X4327),X4326)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left])]) ).
fof(i_0_1618,plain,
! [X4222,X4223,X4224,X4225] :
( ~ class_Rings_Ocomm__semiring__1(X4225)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),c_Groups_Oplus__class_Oplus(X4225,X4224,X4223)),X4222) = c_Groups_Oplus__class_Oplus(X4225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4223),X4222)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).
fof(i_0_1619,plain,
! [X3146] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3146),v_r)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk11_0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3146))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1302])])])]) ).
cnf(i_0_1620,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_1303]) ).
fof(i_0_1621,plain,
! [X5562,X5563,X5564] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5564)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5563)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5563,X5562)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5564,X5562),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5564,X5563)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2])]) ).
fof(i_0_1622,plain,
! [X5573,X5574,X5575] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5575,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5574)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5574,X5573)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5575,X5574),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5575,X5573)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg])]) ).
fof(i_0_1623,plain,
! [X5130,X5131,X5132,X5133] :
( ~ class_Rings_Ocomm__semiring__1(X5133)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5133),hAPP(hAPP(c_Power_Opower__class_Opower(X5133),X5132),X5131)),hAPP(hAPP(c_Power_Opower__class_Opower(X5133),X5132),X5130)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5133),X5132),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5131,X5130)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).
fof(i_0_1624,plain,
! [X5239,X5240,X5241,X5242] :
( ~ class_Groups_Omonoid__mult(X5242)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5242),X5241),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5240,X5239)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5242),hAPP(hAPP(c_Power_Opower__class_Opower(X5242),X5241),X5240)),hAPP(hAPP(c_Power_Opower__class_Opower(X5242),X5241),X5239)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).
fof(i_0_1625,plain,
! [X4190,X4191,X4192,X4193] :
( ~ class_Rings_Ocomm__semiring__1(X4193)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4193),X4192),X4191)),X4190) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4193),X4192),X4190)),X4191) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).
fof(i_0_1626,plain,
! [X2974,X2975,X2976] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2975),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2975)),X2974)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X2974) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk8_1(X2976)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X2976) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk8_1(X2976))),X2976)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X2976) ) ),
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_s1])])])])])]) ).
fof(i_0_1627,plain,
! [X4862,X4863,X4864,X4865] :
( ( ~ c_Orderings_Oord__class_Oless(X4865,X4863,c_Rings_Oinverse__class_Odivide(X4865,X4862,X4864))
| c_Orderings_Oord__class_Oless(X4865,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4865),X4863),X4864),X4862)
| ~ c_Orderings_Oord__class_Oless(X4865,c_Groups_Ozero__class_Ozero(X4865),X4864)
| ~ class_Fields_Olinordered__field(X4865) )
& ( ~ c_Orderings_Oord__class_Oless(X4865,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4865),X4863),X4864),X4862)
| c_Orderings_Oord__class_Oless(X4865,X4863,c_Rings_Oinverse__class_Odivide(X4865,X4862,X4864))
| ~ c_Orderings_Oord__class_Oless(X4865,c_Groups_Ozero__class_Ozero(X4865),X4864)
| ~ class_Fields_Olinordered__field(X4865) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq])])]) ).
fof(i_0_1628,plain,
! [X4957,X4958,X4959,X4960] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4960,X4958,c_Rings_Oinverse__class_Odivide(X4960,X4957,X4959))
| c_Orderings_Oord__class_Oless__eq(X4960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4960),X4958),X4959),X4957)
| ~ c_Orderings_Oord__class_Oless(X4960,c_Groups_Ozero__class_Ozero(X4960),X4959)
| ~ class_Fields_Olinordered__field(X4960) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4960),X4958),X4959),X4957)
| c_Orderings_Oord__class_Oless__eq(X4960,X4958,c_Rings_Oinverse__class_Odivide(X4960,X4957,X4959))
| ~ c_Orderings_Oord__class_Oless(X4960,c_Groups_Ozero__class_Ozero(X4960),X4959)
| ~ class_Fields_Olinordered__field(X4960) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq])])]) ).
fof(i_0_1629,plain,
! [X4842,X4843,X4844,X4845] :
( ( ~ c_Orderings_Oord__class_Oless(X4845,c_Rings_Oinverse__class_Odivide(X4845,X4843,X4844),X4842)
| c_Orderings_Oord__class_Oless(X4845,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4845),X4842),X4844),X4843)
| ~ c_Orderings_Oord__class_Oless(X4845,X4844,c_Groups_Ozero__class_Ozero(X4845))
| ~ class_Fields_Olinordered__field(X4845) )
& ( ~ c_Orderings_Oord__class_Oless(X4845,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4845),X4842),X4844),X4843)
| c_Orderings_Oord__class_Oless(X4845,c_Rings_Oinverse__class_Odivide(X4845,X4843,X4844),X4842)
| ~ c_Orderings_Oord__class_Oless(X4845,X4844,c_Groups_Ozero__class_Ozero(X4845))
| ~ class_Fields_Olinordered__field(X4845) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq])])]) ).
fof(i_0_1630,plain,
! [X4937,X4938,X4939,X4940] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4940,c_Rings_Oinverse__class_Odivide(X4940,X4938,X4939),X4937)
| c_Orderings_Oord__class_Oless__eq(X4940,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4940),X4937),X4939),X4938)
| ~ c_Orderings_Oord__class_Oless(X4940,X4939,c_Groups_Ozero__class_Ozero(X4940))
| ~ class_Fields_Olinordered__field(X4940) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4940,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4940),X4937),X4939),X4938)
| c_Orderings_Oord__class_Oless__eq(X4940,c_Rings_Oinverse__class_Odivide(X4940,X4938,X4939),X4937)
| ~ c_Orderings_Oord__class_Oless(X4940,X4939,c_Groups_Ozero__class_Ozero(X4940))
| ~ class_Fields_Olinordered__field(X4940) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq])])]) ).
fof(i_0_1631,plain,
! [X4858,X4859,X4860,X4861] :
( ( ~ c_Orderings_Oord__class_Oless(X4861,c_Rings_Oinverse__class_Odivide(X4861,X4859,X4860),X4858)
| c_Orderings_Oord__class_Oless(X4861,X4859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4861),X4858),X4860))
| ~ c_Orderings_Oord__class_Oless(X4861,c_Groups_Ozero__class_Ozero(X4861),X4860)
| ~ class_Fields_Olinordered__field(X4861) )
& ( ~ c_Orderings_Oord__class_Oless(X4861,X4859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4861),X4858),X4860))
| c_Orderings_Oord__class_Oless(X4861,c_Rings_Oinverse__class_Odivide(X4861,X4859,X4860),X4858)
| ~ c_Orderings_Oord__class_Oless(X4861,c_Groups_Ozero__class_Ozero(X4861),X4860)
| ~ class_Fields_Olinordered__field(X4861) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq])])]) ).
fof(i_0_1632,plain,
! [X4953,X4954,X4955,X4956] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4956,c_Rings_Oinverse__class_Odivide(X4956,X4954,X4955),X4953)
| c_Orderings_Oord__class_Oless__eq(X4956,X4954,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4956),X4953),X4955))
| ~ c_Orderings_Oord__class_Oless(X4956,c_Groups_Ozero__class_Ozero(X4956),X4955)
| ~ class_Fields_Olinordered__field(X4956) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4956,X4954,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4956),X4953),X4955))
| c_Orderings_Oord__class_Oless__eq(X4956,c_Rings_Oinverse__class_Odivide(X4956,X4954,X4955),X4953)
| ~ c_Orderings_Oord__class_Oless(X4956,c_Groups_Ozero__class_Ozero(X4956),X4955)
| ~ class_Fields_Olinordered__field(X4956) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq])])]) ).
fof(i_0_1633,plain,
! [X4846,X4847,X4848,X4849] :
( ( ~ c_Orderings_Oord__class_Oless(X4849,X4847,c_Rings_Oinverse__class_Odivide(X4849,X4846,X4848))
| c_Orderings_Oord__class_Oless(X4849,X4846,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4849),X4847),X4848))
| ~ c_Orderings_Oord__class_Oless(X4849,X4848,c_Groups_Ozero__class_Ozero(X4849))
| ~ class_Fields_Olinordered__field(X4849) )
& ( ~ c_Orderings_Oord__class_Oless(X4849,X4846,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4849),X4847),X4848))
| c_Orderings_Oord__class_Oless(X4849,X4847,c_Rings_Oinverse__class_Odivide(X4849,X4846,X4848))
| ~ c_Orderings_Oord__class_Oless(X4849,X4848,c_Groups_Ozero__class_Ozero(X4849))
| ~ class_Fields_Olinordered__field(X4849) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq])])]) ).
fof(i_0_1634,plain,
! [X4941,X4942,X4943,X4944] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4944,X4942,c_Rings_Oinverse__class_Odivide(X4944,X4941,X4943))
| c_Orderings_Oord__class_Oless__eq(X4944,X4941,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4944),X4942),X4943))
| ~ c_Orderings_Oord__class_Oless(X4944,X4943,c_Groups_Ozero__class_Ozero(X4944))
| ~ class_Fields_Olinordered__field(X4944) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4944,X4941,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4944),X4942),X4943))
| c_Orderings_Oord__class_Oless__eq(X4944,X4942,c_Rings_Oinverse__class_Odivide(X4944,X4941,X4943))
| ~ c_Orderings_Oord__class_Oless(X4944,X4943,c_Groups_Ozero__class_Ozero(X4944))
| ~ class_Fields_Olinordered__field(X4944) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq])])]) ).
fof(i_0_1635,plain,
! [X4854,X4855,X4856,X4857] :
( ~ class_Fields_Olinordered__field(X4857)
| ~ c_Orderings_Oord__class_Oless(X4857,c_Groups_Ozero__class_Ozero(X4857),X4856)
| ~ c_Orderings_Oord__class_Oless(X4857,X4855,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4857),X4854),X4856))
| c_Orderings_Oord__class_Oless(X4857,c_Rings_Oinverse__class_Odivide(X4857,X4855,X4856),X4854) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less])]) ).
fof(i_0_1636,plain,
! [X4949,X4950,X4951,X4952] :
( ~ class_Fields_Olinordered__field(X4952)
| ~ c_Orderings_Oord__class_Oless(X4952,c_Groups_Ozero__class_Ozero(X4952),X4951)
| ~ c_Orderings_Oord__class_Oless__eq(X4952,X4950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4952),X4949),X4951))
| c_Orderings_Oord__class_Oless__eq(X4952,c_Rings_Oinverse__class_Odivide(X4952,X4950,X4951),X4949) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le])]) ).
fof(i_0_1637,plain,
! [X4850,X4851,X4852,X4853] :
( ~ class_Fields_Olinordered__field(X4853)
| ~ c_Orderings_Oord__class_Oless(X4853,c_Groups_Ozero__class_Ozero(X4853),X4852)
| ~ c_Orderings_Oord__class_Oless(X4853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4853),X4851),X4852),X4850)
| c_Orderings_Oord__class_Oless(X4853,X4851,c_Rings_Oinverse__class_Odivide(X4853,X4850,X4852)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos])]) ).
fof(i_0_1638,plain,
! [X4945,X4946,X4947,X4948] :
( ~ class_Fields_Olinordered__field(X4948)
| ~ c_Orderings_Oord__class_Oless(X4948,c_Groups_Ozero__class_Ozero(X4948),X4947)
| ~ c_Orderings_Oord__class_Oless__eq(X4948,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4948),X4946),X4947),X4945)
| c_Orderings_Oord__class_Oless__eq(X4948,X4946,c_Rings_Oinverse__class_Odivide(X4948,X4945,X4947)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos])]) ).
fof(i_0_1639,plain,
! [X4655,X4656,X4657,X4658,X4659,X4660] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4660)
| X4659 = c_Groups_Ozero__class_Ozero(X4660)
| X4658 != X4657
| X4656 = X4655
| c_Groups_Oplus__class_Oplus(X4660,X4658,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4660),X4659),X4656)) != c_Groups_Oplus__class_Oplus(X4660,X4657,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4660),X4659),X4655)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).
fof(i_0_1640,plain,
! [X5175,X5176,X5177] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5177)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5177),X5176),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5177),X5175))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5176,X5175) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).
fof(i_0_1641,plain,
! [X4994,X4995,X4996] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4996),X4995),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4996),X4994))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4995,X4994)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4996) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4995,X4994)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4996),X4995),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4996),X4994))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4996) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).
fof(i_0_1642,plain,
! [X5039,X5040,X5041] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5040),X5041),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5039),X5041))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5040,X5039)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5041) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5040,X5039)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5040),X5041),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5039),X5041))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5041) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1])])]) ).
fof(i_0_1643,plain,
! [X4911,X4912,X4913] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4913),X4912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4911),X4912))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4912)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4913,X4911) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4912)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4913),X4912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4911),X4912)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4913,X4911)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4913),X4912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4911),X4912)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).
fof(i_0_1644,plain,
! [X4988,X4989,X4990] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4990),X4989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4990),X4988))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4989,X4988)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4990) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4989,X4988)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4990),X4989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4990),X4988))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4990) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).
fof(i_0_1645,plain,
! [X4914,X4915,X4916] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4916),X4915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4916),X4914))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4916)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4915,X4914) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4916)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4916),X4915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4916),X4914)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4915,X4914)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4916),X4915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4916),X4914)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).
fof(i_0_1646,plain,
! [X5048,X5049,X5050] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5049),X5050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5048),X5050))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5049,X5048)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5050) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5049,X5048)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5049),X5050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5048),X5050))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5050) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1])])]) ).
fof(i_0_1647,plain,
! [X5051,X5052,X5053] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5053),X5052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5053),X5051))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5052,X5051)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5053) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5052,X5051)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5053),X5052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5053),X5051))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5053) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2])])]) ).
fof(i_0_1648,plain,
! [X3970,X3971] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3971),X3970)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3970,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3971),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RComplete_Onatceiling(X3970) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3971,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__eq])]) ).
fof(i_0_1649,plain,
! [X5667,X5668,X5669] :
( ~ class_RealVector_Oreal__normed__vector(X5669)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5669,X5668),c_RealVector_Onorm__class_Onorm(X5669,X5667)),c_RealVector_Onorm__class_Onorm(X5669,c_Groups_Ominus__class_Ominus(X5669,X5668,X5667))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq2])]) ).
fof(i_0_1650,plain,
! [X2989,X2990,X2991] :
( ~ class_RealVector_Oreal__normed__vector(X2991)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2991,c_Groups_Oplus__class_Oplus(X2991,X2990,X2989)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2991,X2990),c_RealVector_Onorm__class_Onorm(X2991,X2989))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq])]) ).
cnf(i_0_1651,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk36_2(X2,X1))))
| ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1276]) ).
cnf(i_0_1652,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk38_2(X2,X1))))
| ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1277]) ).
fof(i_0_1653,plain,
! [X3701,X3702,X3703,X3704] :
( ~ class_Rings_Ocomm__semiring__0(X3704)
| hAPP(c_Polynomial_Opoly(X3704,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3704),X3703,X3702)),X3701) = c_Groups_Oplus__class_Oplus(X3704,hAPP(c_Polynomial_Opoly(X3704,X3703),X3701),hAPP(c_Polynomial_Opoly(X3704,X3702),X3701)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__add])]) ).
fof(i_0_1654,plain,
! [X5417,X5418,X5419] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5419),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5418,X5417)),X5417) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5419),X5418),X5417),
inference(variable_rename,[status(thm)],[fact_zmod__simps_I3_J]) ).
fof(i_0_1655,plain,
! [X5414,X5415,X5416] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5416),X5415),X5414) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5416),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5415,X5414)),X5414),
inference(variable_rename,[status(thm)],[fact_zmod__zmult1__eq]) ).
fof(i_0_1656,plain,
! [X5756,X5757,X5758] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5756,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5757,X5758))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5756,X5758),X5757)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5758,X5757) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5756,X5758),X5757)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5756,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5757,X5758))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5758,X5757) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).
fof(i_0_1657,plain,
! [X5343,X5344,X5345] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5345,X5344)),X5343) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5345),X5343),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5344),X5343)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(i_0_1658,plain,
! [X4426,X4427,X4428] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4428,X4427)),X4426) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4428),X4426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4427),X4426)),
inference(variable_rename,[status(thm)],[fact_mod__mult__distrib]) ).
fof(i_0_1659,plain,
! [X4386,X4387,X4388] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4388,X4387)),X4386) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4388),X4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4387),X4386)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).
fof(i_0_1660,plain,
! [X5016,X5017,X5018] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5018,X5017)),X5016) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5018),X5016),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5017),X5016)),
inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).
cnf(i_0_1661,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_1304]) ).
fof(i_0_1662,plain,
! [X4156,X4157,X4158] :
( ~ class_Divides_Osemiring__div(X4158)
| c_Groups_Oplus__class_Oplus(X4158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4158),X4157),c_Divides_Odiv__class_Odiv(X4158,X4156,X4157)),c_Divides_Odiv__class_Omod(X4158,X4156,X4157)) = X4156 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality2])]) ).
fof(i_0_1663,plain,
! [X5143,X5144,X5145] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5145)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5145,hAPP(hAPP(c_Power_Opower__class_Opower(X5145),X5144),X5143)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5145,X5144)),X5143)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power__ineq])]) ).
fof(i_0_1664,plain,
! [X3301,X3302,X3303,X3304] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3304)
| ~ c_Orderings_Oord__class_Oless(X3304,c_Groups_Oplus__class_Oplus(X3304,X3303,X3302),c_Groups_Oplus__class_Oplus(X3304,X3301,X3302))
| c_Orderings_Oord__class_Oless(X3304,X3303,X3301) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_1665,plain,
! [X3280,X3281,X3282,X3283] :
( ( ~ c_Orderings_Oord__class_Oless(X3283,c_Groups_Oplus__class_Oplus(X3283,X3282,X3281),c_Groups_Oplus__class_Oplus(X3283,X3280,X3281))
| c_Orderings_Oord__class_Oless(X3283,X3282,X3280)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3283) )
& ( ~ c_Orderings_Oord__class_Oless(X3283,X3282,X3280)
| c_Orderings_Oord__class_Oless(X3283,c_Groups_Oplus__class_Oplus(X3283,X3282,X3281),c_Groups_Oplus__class_Oplus(X3283,X3280,X3281))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3283) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_1666,plain,
! [X3305,X3306,X3307,X3308] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3308)
| ~ c_Orderings_Oord__class_Oless(X3308,c_Groups_Oplus__class_Oplus(X3308,X3307,X3306),c_Groups_Oplus__class_Oplus(X3308,X3307,X3305))
| c_Orderings_Oord__class_Oless(X3308,X3306,X3305) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_1667,plain,
! [X3284,X3285,X3286,X3287] :
( ( ~ c_Orderings_Oord__class_Oless(X3287,c_Groups_Oplus__class_Oplus(X3287,X3286,X3285),c_Groups_Oplus__class_Oplus(X3287,X3286,X3284))
| c_Orderings_Oord__class_Oless(X3287,X3285,X3284)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3287) )
& ( ~ c_Orderings_Oord__class_Oless(X3287,X3285,X3284)
| c_Orderings_Oord__class_Oless(X3287,c_Groups_Oplus__class_Oplus(X3287,X3286,X3285),c_Groups_Oplus__class_Oplus(X3287,X3286,X3284))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3287) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_1668,plain,
! [X3272,X3273,X3274,X3275] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3275)
| ~ c_Orderings_Oord__class_Oless__eq(X3275,c_Groups_Oplus__class_Oplus(X3275,X3274,X3273),c_Groups_Oplus__class_Oplus(X3275,X3272,X3273))
| c_Orderings_Oord__class_Oless__eq(X3275,X3274,X3272) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_1669,plain,
! [X3251,X3252,X3253,X3254] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3254,c_Groups_Oplus__class_Oplus(X3254,X3253,X3252),c_Groups_Oplus__class_Oplus(X3254,X3251,X3252))
| c_Orderings_Oord__class_Oless__eq(X3254,X3253,X3251)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3254) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3254,X3253,X3251)
| c_Orderings_Oord__class_Oless__eq(X3254,c_Groups_Oplus__class_Oplus(X3254,X3253,X3252),c_Groups_Oplus__class_Oplus(X3254,X3251,X3252))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3254) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_1670,plain,
! [X3276,X3277,X3278,X3279] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3279)
| ~ c_Orderings_Oord__class_Oless__eq(X3279,c_Groups_Oplus__class_Oplus(X3279,X3278,X3277),c_Groups_Oplus__class_Oplus(X3279,X3278,X3276))
| c_Orderings_Oord__class_Oless__eq(X3279,X3277,X3276) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_1671,plain,
! [X3255,X3256,X3257,X3258] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3258,c_Groups_Oplus__class_Oplus(X3258,X3257,X3256),c_Groups_Oplus__class_Oplus(X3258,X3257,X3255))
| c_Orderings_Oord__class_Oless__eq(X3258,X3256,X3255)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3258) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3258,X3256,X3255)
| c_Orderings_Oord__class_Oless__eq(X3258,c_Groups_Oplus__class_Oplus(X3258,X3257,X3256),c_Groups_Oplus__class_Oplus(X3258,X3257,X3255))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3258) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
cnf(i_0_1672,plain,
( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = X2
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1305]) ).
cnf(i_0_1673,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_1306]) ).
cnf(i_0_1674,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_1307]) ).
cnf(i_0_1675,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_1308]) ).
fof(i_0_1676,plain,
! [X5699,X5700,X5701] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5701,X5700)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5701,X5699)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5700,X5701),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5699,X5701)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5700,X5699) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).
fof(i_0_1677,plain,
! [X4067,X4068] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4068,X4067)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4068),c_RealDef_Oreal(tc_Nat_Onat,X4067))),
inference(variable_rename,[status(thm)],[fact_real__of__nat__div4]) ).
fof(i_0_1678,plain,
! [X5258,X5259,X5260] :
( ~ class_Rings_Olinordered__semidom(X5260)
| ~ c_Orderings_Oord__class_Oless(X5260,c_Groups_Oone__class_Oone(X5260),X5259)
| c_Orderings_Oord__class_Oless(X5260,c_Groups_Oone__class_Oone(X5260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5260),X5259),hAPP(hAPP(c_Power_Opower__class_Opower(X5260),X5259),X5258))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).
fof(i_0_1679,plain,
! [X5159,X5160,X5161] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5161),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5160,X5159)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5161),X5160)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5161),X5159)),
inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(i_0_1680,plain,
! [X3682,X3683,X3684] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3684,X3683),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3684,X3682))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3683,X3682) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3683,X3682)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3684,X3683),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3684,X3682)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_1681,plain,
! [X3571,X3572,X3573] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3573,X3572),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3573,X3571))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3572,X3571) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3572,X3571)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3573,X3572),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3573,X3571)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_1682,plain,
! [X5382,X5383,X5384] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5384)
| X5384 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5383,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5384),X5382))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5383)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5382,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_1683,plain,
! [X5243,X5244,X5245] :
( ~ class_Fields_Ofield__inverse__zero(X5245)
| c_Rings_Oinverse__class_Odivide(X5245,c_Groups_Oone__class_Oone(X5245),hAPP(hAPP(c_Power_Opower__class_Opower(X5245),X5244),X5243)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5245),c_Rings_Oinverse__class_Odivide(X5245,c_Groups_Oone__class_Oone(X5245),X5244)),X5243) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__over])]) ).
fof(i_0_1684,plain,
! [X3029,X3030,X3031,X3032] :
( ~ class_Fields_Olinordered__field(X3032)
| ~ c_Orderings_Oord__class_Oless(X3032,X3031,X3030)
| ~ c_Orderings_Oord__class_Oless(X3032,c_Groups_Ozero__class_Ozero(X3032),X3029)
| c_Orderings_Oord__class_Oless(X3032,c_Rings_Oinverse__class_Odivide(X3032,X3031,X3029),c_Rings_Oinverse__class_Odivide(X3032,X3030,X3029)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono])]) ).
fof(i_0_1685,plain,
! [X3012,X3013,X3014,X3015] :
( ~ class_Fields_Olinordered__field__inverse__zero(X3015)
| ~ c_Orderings_Oord__class_Oless__eq(X3015,X3014,X3013)
| ~ c_Orderings_Oord__class_Oless__eq(X3015,c_Groups_Ozero__class_Ozero(X3015),X3012)
| c_Orderings_Oord__class_Oless__eq(X3015,c_Rings_Oinverse__class_Odivide(X3015,X3014,X3012),c_Rings_Oinverse__class_Odivide(X3015,X3013,X3012)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono])]) ).
fof(i_0_1686,plain,
! [X3025,X3026,X3027,X3028] :
( ~ class_Fields_Olinordered__field(X3028)
| ~ c_Orderings_Oord__class_Oless(X3028,X3027,X3026)
| ~ c_Orderings_Oord__class_Oless(X3028,X3025,c_Groups_Ozero__class_Ozero(X3028))
| c_Orderings_Oord__class_Oless(X3028,c_Rings_Oinverse__class_Odivide(X3028,X3026,X3025),c_Rings_Oinverse__class_Odivide(X3028,X3027,X3025)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg])]) ).
fof(i_0_1687,plain,
! [X3008,X3009,X3010,X3011] :
( ~ class_Fields_Olinordered__field__inverse__zero(X3011)
| ~ c_Orderings_Oord__class_Oless__eq(X3011,X3010,X3009)
| ~ c_Orderings_Oord__class_Oless__eq(X3011,X3008,c_Groups_Ozero__class_Ozero(X3011))
| c_Orderings_Oord__class_Oless__eq(X3011,c_Rings_Oinverse__class_Odivide(X3011,X3009,X3008),c_Rings_Oinverse__class_Odivide(X3011,X3010,X3008)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg])]) ).
fof(i_0_1688,plain,
! [X5379,X5380,X5381] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5381)
| X5381 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5380,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5381),X5379))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5380,X5381)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5379) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).
fof(i_0_1689,plain,
! [X5446,X5447] : X5447 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5446),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5447,X5446)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5447,X5446)),
inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality]) ).
fof(i_0_1690,plain,
! [X5298,X5299,X5300,X5301] :
( ~ class_Rings_Olinordered__semidom(X5301)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5301),X5300),X5299) != hAPP(hAPP(c_Power_Opower__class_Opower(X5301),X5298),X5299)
| ~ c_Orderings_Oord__class_Oless__eq(X5301,c_Groups_Ozero__class_Ozero(X5301),X5300)
| ~ c_Orderings_Oord__class_Oless__eq(X5301,c_Groups_Ozero__class_Ozero(X5301),X5298)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5299)
| X5300 = X5298 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).
fof(i_0_1691,plain,
! [X4664,X4665,X4666] :
( ~ class_Rings_Ocomm__semiring__1(X4666)
| c_Groups_Oplus__class_Oplus(X4666,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4666),X4665),X4664),X4664) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4666),c_Groups_Oplus__class_Oplus(X4666,X4665,c_Groups_Oone__class_Oone(X4666))),X4664) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).
fof(i_0_1692,plain,
! [X4667,X4668,X4669] :
( ~ class_Rings_Ocomm__semiring__1(X4669)
| c_Groups_Oplus__class_Oplus(X4669,X4668,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4669),X4667),X4668)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4669),c_Groups_Oplus__class_Oplus(X4669,X4667,c_Groups_Oone__class_Oone(X4669))),X4668) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).
fof(i_0_1693,plain,
! [X4021,X4022] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4022),X4021)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4021,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4022),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RComplete_Onatfloor(X4021) = X4022 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__eq])]) ).
fof(i_0_1694,plain,
! [X4831,X4832,X4833] :
( ~ class_Rings_Olinordered__idom(X4833)
| ~ c_Orderings_Oord__class_Oless__eq(X4833,c_Groups_Ozero__class_Ozero(X4833),X4832)
| ~ c_Orderings_Oord__class_Oless__eq(X4833,c_Groups_Ozero__class_Ozero(X4833),X4831)
| ~ c_Orderings_Oord__class_Oless__eq(X4833,X4831,c_Groups_Oone__class_Oone(X4833))
| c_Orderings_Oord__class_Oless__eq(X4833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4833),X4832),X4831),X4832) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).
fof(i_0_1695,plain,
! [X4828,X4829,X4830] :
( ~ class_Rings_Olinordered__idom(X4830)
| ~ c_Orderings_Oord__class_Oless__eq(X4830,c_Groups_Ozero__class_Ozero(X4830),X4829)
| ~ c_Orderings_Oord__class_Oless__eq(X4830,c_Groups_Ozero__class_Ozero(X4830),X4828)
| ~ c_Orderings_Oord__class_Oless__eq(X4830,X4828,c_Groups_Oone__class_Oone(X4830))
| c_Orderings_Oord__class_Oless__eq(X4830,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4830),X4828),X4829),X4829) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).
fof(i_0_1696,plain,
! [X5054,X5055,X5056,X5057] :
( ~ class_RealVector_Oreal__normed__vector(X5057)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5056,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5057,X5055),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5056),c_RealVector_Onorm__class_Onorm(X5057,X5054)))
| X5055 = c_Groups_Ozero__class_Ozero(X5057) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ratiotest__lemma])]) ).
fof(i_0_1697,plain,
! [X4632,X4633,X4634,X4635] :
( ~ class_Rings_Olinordered__semiring__strict(X4635)
| ~ c_Orderings_Oord__class_Oless(X4635,X4634,X4633)
| ~ c_Orderings_Oord__class_Oless(X4635,c_Groups_Ozero__class_Ozero(X4635),X4632)
| c_Orderings_Oord__class_Oless(X4635,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4635),X4634),X4632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4635),X4633),X4632)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).
fof(i_0_1698,plain,
! [X4640,X4641,X4642,X4643] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X4643)
| ~ c_Orderings_Oord__class_Oless(X4643,X4642,X4641)
| ~ c_Orderings_Oord__class_Oless(X4643,c_Groups_Ozero__class_Ozero(X4643),X4640)
| c_Orderings_Oord__class_Oless(X4643,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4643),X4640),X4642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4643),X4640),X4641)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).
fof(i_0_1699,plain,
! [X4636,X4637,X4638,X4639] :
( ~ class_Rings_Olinordered__semiring__strict(X4639)
| ~ c_Orderings_Oord__class_Oless(X4639,X4638,X4637)
| ~ c_Orderings_Oord__class_Oless(X4639,c_Groups_Ozero__class_Ozero(X4639),X4636)
| c_Orderings_Oord__class_Oless(X4639,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4639),X4636),X4638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4639),X4636),X4637)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).
fof(i_0_1700,plain,
! [X5208,X5209,X5210,X5211] :
( ~ class_Rings_Olinordered__semidom(X5211)
| ~ c_Orderings_Oord__class_Oless__eq(X5211,X5210,X5209)
| ~ c_Orderings_Oord__class_Oless__eq(X5211,c_Groups_Ozero__class_Ozero(X5211),X5210)
| c_Orderings_Oord__class_Oless__eq(X5211,hAPP(hAPP(c_Power_Opower__class_Opower(X5211),X5210),X5208),hAPP(hAPP(c_Power_Opower__class_Opower(X5211),X5209),X5208)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).
fof(i_0_1701,plain,
! [X4557,X4558,X4559,X4560] :
( ~ class_Rings_Oordered__semiring(X4560)
| ~ c_Orderings_Oord__class_Oless__eq(X4560,X4559,X4558)
| ~ c_Orderings_Oord__class_Oless__eq(X4560,c_Groups_Ozero__class_Ozero(X4560),X4557)
| c_Orderings_Oord__class_Oless__eq(X4560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4560),X4559),X4557),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4560),X4558),X4557)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).
fof(i_0_1702,plain,
! [X4565,X4566,X4567,X4568] :
( ~ class_Rings_Oordered__comm__semiring(X4568)
| ~ c_Orderings_Oord__class_Oless__eq(X4568,X4567,X4566)
| ~ c_Orderings_Oord__class_Oless__eq(X4568,c_Groups_Ozero__class_Ozero(X4568),X4565)
| c_Orderings_Oord__class_Oless__eq(X4568,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4568),X4565),X4567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4568),X4565),X4566)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).
fof(i_0_1703,plain,
! [X4561,X4562,X4563,X4564] :
( ~ class_Rings_Oordered__semiring(X4564)
| ~ c_Orderings_Oord__class_Oless__eq(X4564,X4563,X4562)
| ~ c_Orderings_Oord__class_Oless__eq(X4564,c_Groups_Ozero__class_Ozero(X4564),X4561)
| c_Orderings_Oord__class_Oless__eq(X4564,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4564),X4561),X4563),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4564),X4561),X4562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).
fof(i_0_1704,plain,
! [X4644,X4645,X4646,X4647] :
( ~ class_Rings_Olinordered__ring__strict(X4647)
| ~ c_Orderings_Oord__class_Oless(X4647,X4646,X4645)
| ~ c_Orderings_Oord__class_Oless(X4647,X4644,c_Groups_Ozero__class_Ozero(X4647))
| c_Orderings_Oord__class_Oless(X4647,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4647),X4645),X4644),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4647),X4646),X4644)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).
fof(i_0_1705,plain,
! [X4648,X4649,X4650,X4651] :
( ~ class_Rings_Olinordered__ring__strict(X4651)
| ~ c_Orderings_Oord__class_Oless(X4651,X4650,X4649)
| ~ c_Orderings_Oord__class_Oless(X4651,X4648,c_Groups_Ozero__class_Ozero(X4651))
| c_Orderings_Oord__class_Oless(X4651,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4651),X4648),X4649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4651),X4648),X4650)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).
fof(i_0_1706,plain,
! [X4569,X4570,X4571,X4572] :
( ~ class_Rings_Oordered__ring(X4572)
| ~ c_Orderings_Oord__class_Oless__eq(X4572,X4571,X4570)
| ~ c_Orderings_Oord__class_Oless__eq(X4572,X4569,c_Groups_Ozero__class_Ozero(X4572))
| c_Orderings_Oord__class_Oless__eq(X4572,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4572),X4570),X4569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4572),X4571),X4569)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).
fof(i_0_1707,plain,
! [X4573,X4574,X4575,X4576] :
( ~ class_Rings_Oordered__ring(X4576)
| ~ c_Orderings_Oord__class_Oless__eq(X4576,X4575,X4574)
| ~ c_Orderings_Oord__class_Oless__eq(X4576,X4573,c_Groups_Ozero__class_Ozero(X4576))
| c_Orderings_Oord__class_Oless__eq(X4576,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4576),X4573),X4574),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4576),X4573),X4575)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).
fof(i_0_1708,plain,
! [X5764,X5765,X5766] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5766,X5765)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5764,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5765,X5764),X5766)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).
fof(i_0_1709,plain,
! [X3296,X3297,X3298,X3299,X3300] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3300)
| ~ c_Orderings_Oord__class_Oless(X3300,X3299,X3298)
| ~ c_Orderings_Oord__class_Oless(X3300,X3297,X3296)
| c_Orderings_Oord__class_Oless(X3300,c_Groups_Oplus__class_Oplus(X3300,X3299,X3297),c_Groups_Oplus__class_Oplus(X3300,X3298,X3296)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_1710,plain,
! [X3406,X3407,X3408,X3409,X3410] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3410)
| ~ c_Orderings_Oord__class_Oless__eq(X3410,X3409,X3408)
| ~ c_Orderings_Oord__class_Oless(X3410,X3407,X3406)
| c_Orderings_Oord__class_Oless(X3410,c_Groups_Oplus__class_Oplus(X3410,X3409,X3407),c_Groups_Oplus__class_Oplus(X3410,X3408,X3406)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_1711,plain,
! [X3401,X3402,X3403,X3404,X3405] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3405)
| ~ c_Orderings_Oord__class_Oless(X3405,X3404,X3403)
| ~ c_Orderings_Oord__class_Oless__eq(X3405,X3402,X3401)
| c_Orderings_Oord__class_Oless(X3405,c_Groups_Oplus__class_Oplus(X3405,X3404,X3402),c_Groups_Oplus__class_Oplus(X3405,X3403,X3401)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_1712,plain,
! [X3267,X3268,X3269,X3270,X3271] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3271)
| ~ c_Orderings_Oord__class_Oless__eq(X3271,X3270,X3269)
| ~ c_Orderings_Oord__class_Oless__eq(X3271,X3268,X3267)
| c_Orderings_Oord__class_Oless__eq(X3271,c_Groups_Oplus__class_Oplus(X3271,X3270,X3268),c_Groups_Oplus__class_Oplus(X3271,X3269,X3267)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_1713,plain,
! [X5510,X5511] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5511)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5511,X5510),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5511,X5510) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5511,X5510) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__trivial])]) ).
fof(i_0_1714,plain,
! [X5272,X5273,X5274,X5275] :
( ~ class_Rings_Olinordered__semidom(X5275)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5274,X5273)
| ~ c_Orderings_Oord__class_Oless(X5275,c_Groups_Oone__class_Oone(X5275),X5272)
| c_Orderings_Oord__class_Oless(X5275,hAPP(hAPP(c_Power_Opower__class_Opower(X5275),X5272),X5274),hAPP(hAPP(c_Power_Opower__class_Opower(X5275),X5272),X5273)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).
fof(i_0_1715,plain,
! [X5284,X5285,X5286,X5287] :
( ~ class_Rings_Olinordered__semidom(X5287)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5286,X5285)
| ~ c_Orderings_Oord__class_Oless__eq(X5287,c_Groups_Oone__class_Oone(X5287),X5284)
| c_Orderings_Oord__class_Oless__eq(X5287,hAPP(hAPP(c_Power_Opower__class_Opower(X5287),X5284),X5286),hAPP(hAPP(c_Power_Opower__class_Opower(X5287),X5284),X5285)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).
fof(i_0_1716,plain,
! [X4015,X4016,X4018] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk34_2(X4015,X4016),X4015)
| ~ hBOOL(hAPP(X4016,X4015))
| hBOOL(hAPP(X4016,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4018,esk34_2(X4015,X4016))
| ~ hBOOL(hAPP(X4016,X4018))
| ~ hBOOL(hAPP(X4016,X4015))
| hBOOL(hAPP(X4016,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X4016,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk34_2(X4015,X4016),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X4016,X4015))
| hBOOL(hAPP(X4016,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_1309])])])])]) ).
fof(i_0_1717,plain,
! [X3357,X3358,X3359,X3360] :
( ~ class_Rings_Odivision__ring(X3360)
| c_Rings_Oinverse__class_Odivide(X3360,c_Groups_Oplus__class_Oplus(X3360,X3359,X3358),X3357) = c_Groups_Oplus__class_Oplus(X3360,c_Rings_Oinverse__class_Odivide(X3360,X3359,X3357),c_Rings_Oinverse__class_Odivide(X3360,X3358,X3357)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__distrib])]) ).
fof(i_0_1718,plain,
! [X3119,X3120,X3121,X3122] :
( ~ class_RealVector_Oreal__normed__field(X3122)
| c_Rings_Oinverse__class_Odivide(X3122,c_Groups_Oplus__class_Oplus(X3122,X3121,X3120),X3119) = c_Groups_Oplus__class_Oplus(X3122,c_Rings_Oinverse__class_Odivide(X3122,X3121,X3119),c_Rings_Oinverse__class_Odivide(X3122,X3120,X3119)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Oadd])]) ).
cnf(i_0_1719,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1310]) ).
fof(i_0_1720,plain,
! [X5578,X5579,X5580] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5580,X5579)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5578)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5580,X5578),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5579,X5578)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1])]) ).
fof(i_0_1721,plain,
! [X4071,X4072,X4073] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4073)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4073,X4072)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4071,X4072),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4071,X4073)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono2])]) ).
fof(i_0_1722,plain,
! [X5581,X5582,X5583] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5583,X5582)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5581,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,X5582,X5581),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5583,X5581)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg])]) ).
fof(i_0_1723,plain,
! [X5385,X5386,X5387] :
( ( ~ hBOOL(hAPP(X5387,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5386,X5385)))
| epred2_3(X5387,X5385,X5386) )
& ( ~ epred2_3(X5387,X5385,X5386)
| hBOOL(hAPP(X5387,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5386,X5385))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1311])]) ).
fof(i_0_1724,plain,
! [X5328,X5329,X5330] :
( ( ~ hBOOL(hAPP(X5330,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5329,X5328)))
| epred1_3(X5330,X5328,X5329) )
& ( ~ epred1_3(X5330,X5328,X5329)
| hBOOL(hAPP(X5330,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5329,X5328))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1312])]) ).
fof(i_0_1725,plain,
! [X5550,X5551,X5552,X5553] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5553,X5552)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5551,X5550)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5553,X5551),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5552,X5550)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).
fof(i_0_1726,plain,
! [X5776,X5777,X5778] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5778,X5777)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5776,X5778)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5778,X5776),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5777,X5776)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).
fof(i_0_1727,plain,
! [X5731,X5732,X5733] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5733,X5732)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5733,X5731)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5731,X5732),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5731,X5733)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).
fof(i_0_1728,plain,
! [X3669,X3670,X3671,X3672] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3672,X3671)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3670,X3669)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3672,X3670),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3671,X3669)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_1729,plain,
! [X3558,X3559,X3560,X3561] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3561,X3560)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3559,X3558)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3561,X3559),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3560,X3558)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_1730,plain,
! [X4435,X4436,X4437,X4438] :
( ~ class_Divides_Osemiring__div(X4438)
| c_Divides_Odiv__class_Omod(X4438,c_Groups_Oplus__class_Oplus(X4438,X4437,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4438),X4436),X4435)),X4436) = c_Divides_Odiv__class_Omod(X4438,X4437,X4436) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2])]) ).
fof(i_0_1731,plain,
! [X4439,X4440,X4441,X4442] :
( ~ class_Divides_Osemiring__div(X4442)
| c_Divides_Odiv__class_Omod(X4442,c_Groups_Oplus__class_Oplus(X4442,X4441,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4442),X4440),X4439)),X4439) = c_Divides_Odiv__class_Omod(X4442,X4441,X4439) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])]) ).
fof(i_0_1732,plain,
! [X4652,X4653,X4654] :
( ( X4653 = c_Groups_Ozero__class_Ozero(X4654)
| c_Groups_Oplus__class_Oplus(X4654,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4654),X4653),X4653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4654),X4652),X4652)) != c_Groups_Ozero__class_Ozero(X4654)
| ~ class_Rings_Olinordered__ring__strict(X4654) )
& ( X4652 = c_Groups_Ozero__class_Ozero(X4654)
| c_Groups_Oplus__class_Oplus(X4654,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4654),X4653),X4653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4654),X4652),X4652)) != c_Groups_Ozero__class_Ozero(X4654)
| ~ class_Rings_Olinordered__ring__strict(X4654) )
& ( X4653 != c_Groups_Ozero__class_Ozero(X4654)
| X4652 != c_Groups_Ozero__class_Ozero(X4654)
| c_Groups_Oplus__class_Oplus(X4654,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4654),X4653),X4653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4654),X4652),X4652)) = c_Groups_Ozero__class_Ozero(X4654)
| ~ class_Rings_Olinordered__ring__strict(X4654) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).
cnf(i_0_1733,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_1313]) ).
cnf(i_0_1734,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_1314]) ).
fof(i_0_1735,plain,
! [X4410,X4411,X4412,X4413] :
( ~ class_Divides_Osemiring__div(X4413)
| c_Divides_Odiv__class_Omod(X4413,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4413),X4412),X4411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4413),X4412),X4410)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4413),X4412),c_Divides_Odiv__class_Omod(X4413,X4411,X4410)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1])]) ).
fof(i_0_1736,plain,
! [X4322,X4323,X4324,X4325] :
( ~ class_RealVector_Oreal__normed__algebra(X4325)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4325),X4324),c_Groups_Oplus__class_Oplus(X4325,X4323,X4322)) = c_Groups_Oplus__class_Oplus(X4325,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4325),X4324),X4323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4325),X4324),X4322)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd])]) ).
fof(i_0_1737,plain,
! [X4318,X4319,X4320,X4321] :
( ~ class_RealVector_Oreal__normed__algebra(X4321)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4321),X4320),c_Groups_Oplus__class_Oplus(X4321,X4319,X4318)) = c_Groups_Oplus__class_Oplus(X4321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4321),X4320),X4319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4321),X4320),X4318)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right])]) ).
fof(i_0_1738,plain,
! [X4213,X4214,X4215,X4216] :
( ~ class_Rings_Ocomm__semiring__1(X4216)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4216),X4215),c_Groups_Oplus__class_Oplus(X4216,X4214,X4213)) = c_Groups_Oplus__class_Oplus(X4216,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4216),X4215),X4214),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4216),X4215),X4213)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).
fof(i_0_1739,plain,
! [X4745,X4746,X4747] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4747)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4747),X4746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4747),X4745)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4746,X4745)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4747),X4746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4747),X4745)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4747)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4746,X4745)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4747),X4746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4747),X4745)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).
fof(i_0_1740,plain,
! [X4742,X4743,X4744] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4743)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4744),X4743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4742),X4743)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4744,X4742)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4744),X4743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4742),X4743)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4743)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4744,X4742)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4744),X4743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4742),X4743)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).
fof(i_0_1741,plain,
! [X5560,X5561] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5560,X5561)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5561,X5560))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5561) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5560)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5561,X5560))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5561) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5560,X5561)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5560)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5561,X5560))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5561) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])]) ).
fof(i_0_1742,plain,
! [X4619,X4620,X4621] :
( ~ class_Rings_Olinordered__semiring__strict(X4621)
| ~ c_Orderings_Oord__class_Oless(X4621,c_Groups_Ozero__class_Ozero(X4621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4621),X4620),X4619))
| ~ c_Orderings_Oord__class_Oless(X4621,c_Groups_Ozero__class_Ozero(X4621),X4619)
| c_Orderings_Oord__class_Oless(X4621,c_Groups_Ozero__class_Ozero(X4621),X4620) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).
fof(i_0_1743,plain,
! [X4616,X4617,X4618] :
( ~ class_Rings_Olinordered__semiring__strict(X4618)
| ~ c_Orderings_Oord__class_Oless(X4618,c_Groups_Ozero__class_Ozero(X4618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4618),X4617),X4616))
| ~ c_Orderings_Oord__class_Oless(X4618,c_Groups_Ozero__class_Ozero(X4618),X4617)
| c_Orderings_Oord__class_Oless(X4618,c_Groups_Ozero__class_Ozero(X4618),X4616) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).
cnf(i_0_1744,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1305]) ).
fof(i_0_1745,plain,
! [X5190,X5191,X5192] :
( ~ class_Groups_Omonoid__mult(X5192)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5192),hAPP(hAPP(c_Power_Opower__class_Opower(X5192),X5191),X5190)),X5191) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5192),X5191),hAPP(hAPP(c_Power_Opower__class_Opower(X5192),X5191),X5190)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).
fof(i_0_1746,plain,
! [X4289,X4290,X4291,X4292] :
( ~ class_Groups_Oab__semigroup__mult(X4292)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4292),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4292),X4291),X4290)),X4289) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4292),X4291),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4292),X4290),X4289)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).
fof(i_0_1747,plain,
! [X4194,X4195,X4196,X4197] :
( ~ class_Rings_Ocomm__semiring__1(X4197)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4197),X4196),X4195)),X4194) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4197),X4196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4197),X4195),X4194)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).
fof(i_0_1748,plain,
! [X4198,X4199,X4200,X4201] :
( ~ class_Rings_Ocomm__semiring__1(X4201)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4201),X4200),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4201),X4199),X4198)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4201),X4200),X4199)),X4198) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).
fof(i_0_1749,plain,
! [X3105,X3106] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3106,X3105)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3106),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X3105)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3106),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X3105))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3106,X3105) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__real__le])]) ).
fof(i_0_1750,plain,
! [X3239,X3240] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3240,X3239)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3240),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3239),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3240),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3239),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3240,X3239) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__real__less])]) ).
cnf(i_0_1751,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk35_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_1315]) ).
cnf(i_0_1752,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_1316]) ).
cnf(i_0_1753,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_1317]) ).
fof(i_0_1754,plain,
! [X5199,X5200,X5201,X5202] :
( ~ class_Groups_Omonoid__mult(X5202)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5202),X5201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5200),X5199)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5202),hAPP(hAPP(c_Power_Opower__class_Opower(X5202),X5201),X5200)),X5199) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).
fof(i_0_1755,plain,
! [X5115,X5116,X5117,X5118] :
( ~ class_Rings_Ocomm__semiring__1(X5118)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5118),hAPP(hAPP(c_Power_Opower__class_Opower(X5118),X5117),X5116)),X5115) = hAPP(hAPP(c_Power_Opower__class_Opower(X5118),X5117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5116),X5115)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).
fof(i_0_1756,plain,
! [X5333,X5334,X5335] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5335,X5334)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5333)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5333),X5335),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5333),X5334)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).
fof(i_0_1757,plain,
! [X4739,X4740,X4741] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4741,X4740)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4739)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4741),X4739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4740),X4739)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).
fof(i_0_1758,plain,
! [X4736,X4737,X4738] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4738,X4737)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4736)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4736),X4738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4736),X4737)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).
fof(i_0_1759,plain,
! [X5034,X5035,X5036] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5036)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5035,X5034)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5036),X5035),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5036),X5034)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__mono2])]) ).
fof(i_0_1760,plain,
! [X5781,X5782,X5783] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5783,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5782,X5781))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5783,X5781),X5782) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5783,X5781),X5782)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5783,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5782,X5781)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).
fof(i_0_1761,plain,
! [X5767,X5768,X5769] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5769,X5768),X5767)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5769,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5767,X5768)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5769,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5767,X5768))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5769,X5768),X5767) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).
fof(i_0_1762,plain,
! [X4379,X4380,X4381,X4382] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4382,X4381)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4380,X4379)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4382),X4380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4381),X4379)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).
fof(i_0_1763,plain,
! [X5030,X5031,X5032,X5033] :
( ~ class_Fields_Ofield(X5033)
| c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X5033),X5032,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5033)),X5031),X5030)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X5033),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X5033),X5032,X5031),X5030) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__div__mult__right])]) ).
fof(i_0_1764,plain,
! [X5745,X5746,X5747] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5747,X5746)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5746,X5747),X5745) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5746,X5745),X5747) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).
fof(i_0_1765,plain,
! [X5742,X5743,X5744] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5744,X5743)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5743,X5742),X5744) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5743,X5744),X5742) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).
fof(i_0_1766,plain,
! [X5748,X5749,X5750] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5750,X5749)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5748,X5749),X5750) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5748,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5749,X5750)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).
fof(i_0_1767,plain,
! [X5770,X5771,X5772] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5772,X5771)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5770,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5771,X5772)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5770,X5772),X5771) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).
fof(i_0_1768,plain,
! [X5759,X5760,X5761] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5761,X5760)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5759,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5760,X5761)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5759,X5760),X5761) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).
fof(i_0_1769,plain,
! [X5556,X5557] :
( ( ~ 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,X5556,X5557))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5556)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5557) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5556)
| 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,X5556,X5557))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5557) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])]) ).
fof(i_0_1770,plain,
! [X5590,X5591] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5590,X5591),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5590)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5591,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5590)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5590,X5591),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5591,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_1771,plain,
! [X5592,X5593] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5592,X5593),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5592,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5593) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5592,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5592,X5593),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5593) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])]) ).
fof(i_0_1772,plain,
! [X5569,X5570] :
( ( ~ 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,X5569,X5570))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5569,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5570,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5569,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,X5569,X5570))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5570,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_1773,plain,
! [X3474,X3475,X3476] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3476),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3476)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3475)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3474,X3475)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3474,esk21_0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk23_1(X3474)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3474,esk21_0) )
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk23_1(X3474))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,esk22_1(X3474))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3474,esk21_0) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3474,esk22_1(X3474))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3474,esk21_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096])])])])]) ).
fof(i_0_1774,plain,
! [X2960,X2961,X2962,X2963] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2962),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2962)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2961)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2960,X2961)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2960,v_s____) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk4_1(X2963)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2963,v_s____) )
& ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk4_1(X2963))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,esk3_1(X2963))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2963,v_s____) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2963,esk3_1(X2963))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2963,v_s____) ) ),
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_s])])])])])]) ).
fof(i_0_1775,plain,
! [X5558,X5559] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5558,X5559))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5559,X5558)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5559) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5559,X5558)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5558,X5559))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5559) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])]) ).
fof(i_0_1776,plain,
! [X3045,X3046,X3047] :
( ( c_Orderings_Oord__class_Oless(X3047,X3046,c_Groups_Ozero__class_Ozero(X3047))
| c_Orderings_Oord__class_Oless(X3047,c_Groups_Ozero__class_Ozero(X3047),X3046)
| ~ c_Orderings_Oord__class_Oless(X3047,c_Rings_Oinverse__class_Odivide(X3047,X3046,X3045),c_Groups_Ozero__class_Ozero(X3047))
| ~ class_Fields_Olinordered__field__inverse__zero(X3047) )
& ( c_Orderings_Oord__class_Oless(X3047,c_Groups_Ozero__class_Ozero(X3047),X3045)
| c_Orderings_Oord__class_Oless(X3047,c_Groups_Ozero__class_Ozero(X3047),X3046)
| ~ c_Orderings_Oord__class_Oless(X3047,c_Rings_Oinverse__class_Odivide(X3047,X3046,X3045),c_Groups_Ozero__class_Ozero(X3047))
| ~ class_Fields_Olinordered__field__inverse__zero(X3047) )
& ( c_Orderings_Oord__class_Oless(X3047,X3046,c_Groups_Ozero__class_Ozero(X3047))
| c_Orderings_Oord__class_Oless(X3047,X3045,c_Groups_Ozero__class_Ozero(X3047))
| ~ c_Orderings_Oord__class_Oless(X3047,c_Rings_Oinverse__class_Odivide(X3047,X3046,X3045),c_Groups_Ozero__class_Ozero(X3047))
| ~ class_Fields_Olinordered__field__inverse__zero(X3047) )
& ( c_Orderings_Oord__class_Oless(X3047,c_Groups_Ozero__class_Ozero(X3047),X3045)
| c_Orderings_Oord__class_Oless(X3047,X3045,c_Groups_Ozero__class_Ozero(X3047))
| ~ c_Orderings_Oord__class_Oless(X3047,c_Rings_Oinverse__class_Odivide(X3047,X3046,X3045),c_Groups_Ozero__class_Ozero(X3047))
| ~ class_Fields_Olinordered__field__inverse__zero(X3047) )
& ( ~ c_Orderings_Oord__class_Oless(X3047,c_Groups_Ozero__class_Ozero(X3047),X3046)
| ~ c_Orderings_Oord__class_Oless(X3047,X3045,c_Groups_Ozero__class_Ozero(X3047))
| c_Orderings_Oord__class_Oless(X3047,c_Rings_Oinverse__class_Odivide(X3047,X3046,X3045),c_Groups_Ozero__class_Ozero(X3047))
| ~ class_Fields_Olinordered__field__inverse__zero(X3047) )
& ( ~ c_Orderings_Oord__class_Oless(X3047,X3046,c_Groups_Ozero__class_Ozero(X3047))
| ~ c_Orderings_Oord__class_Oless(X3047,c_Groups_Ozero__class_Ozero(X3047),X3045)
| c_Orderings_Oord__class_Oless(X3047,c_Rings_Oinverse__class_Odivide(X3047,X3046,X3045),c_Groups_Ozero__class_Ozero(X3047))
| ~ class_Fields_Olinordered__field__inverse__zero(X3047) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff])])]) ).
fof(i_0_1777,plain,
! [X3016,X3017,X3018] :
( ( c_Orderings_Oord__class_Oless__eq(X3018,X3017,c_Groups_Ozero__class_Ozero(X3018))
| c_Orderings_Oord__class_Oless__eq(X3018,c_Groups_Ozero__class_Ozero(X3018),X3017)
| ~ c_Orderings_Oord__class_Oless__eq(X3018,c_Rings_Oinverse__class_Odivide(X3018,X3017,X3016),c_Groups_Ozero__class_Ozero(X3018))
| ~ class_Fields_Olinordered__field__inverse__zero(X3018) )
& ( c_Orderings_Oord__class_Oless__eq(X3018,c_Groups_Ozero__class_Ozero(X3018),X3016)
| c_Orderings_Oord__class_Oless__eq(X3018,c_Groups_Ozero__class_Ozero(X3018),X3017)
| ~ c_Orderings_Oord__class_Oless__eq(X3018,c_Rings_Oinverse__class_Odivide(X3018,X3017,X3016),c_Groups_Ozero__class_Ozero(X3018))
| ~ class_Fields_Olinordered__field__inverse__zero(X3018) )
& ( c_Orderings_Oord__class_Oless__eq(X3018,X3017,c_Groups_Ozero__class_Ozero(X3018))
| c_Orderings_Oord__class_Oless__eq(X3018,X3016,c_Groups_Ozero__class_Ozero(X3018))
| ~ c_Orderings_Oord__class_Oless__eq(X3018,c_Rings_Oinverse__class_Odivide(X3018,X3017,X3016),c_Groups_Ozero__class_Ozero(X3018))
| ~ class_Fields_Olinordered__field__inverse__zero(X3018) )
& ( c_Orderings_Oord__class_Oless__eq(X3018,c_Groups_Ozero__class_Ozero(X3018),X3016)
| c_Orderings_Oord__class_Oless__eq(X3018,X3016,c_Groups_Ozero__class_Ozero(X3018))
| ~ c_Orderings_Oord__class_Oless__eq(X3018,c_Rings_Oinverse__class_Odivide(X3018,X3017,X3016),c_Groups_Ozero__class_Ozero(X3018))
| ~ class_Fields_Olinordered__field__inverse__zero(X3018) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3018,c_Groups_Ozero__class_Ozero(X3018),X3017)
| ~ c_Orderings_Oord__class_Oless__eq(X3018,X3016,c_Groups_Ozero__class_Ozero(X3018))
| c_Orderings_Oord__class_Oless__eq(X3018,c_Rings_Oinverse__class_Odivide(X3018,X3017,X3016),c_Groups_Ozero__class_Ozero(X3018))
| ~ class_Fields_Olinordered__field__inverse__zero(X3018) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3018,X3017,c_Groups_Ozero__class_Ozero(X3018))
| ~ c_Orderings_Oord__class_Oless__eq(X3018,c_Groups_Ozero__class_Ozero(X3018),X3016)
| c_Orderings_Oord__class_Oless__eq(X3018,c_Rings_Oinverse__class_Odivide(X3018,X3017,X3016),c_Groups_Ozero__class_Ozero(X3018))
| ~ class_Fields_Olinordered__field__inverse__zero(X3018) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff])])]) ).
fof(i_0_1778,plain,
! [X3048,X3049,X3050] :
( ( c_Orderings_Oord__class_Oless(X3050,X3049,c_Groups_Ozero__class_Ozero(X3050))
| c_Orderings_Oord__class_Oless(X3050,c_Groups_Ozero__class_Ozero(X3050),X3049)
| ~ c_Orderings_Oord__class_Oless(X3050,c_Groups_Ozero__class_Ozero(X3050),c_Rings_Oinverse__class_Odivide(X3050,X3049,X3048))
| ~ class_Fields_Olinordered__field__inverse__zero(X3050) )
& ( c_Orderings_Oord__class_Oless(X3050,X3048,c_Groups_Ozero__class_Ozero(X3050))
| c_Orderings_Oord__class_Oless(X3050,c_Groups_Ozero__class_Ozero(X3050),X3049)
| ~ c_Orderings_Oord__class_Oless(X3050,c_Groups_Ozero__class_Ozero(X3050),c_Rings_Oinverse__class_Odivide(X3050,X3049,X3048))
| ~ class_Fields_Olinordered__field__inverse__zero(X3050) )
& ( c_Orderings_Oord__class_Oless(X3050,X3049,c_Groups_Ozero__class_Ozero(X3050))
| c_Orderings_Oord__class_Oless(X3050,c_Groups_Ozero__class_Ozero(X3050),X3048)
| ~ c_Orderings_Oord__class_Oless(X3050,c_Groups_Ozero__class_Ozero(X3050),c_Rings_Oinverse__class_Odivide(X3050,X3049,X3048))
| ~ class_Fields_Olinordered__field__inverse__zero(X3050) )
& ( c_Orderings_Oord__class_Oless(X3050,X3048,c_Groups_Ozero__class_Ozero(X3050))
| c_Orderings_Oord__class_Oless(X3050,c_Groups_Ozero__class_Ozero(X3050),X3048)
| ~ c_Orderings_Oord__class_Oless(X3050,c_Groups_Ozero__class_Ozero(X3050),c_Rings_Oinverse__class_Odivide(X3050,X3049,X3048))
| ~ class_Fields_Olinordered__field__inverse__zero(X3050) )
& ( ~ c_Orderings_Oord__class_Oless(X3050,c_Groups_Ozero__class_Ozero(X3050),X3049)
| ~ c_Orderings_Oord__class_Oless(X3050,c_Groups_Ozero__class_Ozero(X3050),X3048)
| c_Orderings_Oord__class_Oless(X3050,c_Groups_Ozero__class_Ozero(X3050),c_Rings_Oinverse__class_Odivide(X3050,X3049,X3048))
| ~ class_Fields_Olinordered__field__inverse__zero(X3050) )
& ( ~ c_Orderings_Oord__class_Oless(X3050,X3049,c_Groups_Ozero__class_Ozero(X3050))
| ~ c_Orderings_Oord__class_Oless(X3050,X3048,c_Groups_Ozero__class_Ozero(X3050))
| c_Orderings_Oord__class_Oless(X3050,c_Groups_Ozero__class_Ozero(X3050),c_Rings_Oinverse__class_Odivide(X3050,X3049,X3048))
| ~ class_Fields_Olinordered__field__inverse__zero(X3050) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff])])]) ).
fof(i_0_1779,plain,
! [X3019,X3020,X3021] :
( ( c_Orderings_Oord__class_Oless__eq(X3021,X3020,c_Groups_Ozero__class_Ozero(X3021))
| c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),X3020)
| ~ c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),c_Rings_Oinverse__class_Odivide(X3021,X3020,X3019))
| ~ class_Fields_Olinordered__field__inverse__zero(X3021) )
& ( c_Orderings_Oord__class_Oless__eq(X3021,X3019,c_Groups_Ozero__class_Ozero(X3021))
| c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),X3020)
| ~ c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),c_Rings_Oinverse__class_Odivide(X3021,X3020,X3019))
| ~ class_Fields_Olinordered__field__inverse__zero(X3021) )
& ( c_Orderings_Oord__class_Oless__eq(X3021,X3020,c_Groups_Ozero__class_Ozero(X3021))
| c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),X3019)
| ~ c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),c_Rings_Oinverse__class_Odivide(X3021,X3020,X3019))
| ~ class_Fields_Olinordered__field__inverse__zero(X3021) )
& ( c_Orderings_Oord__class_Oless__eq(X3021,X3019,c_Groups_Ozero__class_Ozero(X3021))
| c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),X3019)
| ~ c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),c_Rings_Oinverse__class_Odivide(X3021,X3020,X3019))
| ~ class_Fields_Olinordered__field__inverse__zero(X3021) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),X3020)
| ~ c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),X3019)
| c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),c_Rings_Oinverse__class_Odivide(X3021,X3020,X3019))
| ~ class_Fields_Olinordered__field__inverse__zero(X3021) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3021,X3020,c_Groups_Ozero__class_Ozero(X3021))
| ~ c_Orderings_Oord__class_Oless__eq(X3021,X3019,c_Groups_Ozero__class_Ozero(X3021))
| c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),c_Rings_Oinverse__class_Odivide(X3021,X3020,X3019))
| ~ class_Fields_Olinordered__field__inverse__zero(X3021) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff])])]) ).
fof(i_0_1780,plain,
! [X4041,X4042] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4042)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4041)
| c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4042,c_RealDef_Oreal(tc_Nat_Onat,X4041))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X4042),X4041) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__div__nat])]) ).
fof(i_0_1781,plain,
! [X4443,X4444,X4445] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4445),X4444),X4443),X4444) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4443,X4444),
inference(variable_rename,[status(thm)],[fact_mod__mult__self3]) ).
fof(i_0_1782,plain,
! [X5321,X5322,X5323] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5323)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5322,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5321),X5323)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5322,X5321),X5323) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq])]) ).
fof(i_0_1783,plain,
! [X4539,X4540,X4541] :
( ( c_Orderings_Oord__class_Oless__eq(X4541,X4540,c_Groups_Ozero__class_Ozero(X4541))
| c_Orderings_Oord__class_Oless__eq(X4541,c_Groups_Ozero__class_Ozero(X4541),X4540)
| ~ c_Orderings_Oord__class_Oless__eq(X4541,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4541),X4540),X4539),c_Groups_Ozero__class_Ozero(X4541))
| ~ class_Rings_Olinordered__ring__strict(X4541) )
& ( c_Orderings_Oord__class_Oless__eq(X4541,c_Groups_Ozero__class_Ozero(X4541),X4539)
| c_Orderings_Oord__class_Oless__eq(X4541,c_Groups_Ozero__class_Ozero(X4541),X4540)
| ~ c_Orderings_Oord__class_Oless__eq(X4541,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4541),X4540),X4539),c_Groups_Ozero__class_Ozero(X4541))
| ~ class_Rings_Olinordered__ring__strict(X4541) )
& ( c_Orderings_Oord__class_Oless__eq(X4541,X4540,c_Groups_Ozero__class_Ozero(X4541))
| c_Orderings_Oord__class_Oless__eq(X4541,X4539,c_Groups_Ozero__class_Ozero(X4541))
| ~ c_Orderings_Oord__class_Oless__eq(X4541,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4541),X4540),X4539),c_Groups_Ozero__class_Ozero(X4541))
| ~ class_Rings_Olinordered__ring__strict(X4541) )
& ( c_Orderings_Oord__class_Oless__eq(X4541,c_Groups_Ozero__class_Ozero(X4541),X4539)
| c_Orderings_Oord__class_Oless__eq(X4541,X4539,c_Groups_Ozero__class_Ozero(X4541))
| ~ c_Orderings_Oord__class_Oless__eq(X4541,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4541),X4540),X4539),c_Groups_Ozero__class_Ozero(X4541))
| ~ class_Rings_Olinordered__ring__strict(X4541) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4541,c_Groups_Ozero__class_Ozero(X4541),X4540)
| ~ c_Orderings_Oord__class_Oless__eq(X4541,X4539,c_Groups_Ozero__class_Ozero(X4541))
| c_Orderings_Oord__class_Oless__eq(X4541,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4541),X4540),X4539),c_Groups_Ozero__class_Ozero(X4541))
| ~ class_Rings_Olinordered__ring__strict(X4541) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4541,X4540,c_Groups_Ozero__class_Ozero(X4541))
| ~ c_Orderings_Oord__class_Oless__eq(X4541,c_Groups_Ozero__class_Ozero(X4541),X4539)
| c_Orderings_Oord__class_Oless__eq(X4541,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4541),X4540),X4539),c_Groups_Ozero__class_Ozero(X4541))
| ~ class_Rings_Olinordered__ring__strict(X4541) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).
fof(i_0_1784,plain,
! [X4536,X4537,X4538] :
( ( c_Orderings_Oord__class_Oless__eq(X4538,X4537,c_Groups_Ozero__class_Ozero(X4538))
| c_Orderings_Oord__class_Oless__eq(X4538,c_Groups_Ozero__class_Ozero(X4538),X4537)
| ~ c_Orderings_Oord__class_Oless__eq(X4538,c_Groups_Ozero__class_Ozero(X4538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4538),X4537),X4536))
| ~ class_Rings_Olinordered__ring__strict(X4538) )
& ( c_Orderings_Oord__class_Oless__eq(X4538,X4536,c_Groups_Ozero__class_Ozero(X4538))
| c_Orderings_Oord__class_Oless__eq(X4538,c_Groups_Ozero__class_Ozero(X4538),X4537)
| ~ c_Orderings_Oord__class_Oless__eq(X4538,c_Groups_Ozero__class_Ozero(X4538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4538),X4537),X4536))
| ~ class_Rings_Olinordered__ring__strict(X4538) )
& ( c_Orderings_Oord__class_Oless__eq(X4538,X4537,c_Groups_Ozero__class_Ozero(X4538))
| c_Orderings_Oord__class_Oless__eq(X4538,c_Groups_Ozero__class_Ozero(X4538),X4536)
| ~ c_Orderings_Oord__class_Oless__eq(X4538,c_Groups_Ozero__class_Ozero(X4538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4538),X4537),X4536))
| ~ class_Rings_Olinordered__ring__strict(X4538) )
& ( c_Orderings_Oord__class_Oless__eq(X4538,X4536,c_Groups_Ozero__class_Ozero(X4538))
| c_Orderings_Oord__class_Oless__eq(X4538,c_Groups_Ozero__class_Ozero(X4538),X4536)
| ~ c_Orderings_Oord__class_Oless__eq(X4538,c_Groups_Ozero__class_Ozero(X4538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4538),X4537),X4536))
| ~ class_Rings_Olinordered__ring__strict(X4538) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4538,c_Groups_Ozero__class_Ozero(X4538),X4537)
| ~ c_Orderings_Oord__class_Oless__eq(X4538,c_Groups_Ozero__class_Ozero(X4538),X4536)
| c_Orderings_Oord__class_Oless__eq(X4538,c_Groups_Ozero__class_Ozero(X4538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4538),X4537),X4536))
| ~ class_Rings_Olinordered__ring__strict(X4538) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4538,X4537,c_Groups_Ozero__class_Ozero(X4538))
| ~ c_Orderings_Oord__class_Oless__eq(X4538,X4536,c_Groups_Ozero__class_Ozero(X4538))
| c_Orderings_Oord__class_Oless__eq(X4538,c_Groups_Ozero__class_Ozero(X4538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4538),X4537),X4536))
| ~ class_Rings_Olinordered__ring__strict(X4538) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).
fof(i_0_1785,plain,
! [X5457,X5458,X5459] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(X5459,X5458)),X5457) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5459),X5457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5457)),X5458)),
inference(variable_rename,[status(thm)],[fact_DeMoivre2]) ).
fof(i_0_1786,plain,
! [X5340,X5341,X5342] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5342),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5341,X5340)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5342),X5341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5342),X5340)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(i_0_1787,plain,
! [X4432,X4433,X4434] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4434),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4433,X4432)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4434),X4433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4434),X4432)),
inference(variable_rename,[status(thm)],[fact_mod__mult__distrib2]) ).
fof(i_0_1788,plain,
! [X4383,X4384,X4385] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4385),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4384,X4383)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4385),X4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4385),X4383)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).
fof(i_0_1789,plain,
! [X4503,X4504,X4505] :
( ~ class_Divides_Oring__div(X4505)
| c_Divides_Odiv__class_Omod(X4505,c_Groups_Ouminus__class_Ouminus(X4505,X4504),X4503) = c_Divides_Odiv__class_Omod(X4505,c_Groups_Ouminus__class_Ouminus(X4505,c_Divides_Odiv__class_Omod(X4505,X4504,X4503)),X4503) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__eq])]) ).
fof(i_0_1790,plain,
! [X4670,X4671] :
( ~ class_Rings_Ocomm__semiring__1(X4671)
| c_Groups_Oplus__class_Oplus(X4671,X4670,X4670) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4671),c_Groups_Oplus__class_Oplus(X4671,c_Groups_Oone__class_Oone(X4671),c_Groups_Oone__class_Oone(X4671))),X4670) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).
fof(i_0_1791,plain,
! [X4985,X4986,X4987] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4987)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4987),X4986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4987),X4985)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4986,X4985) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1])]) ).
fof(i_0_1792,plain,
! [X5042,X5043] :
( ( X5043 = 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),X5043),X5043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5042),X5042)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X5042 = 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),X5043),X5043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5042),X5042)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X5043 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X5042 != 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),X5043),X5043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5042),X5042)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__two__squares__add__zero__iff])])]) ).
cnf(i_0_1793,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_1318]) ).
cnf(i_0_1794,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_1319]) ).
cnf(i_0_1795,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_1320]) ).
cnf(i_0_1796,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_1321]) ).
fof(i_0_1797,plain,
! [X3036,X3037,X3038] :
( ~ class_Fields_Olinordered__field(X3038)
| ~ c_Orderings_Oord__class_Oless(X3038,X3037,c_Groups_Ozero__class_Ozero(X3038))
| ~ c_Orderings_Oord__class_Oless(X3038,c_Groups_Ozero__class_Ozero(X3038),X3036)
| c_Orderings_Oord__class_Oless(X3038,c_Rings_Oinverse__class_Odivide(X3038,X3037,X3036),c_Groups_Ozero__class_Ozero(X3038)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__pos])]) ).
fof(i_0_1798,plain,
! [X3039,X3040,X3041] :
( ~ class_Fields_Olinordered__field(X3041)
| ~ c_Orderings_Oord__class_Oless(X3041,c_Groups_Ozero__class_Ozero(X3041),X3040)
| ~ c_Orderings_Oord__class_Oless(X3041,X3039,c_Groups_Ozero__class_Ozero(X3041))
| c_Orderings_Oord__class_Oless(X3041,c_Rings_Oinverse__class_Odivide(X3041,X3040,X3039),c_Groups_Ozero__class_Ozero(X3041)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__neg])]) ).
fof(i_0_1799,plain,
! [X3087,X3088,X3089] :
( ~ class_Fields_Olinordered__field(X3089)
| ~ c_Orderings_Oord__class_Oless__eq(X3089,c_Groups_Ozero__class_Ozero(X3089),X3088)
| ~ c_Orderings_Oord__class_Oless(X3089,X3087,c_Groups_Ozero__class_Ozero(X3089))
| c_Orderings_Oord__class_Oless__eq(X3089,c_Rings_Oinverse__class_Odivide(X3089,X3088,X3087),c_Groups_Ozero__class_Ozero(X3089)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg])]) ).
fof(i_0_1800,plain,
! [X3069,X3070,X3071] :
( ~ class_Fields_Olinordered__field(X3071)
| ~ c_Orderings_Oord__class_Oless__eq(X3071,X3070,c_Groups_Ozero__class_Ozero(X3071))
| ~ c_Orderings_Oord__class_Oless(X3071,c_Groups_Ozero__class_Ozero(X3071),X3069)
| c_Orderings_Oord__class_Oless__eq(X3071,c_Rings_Oinverse__class_Odivide(X3071,X3070,X3069),c_Groups_Ozero__class_Ozero(X3071)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos])]) ).
fof(i_0_1801,plain,
! [X3398,X3399,X3400] :
( ~ class_Groups_Oordered__comm__monoid__add(X3400)
| ~ c_Orderings_Oord__class_Oless(X3400,X3399,c_Groups_Ozero__class_Ozero(X3400))
| ~ c_Orderings_Oord__class_Oless(X3400,X3398,c_Groups_Ozero__class_Ozero(X3400))
| c_Orderings_Oord__class_Oless(X3400,c_Groups_Oplus__class_Oplus(X3400,X3399,X3398),c_Groups_Ozero__class_Ozero(X3400)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_1802,plain,
! [X3168,X3169,X3170] :
( ~ class_Groups_Oordered__comm__monoid__add(X3170)
| ~ c_Orderings_Oord__class_Oless__eq(X3170,X3169,c_Groups_Ozero__class_Ozero(X3170))
| ~ c_Orderings_Oord__class_Oless(X3170,X3168,c_Groups_Ozero__class_Ozero(X3170))
| c_Orderings_Oord__class_Oless(X3170,c_Groups_Oplus__class_Oplus(X3170,X3169,X3168),c_Groups_Ozero__class_Ozero(X3170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_1803,plain,
! [X3171,X3172,X3173] :
( ~ class_Groups_Oordered__comm__monoid__add(X3173)
| ~ c_Orderings_Oord__class_Oless(X3173,X3172,c_Groups_Ozero__class_Ozero(X3173))
| ~ c_Orderings_Oord__class_Oless__eq(X3173,X3171,c_Groups_Ozero__class_Ozero(X3173))
| c_Orderings_Oord__class_Oless(X3173,c_Groups_Oplus__class_Oplus(X3173,X3172,X3171),c_Groups_Ozero__class_Ozero(X3173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_1804,plain,
! [X3384,X3385,X3386] :
( ~ class_Groups_Oordered__comm__monoid__add(X3386)
| ~ c_Orderings_Oord__class_Oless__eq(X3386,X3385,c_Groups_Ozero__class_Ozero(X3386))
| ~ c_Orderings_Oord__class_Oless__eq(X3386,X3384,c_Groups_Ozero__class_Ozero(X3386))
| c_Orderings_Oord__class_Oless__eq(X3386,c_Groups_Oplus__class_Oplus(X3386,X3385,X3384),c_Groups_Ozero__class_Ozero(X3386)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_1805,plain,
! [X3391,X3392,X3393] :
( ~ class_Groups_Oordered__comm__monoid__add(X3393)
| ~ c_Orderings_Oord__class_Oless(X3393,c_Groups_Ozero__class_Ozero(X3393),X3392)
| ~ c_Orderings_Oord__class_Oless(X3393,c_Groups_Ozero__class_Ozero(X3393),X3391)
| c_Orderings_Oord__class_Oless(X3393,c_Groups_Ozero__class_Ozero(X3393),c_Groups_Oplus__class_Oplus(X3393,X3392,X3391)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_1806,plain,
! [X3182,X3183,X3184] :
( ~ class_Groups_Oordered__comm__monoid__add(X3184)
| ~ c_Orderings_Oord__class_Oless__eq(X3184,c_Groups_Ozero__class_Ozero(X3184),X3183)
| ~ c_Orderings_Oord__class_Oless(X3184,c_Groups_Ozero__class_Ozero(X3184),X3182)
| c_Orderings_Oord__class_Oless(X3184,c_Groups_Ozero__class_Ozero(X3184),c_Groups_Oplus__class_Oplus(X3184,X3183,X3182)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_1807,plain,
! [X3185,X3186,X3187] :
( ~ class_Groups_Oordered__comm__monoid__add(X3187)
| ~ c_Orderings_Oord__class_Oless(X3187,c_Groups_Ozero__class_Ozero(X3187),X3186)
| ~ c_Orderings_Oord__class_Oless__eq(X3187,c_Groups_Ozero__class_Ozero(X3187),X3185)
| c_Orderings_Oord__class_Oless(X3187,c_Groups_Ozero__class_Ozero(X3187),c_Groups_Oplus__class_Oplus(X3187,X3186,X3185)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_1808,plain,
! [X3042,X3043,X3044] :
( ~ class_Fields_Olinordered__field(X3044)
| ~ c_Orderings_Oord__class_Oless(X3044,c_Groups_Ozero__class_Ozero(X3044),X3043)
| ~ c_Orderings_Oord__class_Oless(X3044,c_Groups_Ozero__class_Ozero(X3044),X3042)
| c_Orderings_Oord__class_Oless(X3044,c_Groups_Ozero__class_Ozero(X3044),c_Rings_Oinverse__class_Odivide(X3044,X3043,X3042)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__pos])]) ).
fof(i_0_1809,plain,
! [X3370,X3371,X3372] :
( ~ class_Groups_Oordered__comm__monoid__add(X3372)
| ~ c_Orderings_Oord__class_Oless__eq(X3372,c_Groups_Ozero__class_Ozero(X3372),X3371)
| ~ c_Orderings_Oord__class_Oless__eq(X3372,c_Groups_Ozero__class_Ozero(X3372),X3370)
| c_Orderings_Oord__class_Oless__eq(X3372,c_Groups_Ozero__class_Ozero(X3372),c_Groups_Oplus__class_Oplus(X3372,X3371,X3370)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_1810,plain,
! [X3090,X3091,X3092] :
( ~ class_Fields_Olinordered__field(X3092)
| ~ c_Orderings_Oord__class_Oless__eq(X3092,c_Groups_Ozero__class_Ozero(X3092),X3091)
| ~ c_Orderings_Oord__class_Oless(X3092,c_Groups_Ozero__class_Ozero(X3092),X3090)
| c_Orderings_Oord__class_Oless__eq(X3092,c_Groups_Ozero__class_Ozero(X3092),c_Rings_Oinverse__class_Odivide(X3092,X3091,X3090)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos])]) ).
fof(i_0_1811,plain,
! [X3033,X3034,X3035] :
( ~ class_Fields_Olinordered__field(X3035)
| ~ c_Orderings_Oord__class_Oless(X3035,X3034,c_Groups_Ozero__class_Ozero(X3035))
| ~ c_Orderings_Oord__class_Oless(X3035,X3033,c_Groups_Ozero__class_Ozero(X3035))
| c_Orderings_Oord__class_Oless(X3035,c_Groups_Ozero__class_Ozero(X3035),c_Rings_Oinverse__class_Odivide(X3035,X3034,X3033)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__neg])]) ).
fof(i_0_1812,plain,
! [X3066,X3067,X3068] :
( ~ class_Fields_Olinordered__field(X3068)
| ~ c_Orderings_Oord__class_Oless__eq(X3068,X3067,c_Groups_Ozero__class_Ozero(X3068))
| ~ c_Orderings_Oord__class_Oless(X3068,X3066,c_Groups_Ozero__class_Ozero(X3068))
| c_Orderings_Oord__class_Oless__eq(X3068,c_Groups_Ozero__class_Ozero(X3068),c_Rings_Oinverse__class_Odivide(X3068,X3067,X3066)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg])]) ).
fof(i_0_1813,plain,
! [X3972,X3973,X3975] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_2(X3972,X3973))
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3975),X3973)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3972),X3975)),esk33_2(X3972,X3973)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__bound__exists])])])]) ).
fof(i_0_1814,plain,
! [X3685,X3686] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3686,X3685))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3686)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3685) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3686)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3686,X3685)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3685)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3686,X3685)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_1815,plain,
! [X3059,X3060] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3060,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3059)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3060,X3059)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3060)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3059,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3060,X3059)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3060)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3060,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3060,X3059)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3059,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3060,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3060,X3059)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3060)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3059)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3060,X3059)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3059,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3059)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3060,X3059)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__le__divide__iff])])]) ).
fof(i_0_1816,plain,
! [X5162,X5163,X5164] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5164),X5163)),X5162) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5163),X5162)),
inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).
fof(i_0_1817,plain,
! [X5346,X5347,X5348] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5348),X5347)),X5346) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5347),X5346)),
inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).
fof(i_0_1818,plain,
! [X4296,X4297,X4298] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4298),X4297)),X4296) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4297),X4296)),
inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).
fof(i_0_1819,plain,
! [X5007,X5008,X5009] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5009),X5008)),X5007) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5008),X5007)),
inference(variable_rename,[status(thm)],[fact_real__mult__assoc]) ).
fof(i_0_1820,plain,
! [X4626,X4627,X4628] :
( ~ class_Rings_Olinordered__semiring__strict(X4628)
| ~ c_Orderings_Oord__class_Oless(X4628,X4627,c_Groups_Ozero__class_Ozero(X4628))
| ~ c_Orderings_Oord__class_Oless(X4628,c_Groups_Ozero__class_Ozero(X4628),X4626)
| c_Orderings_Oord__class_Oless(X4628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4628),X4627),X4626),c_Groups_Ozero__class_Ozero(X4628)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).
fof(i_0_1821,plain,
! [X4610,X4611,X4612] :
( ~ class_Rings_Olinordered__semiring__strict(X4612)
| ~ c_Orderings_Oord__class_Oless(X4612,c_Groups_Ozero__class_Ozero(X4612),X4611)
| ~ c_Orderings_Oord__class_Oless(X4612,X4610,c_Groups_Ozero__class_Ozero(X4612))
| c_Orderings_Oord__class_Oless(X4612,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4612),X4611),X4610),c_Groups_Ozero__class_Ozero(X4612)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).
fof(i_0_1822,plain,
! [X4613,X4614,X4615] :
( ~ class_Rings_Olinordered__semiring__strict(X4615)
| ~ c_Orderings_Oord__class_Oless(X4615,c_Groups_Ozero__class_Ozero(X4615),X4614)
| ~ c_Orderings_Oord__class_Oless(X4615,X4613,c_Groups_Ozero__class_Ozero(X4615))
| c_Orderings_Oord__class_Oless(X4615,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4615),X4613),X4614),c_Groups_Ozero__class_Ozero(X4615)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).
fof(i_0_1823,plain,
! [X4590,X4591,X4592] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4592,c_Groups_Ozero__class_Ozero(X4592),X4591)
| ~ c_Orderings_Oord__class_Oless__eq(X4592,X4590,c_Groups_Ozero__class_Ozero(X4592))
| c_Orderings_Oord__class_Oless__eq(X4592,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4592),X4591),X4590),c_Groups_Ozero__class_Ozero(X4592))
| ~ class_Rings_Oordered__cancel__semiring(X4592) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4592,X4591,c_Groups_Ozero__class_Ozero(X4592))
| ~ c_Orderings_Oord__class_Oless__eq(X4592,c_Groups_Ozero__class_Ozero(X4592),X4590)
| c_Orderings_Oord__class_Oless__eq(X4592,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4592),X4591),X4590),c_Groups_Ozero__class_Ozero(X4592))
| ~ class_Rings_Oordered__cancel__semiring(X4592) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).
fof(i_0_1824,plain,
! [X4551,X4552,X4553] :
( ~ class_Rings_Oordered__cancel__semiring(X4553)
| ~ c_Orderings_Oord__class_Oless__eq(X4553,X4552,c_Groups_Ozero__class_Ozero(X4553))
| ~ c_Orderings_Oord__class_Oless__eq(X4553,c_Groups_Ozero__class_Ozero(X4553),X4551)
| c_Orderings_Oord__class_Oless__eq(X4553,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4553),X4552),X4551),c_Groups_Ozero__class_Ozero(X4553)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).
fof(i_0_1825,plain,
! [X4545,X4546,X4547] :
( ~ class_Rings_Oordered__cancel__semiring(X4547)
| ~ c_Orderings_Oord__class_Oless__eq(X4547,c_Groups_Ozero__class_Ozero(X4547),X4546)
| ~ c_Orderings_Oord__class_Oless__eq(X4547,X4545,c_Groups_Ozero__class_Ozero(X4547))
| c_Orderings_Oord__class_Oless__eq(X4547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4547),X4546),X4545),c_Groups_Ozero__class_Ozero(X4547)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).
fof(i_0_1826,plain,
! [X4548,X4549,X4550] :
( ~ class_Rings_Oordered__cancel__semiring(X4550)
| ~ c_Orderings_Oord__class_Oless__eq(X4550,c_Groups_Ozero__class_Ozero(X4550),X4549)
| ~ c_Orderings_Oord__class_Oless__eq(X4550,X4548,c_Groups_Ozero__class_Ozero(X4550))
| c_Orderings_Oord__class_Oless__eq(X4550,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4550),X4548),X4549),c_Groups_Ozero__class_Ozero(X4550)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).
fof(i_0_1827,plain,
! [X4661,X4662,X4663] :
( ~ class_Rings_Olinordered__semidom(X4663)
| ~ c_Orderings_Oord__class_Oless(X4663,c_Groups_Oone__class_Oone(X4663),X4662)
| ~ c_Orderings_Oord__class_Oless(X4663,c_Groups_Oone__class_Oone(X4663),X4661)
| c_Orderings_Oord__class_Oless(X4663,c_Groups_Oone__class_Oone(X4663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4663),X4662),X4661)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).
fof(i_0_1828,plain,
! [X4607,X4608,X4609] :
( ~ class_Rings_Olinordered__semiring__strict(X4609)
| ~ c_Orderings_Oord__class_Oless(X4609,c_Groups_Ozero__class_Ozero(X4609),X4608)
| ~ c_Orderings_Oord__class_Oless(X4609,c_Groups_Ozero__class_Ozero(X4609),X4607)
| c_Orderings_Oord__class_Oless(X4609,c_Groups_Ozero__class_Ozero(X4609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4609),X4608),X4607)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).
fof(i_0_1829,plain,
! [X4587,X4588,X4589] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4589,c_Groups_Ozero__class_Ozero(X4589),X4588)
| ~ c_Orderings_Oord__class_Oless__eq(X4589,c_Groups_Ozero__class_Ozero(X4589),X4587)
| c_Orderings_Oord__class_Oless__eq(X4589,c_Groups_Ozero__class_Ozero(X4589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4589),X4588),X4587))
| ~ class_Rings_Oordered__ring(X4589) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4589,X4588,c_Groups_Ozero__class_Ozero(X4589))
| ~ c_Orderings_Oord__class_Oless__eq(X4589,X4587,c_Groups_Ozero__class_Ozero(X4589))
| c_Orderings_Oord__class_Oless__eq(X4589,c_Groups_Ozero__class_Ozero(X4589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4589),X4588),X4587))
| ~ class_Rings_Oordered__ring(X4589) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).
fof(i_0_1830,plain,
! [X4542,X4543,X4544] :
( ~ class_Rings_Oordered__cancel__semiring(X4544)
| ~ c_Orderings_Oord__class_Oless__eq(X4544,c_Groups_Ozero__class_Ozero(X4544),X4543)
| ~ c_Orderings_Oord__class_Oless__eq(X4544,c_Groups_Ozero__class_Ozero(X4544),X4542)
| c_Orderings_Oord__class_Oless__eq(X4544,c_Groups_Ozero__class_Ozero(X4544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4544),X4543),X4542)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).
fof(i_0_1831,plain,
! [X4629,X4630,X4631] :
( ~ class_Rings_Olinordered__ring__strict(X4631)
| ~ c_Orderings_Oord__class_Oless(X4631,X4630,c_Groups_Ozero__class_Ozero(X4631))
| ~ c_Orderings_Oord__class_Oless(X4631,X4629,c_Groups_Ozero__class_Ozero(X4631))
| c_Orderings_Oord__class_Oless(X4631,c_Groups_Ozero__class_Ozero(X4631),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4631),X4630),X4629)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).
fof(i_0_1832,plain,
! [X4554,X4555,X4556] :
( ~ class_Rings_Oordered__ring(X4556)
| ~ c_Orderings_Oord__class_Oless__eq(X4556,X4555,c_Groups_Ozero__class_Ozero(X4556))
| ~ c_Orderings_Oord__class_Oless__eq(X4556,X4554,c_Groups_Ozero__class_Ozero(X4556))
| c_Orderings_Oord__class_Oless__eq(X4556,c_Groups_Ozero__class_Ozero(X4556),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4556),X4555),X4554)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).
fof(i_0_1833,plain,
! [X3288,X3289,X3290,X3291] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3291)
| ~ c_Orderings_Oord__class_Oless(X3291,X3290,X3289)
| c_Orderings_Oord__class_Oless(X3291,c_Groups_Oplus__class_Oplus(X3291,X3290,X3288),c_Groups_Oplus__class_Oplus(X3291,X3289,X3288)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_1834,plain,
! [X3292,X3293,X3294,X3295] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3295)
| ~ c_Orderings_Oord__class_Oless(X3295,X3294,X3293)
| c_Orderings_Oord__class_Oless(X3295,c_Groups_Oplus__class_Oplus(X3295,X3292,X3294),c_Groups_Oplus__class_Oplus(X3295,X3292,X3293)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_1835,plain,
! [X3259,X3260,X3261,X3262] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3262)
| ~ c_Orderings_Oord__class_Oless__eq(X3262,X3261,X3260)
| c_Orderings_Oord__class_Oless__eq(X3262,c_Groups_Oplus__class_Oplus(X3262,X3261,X3259),c_Groups_Oplus__class_Oplus(X3262,X3260,X3259)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_1836,plain,
! [X3263,X3264,X3265,X3266] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3266)
| ~ c_Orderings_Oord__class_Oless__eq(X3266,X3265,X3264)
| c_Orderings_Oord__class_Oless__eq(X3266,c_Groups_Oplus__class_Oplus(X3266,X3263,X3265),c_Groups_Oplus__class_Oplus(X3266,X3263,X3264)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_1837,plain,
! [X5502,X5503] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5503,X5502)),X5502) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5503),X5502),
inference(variable_rename,[status(thm)],[fact_zminus__zmod]) ).
cnf(i_0_1838,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_1306]) ).
cnf(i_0_1839,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_1322]) ).
cnf(i_0_1840,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_1308]) ).
fof(i_0_1841,plain,
! [X5614,X5615,X5617] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk75_2(X5614,X5615))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5614)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5615) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk75_2(X5614,X5615)),X5615) = X5614
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5614)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5615) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5617)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5617),X5615) != X5614
| X5617 = esk75_2(X5614,X5615)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5614)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5615) ) ),
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_1842,plain,
! [X5156,X5157,X5158] :
( ~ class_Rings_Olinordered__semidom(X5158)
| ~ c_Orderings_Oord__class_Oless(X5158,c_Groups_Oone__class_Oone(X5158),X5157)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5156)
| c_Orderings_Oord__class_Oless(X5158,c_Groups_Oone__class_Oone(X5158),hAPP(hAPP(c_Power_Opower__class_Opower(X5158),X5157),X5156)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).
fof(i_0_1843,plain,
! [X4061,X4062,X4063,X4064] :
( ( ~ c_SEQ_Oincseq(X4062,X4061)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4063,X4064)
| c_Orderings_Oord__class_Oless__eq(X4062,hAPP(X4061,X4063),hAPP(X4061,X4064))
| ~ class_Orderings_Oorder(X4062) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk42_2(X4061,X4062),esk43_2(X4061,X4062))
| c_SEQ_Oincseq(X4062,X4061)
| ~ class_Orderings_Oorder(X4062) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4062,hAPP(X4061,esk42_2(X4061,X4062)),hAPP(X4061,esk43_2(X4061,X4062)))
| c_SEQ_Oincseq(X4062,X4061)
| ~ class_Orderings_Oorder(X4062) ) ),
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_1844,plain,
! [X3938,X3939,X3940,X3941] :
( ( ~ c_SEQ_Odecseq(X3939,X3938)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3940,X3941)
| c_Orderings_Oord__class_Oless__eq(X3939,hAPP(X3938,X3941),hAPP(X3938,X3940))
| ~ class_Orderings_Oorder(X3939) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk31_2(X3938,X3939),esk32_2(X3938,X3939))
| c_SEQ_Odecseq(X3939,X3938)
| ~ class_Orderings_Oorder(X3939) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3939,hAPP(X3938,esk32_2(X3938,X3939)),hAPP(X3938,esk31_2(X3938,X3939)))
| c_SEQ_Odecseq(X3939,X3938)
| ~ class_Orderings_Oorder(X3939) ) ),
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_1845,plain,
! [X4023,X4024] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X4024),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4023)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4024,c_RealDef_Oreal(tc_Nat_Onat,X4023)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ge__natfloor__plus__one__imp__gt])]) ).
fof(i_0_1846,plain,
! [X3174,X3175,X3176,X3177] :
( ~ class_Groups_Oordered__comm__monoid__add(X3177)
| ~ c_Orderings_Oord__class_Oless__eq(X3177,c_Groups_Ozero__class_Ozero(X3177),X3176)
| ~ c_Orderings_Oord__class_Oless(X3177,X3175,X3174)
| c_Orderings_Oord__class_Oless(X3177,X3175,c_Groups_Oplus__class_Oplus(X3177,X3176,X3174)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_1847,plain,
! [X3178,X3179,X3180,X3181] :
( ~ class_Groups_Oordered__comm__monoid__add(X3181)
| ~ c_Orderings_Oord__class_Oless(X3181,c_Groups_Ozero__class_Ozero(X3181),X3180)
| ~ c_Orderings_Oord__class_Oless__eq(X3181,X3179,X3178)
| c_Orderings_Oord__class_Oless(X3181,X3179,c_Groups_Oplus__class_Oplus(X3181,X3180,X3178)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_1848,plain,
! [X3394,X3395,X3396,X3397] :
( ~ class_Rings_Olinordered__semidom(X3397)
| ~ c_Orderings_Oord__class_Oless(X3397,c_Groups_Ozero__class_Ozero(X3397),X3396)
| ~ c_Orderings_Oord__class_Oless(X3397,X3395,X3394)
| c_Orderings_Oord__class_Oless(X3397,X3395,c_Groups_Oplus__class_Oplus(X3397,X3396,X3394)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_1849,plain,
! [X3376,X3377,X3378,X3379] :
( ~ class_Groups_Oordered__comm__monoid__add(X3379)
| ~ c_Orderings_Oord__class_Oless__eq(X3379,c_Groups_Ozero__class_Ozero(X3379),X3378)
| ~ c_Orderings_Oord__class_Oless__eq(X3379,X3377,X3376)
| c_Orderings_Oord__class_Oless__eq(X3379,X3377,c_Groups_Oplus__class_Oplus(X3379,X3378,X3376)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_1850,plain,
! [X3380,X3381,X3382,X3383] :
( ~ class_Groups_Oordered__comm__monoid__add(X3383)
| ~ c_Orderings_Oord__class_Oless__eq(X3383,c_Groups_Ozero__class_Ozero(X3383),X3382)
| ~ c_Orderings_Oord__class_Oless__eq(X3383,X3381,X3380)
| c_Orderings_Oord__class_Oless__eq(X3383,X3381,c_Groups_Oplus__class_Oplus(X3383,X3380,X3382)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_1851,plain,
! [X5044,X5045] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5045),X5045)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5044),X5044)),
inference(variable_rename,[status(thm)],[fact_real__minus__mult__self__le]) ).
fof(i_0_1852,plain,
! [X2957] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2957),v_r)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2957))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_s1m])]) ).
fof(i_0_1853,plain,
! [X5542,X5543,X5544] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5544,X5543)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5544,X5542),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5543,X5542)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).
fof(i_0_1854,plain,
! [X3673,X3674,X3675] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3675,X3674)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3675,X3673),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3674,X3673)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_1855,plain,
! [X5518,X5519,X5520] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5520,X5519)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5518,X5520),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5518,X5519)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).
fof(i_0_1856,plain,
! [X5707,X5708,X5709] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5709,X5708)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5709,X5707),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5708,X5707)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).
fof(i_0_1857,plain,
! [X5710,X5711,X5712] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5712,X5711)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5710,X5711),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5710,X5712)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).
fof(i_0_1858,plain,
! [X4094,X4095,X4096] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4096,X4095)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4096,X4094),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4095,X4094)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])]) ).
fof(i_0_1859,plain,
! [X3562,X3563,X3564] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3564,X3563)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3564,X3562),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3563,X3562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_1860,plain,
! [X3138,X3139,X3140] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3140,X3139)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3138,X3140),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3138,X3139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])]) ).
cnf(i_0_1861,plain,
( X1 = c_Nat_OSuc(esk26_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_1323]) ).
cnf(i_0_1862,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_1324]) ).
fof(i_0_1863,plain,
! [X4077,X4078,X4079] :
( ~ class_Divides_Osemiring__div(X4079)
| X4078 = c_Groups_Ozero__class_Ozero(X4079)
| c_Divides_Odiv__class_Odiv(X4079,c_Groups_Oplus__class_Oplus(X4079,X4078,X4077),X4078) = c_Groups_Oplus__class_Oplus(X4079,c_Divides_Odiv__class_Odiv(X4079,X4077,X4078),c_Groups_Oone__class_Oone(X4079)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self1])]) ).
fof(i_0_1864,plain,
! [X4074,X4075,X4076] :
( ~ class_Divides_Osemiring__div(X4076)
| X4075 = c_Groups_Ozero__class_Ozero(X4076)
| c_Divides_Odiv__class_Odiv(X4076,c_Groups_Oplus__class_Oplus(X4076,X4074,X4075),X4075) = c_Groups_Oplus__class_Oplus(X4076,c_Divides_Odiv__class_Odiv(X4076,X4074,X4075),c_Groups_Oone__class_Oone(X4076)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self2])]) ).
cnf(i_0_1865,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_1325]) ).
cnf(i_0_1866,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_1326]) ).
cnf(i_0_1867,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk26_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_1323]) ).
fof(i_0_1868,plain,
! [X4499,X4500,X4501,X4502] :
( ~ class_Divides_Oring__div(X4502)
| c_Divides_Odiv__class_Omod(X4502,X4501,X4500) != c_Divides_Odiv__class_Omod(X4502,X4499,X4500)
| c_Divides_Odiv__class_Omod(X4502,c_Groups_Ouminus__class_Ouminus(X4502,X4501),X4500) = c_Divides_Odiv__class_Omod(X4502,c_Groups_Ouminus__class_Ouminus(X4502,X4499),X4500) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__cong])]) ).
fof(i_0_1869,plain,
! [X5588,X5589] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5589,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5588)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5589,X5588),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_1870,plain,
! [X5565,X5566] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5566)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5565,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,X5566,X5565),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_1871,plain,
! [X5571,X5572] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5572,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5571)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5572,X5571),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_1872,plain,
! [X5486,X5487] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5487)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5486)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5487,X5486)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J])]) ).
fof(i_0_1873,plain,
! [X5595,X5596] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5596)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5595)
| 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,X5596,X5595)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_1874,plain,
! [X5606,X5607] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5607)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5606)
| 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,X5607,X5606)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).
cnf(i_0_1875,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_1327]) ).
cnf(i_0_1876,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_1323]) ).
fof(i_0_1877,plain,
! [X5702,X5703,X5704] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5703,X5704) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5702,X5704)
| X5703 = X5702
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5704,X5702)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5704,X5703) )
& ( X5703 != X5702
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5703,X5704) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5702,X5704)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5704,X5702)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5704,X5703) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).
fof(i_0_1878,plain,
! [X5464,X5465] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5465)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5464)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5465,X5464),X5465) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])]) ).
fof(i_0_1879,plain,
! [X5794,X5795] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5795)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5794)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5794,X5795),X5794) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).
fof(i_0_1880,plain,
! [X4069,X4070] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X4070)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4069)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4069,X4070),X4069) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less__dividend])]) ).
fof(i_0_1881,plain,
! [X3387,X3388] :
( ( ~ c_Orderings_Oord__class_Oless(X3388,c_Groups_Ozero__class_Ozero(X3388),c_Groups_Oplus__class_Oplus(X3388,X3387,X3387))
| c_Orderings_Oord__class_Oless(X3388,c_Groups_Ozero__class_Ozero(X3388),X3387)
| ~ class_Groups_Olinordered__ab__group__add(X3388) )
& ( ~ c_Orderings_Oord__class_Oless(X3388,c_Groups_Ozero__class_Ozero(X3388),X3387)
| c_Orderings_Oord__class_Oless(X3388,c_Groups_Ozero__class_Ozero(X3388),c_Groups_Oplus__class_Oplus(X3388,X3387,X3387))
| ~ class_Groups_Olinordered__ab__group__add(X3388) ) ),
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_1882,plain,
! [X3366,X3367] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3367,c_Groups_Ozero__class_Ozero(X3367),c_Groups_Oplus__class_Oplus(X3367,X3366,X3366))
| c_Orderings_Oord__class_Oless__eq(X3367,c_Groups_Ozero__class_Ozero(X3367),X3366)
| ~ class_Groups_Olinordered__ab__group__add(X3367) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3367,c_Groups_Ozero__class_Ozero(X3367),X3366)
| c_Orderings_Oord__class_Oless__eq(X3367,c_Groups_Ozero__class_Ozero(X3367),c_Groups_Oplus__class_Oplus(X3367,X3366,X3366))
| ~ class_Groups_Olinordered__ab__group__add(X3367) ) ),
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_1883,plain,
! [X3389,X3390] :
( ( ~ c_Orderings_Oord__class_Oless(X3390,c_Groups_Oplus__class_Oplus(X3390,X3389,X3389),c_Groups_Ozero__class_Ozero(X3390))
| c_Orderings_Oord__class_Oless(X3390,X3389,c_Groups_Ozero__class_Ozero(X3390))
| ~ class_Groups_Olinordered__ab__group__add(X3390) )
& ( ~ c_Orderings_Oord__class_Oless(X3390,X3389,c_Groups_Ozero__class_Ozero(X3390))
| c_Orderings_Oord__class_Oless(X3390,c_Groups_Oplus__class_Oplus(X3390,X3389,X3389),c_Groups_Ozero__class_Ozero(X3390))
| ~ class_Groups_Olinordered__ab__group__add(X3390) ) ),
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_1884,plain,
! [X3471,X3472] :
( ( ~ c_Orderings_Oord__class_Oless(X3472,c_Groups_Oplus__class_Oplus(X3472,X3471,X3471),c_Groups_Ozero__class_Ozero(X3472))
| c_Orderings_Oord__class_Oless(X3472,X3471,c_Groups_Ozero__class_Ozero(X3472))
| ~ class_Rings_Olinordered__idom(X3472) )
& ( ~ c_Orderings_Oord__class_Oless(X3472,X3471,c_Groups_Ozero__class_Ozero(X3472))
| c_Orderings_Oord__class_Oless(X3472,c_Groups_Oplus__class_Oplus(X3472,X3471,X3471),c_Groups_Ozero__class_Ozero(X3472))
| ~ class_Rings_Olinordered__idom(X3472) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_1885,plain,
! [X3368,X3369] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3369,c_Groups_Oplus__class_Oplus(X3369,X3368,X3368),c_Groups_Ozero__class_Ozero(X3369))
| c_Orderings_Oord__class_Oless__eq(X3369,X3368,c_Groups_Ozero__class_Ozero(X3369))
| ~ class_Groups_Olinordered__ab__group__add(X3369) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3369,X3368,c_Groups_Ozero__class_Ozero(X3369))
| c_Orderings_Oord__class_Oless__eq(X3369,c_Groups_Oplus__class_Oplus(X3369,X3368,X3368),c_Groups_Ozero__class_Ozero(X3369))
| ~ class_Groups_Olinordered__ab__group__add(X3369) ) ),
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_1886,plain,
! [X5598,X5599,X5600,X5601] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X5601,X5600)),c_Complex_Orcis(X5599,X5598)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5601),X5599),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5600,X5598)),
inference(variable_rename,[status(thm)],[fact_rcis__mult]) ).
cnf(i_0_1887,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_1328]) ).
fof(i_0_1888,plain,
! [X3999,X4000,X4001,X4002] :
( ~ class_Rings_Ocomm__semiring__1(X4002)
| c_Groups_Oplus__class_Oplus(X4002,c_Groups_Oplus__class_Oplus(X4002,X4001,X4000),X3999) = c_Groups_Oplus__class_Oplus(X4002,c_Groups_Oplus__class_Oplus(X4002,X4001,X3999),X4000) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_1889,plain,
! [X3995,X3996,X3997,X3998] :
( ~ class_Rings_Ocomm__semiring__1(X3998)
| c_Groups_Oplus__class_Oplus(X3998,c_Groups_Oplus__class_Oplus(X3998,X3997,X3996),X3995) = c_Groups_Oplus__class_Oplus(X3998,X3997,c_Groups_Oplus__class_Oplus(X3998,X3996,X3995)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_1890,plain,
! [X3200,X3201,X3202,X3203] :
( ~ class_Groups_Oab__semigroup__add(X3203)
| c_Groups_Oplus__class_Oplus(X3203,c_Groups_Oplus__class_Oplus(X3203,X3202,X3201),X3200) = c_Groups_Oplus__class_Oplus(X3203,X3202,c_Groups_Oplus__class_Oplus(X3203,X3201,X3200)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_1891,plain,
! [X3991,X3992,X3993,X3994] :
( ~ class_Rings_Ocomm__semiring__1(X3994)
| c_Groups_Oplus__class_Oplus(X3994,X3993,c_Groups_Oplus__class_Oplus(X3994,X3992,X3991)) = c_Groups_Oplus__class_Oplus(X3994,c_Groups_Oplus__class_Oplus(X3994,X3993,X3992),X3991) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_1892,plain,
! [X3987,X3988,X3989,X3990] :
( ~ class_Rings_Ocomm__semiring__1(X3990)
| c_Groups_Oplus__class_Oplus(X3990,X3989,c_Groups_Oplus__class_Oplus(X3990,X3988,X3987)) = c_Groups_Oplus__class_Oplus(X3990,X3988,c_Groups_Oplus__class_Oplus(X3990,X3989,X3987)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_1893,plain,
! [X3103,X3104] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3104,X3103))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3104),X3103) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3104),X3103)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3104,X3103)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff])]) ).
fof(i_0_1894,plain,
! [X3099,X3100] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3100,X3099))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3100),X3099) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3100),X3099)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3100,X3099)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__le__add__iff])]) ).
fof(i_0_1895,plain,
! [X3101,X3102] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3102,X3101),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3101,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3102)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3101,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3102))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3102,X3101),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__less__0__iff])]) ).
fof(i_0_1896,plain,
! [X3097,X3098] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3098,X3097),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3097,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3098)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3097,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3098))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3098,X3097),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__le__0__iff])]) ).
fof(i_0_1897,plain,
! [X4716,X4717,X4718,X4719] :
( ( X4718 != c_Groups_Ozero__class_Ozero(X4719)
| c_Divides_Odiv__class_Odiv(X4719,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4719),X4718),X4717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4719),X4718),X4716)) = c_Groups_Ozero__class_Ozero(X4719)
| ~ class_Divides_Osemiring__div(X4719) )
& ( X4718 = c_Groups_Ozero__class_Ozero(X4719)
| c_Divides_Odiv__class_Odiv(X4719,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4719),X4718),X4717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4719),X4718),X4716)) = c_Divides_Odiv__class_Odiv(X4719,X4717,X4716)
| ~ class_Divides_Osemiring__div(X4719) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if])])]) ).
fof(i_0_1898,plain,
! [X4730,X4731,X4732,X4733] :
( ~ class_Divides_Osemiring__div(X4733)
| X4732 = c_Groups_Ozero__class_Ozero(X4733)
| c_Divides_Odiv__class_Odiv(X4733,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4733),X4732),X4731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4733),X4732),X4730)) = c_Divides_Odiv__class_Odiv(X4733,X4731,X4730) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1])]) ).
fof(i_0_1899,plain,
! [X4726,X4727,X4728,X4729] :
( ~ class_Divides_Osemiring__div(X4729)
| X4728 = c_Groups_Ozero__class_Ozero(X4729)
| c_Divides_Odiv__class_Odiv(X4729,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4729),X4727),X4728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4729),X4726),X4728)) = c_Divides_Odiv__class_Odiv(X4729,X4727,X4726) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult2])]) ).
fof(i_0_1900,plain,
! [X4684,X4685,X4686,X4687] :
( ~ class_Fields_Ofield__inverse__zero(X4687)
| X4686 = c_Groups_Ozero__class_Ozero(X4687)
| c_Rings_Oinverse__class_Odivide(X4687,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4687),X4686),X4685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4687),X4686),X4684)) = c_Rings_Oinverse__class_Odivide(X4687,X4685,X4684) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left])]) ).
fof(i_0_1901,plain,
! [X4680,X4681,X4682,X4683] :
( ~ class_Fields_Ofield__inverse__zero(X4683)
| X4682 = c_Groups_Ozero__class_Ozero(X4683)
| c_Rings_Oinverse__class_Odivide(X4683,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4683),X4681),X4682),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4683),X4680),X4682)) = c_Rings_Oinverse__class_Odivide(X4683,X4681,X4680) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])]) ).
cnf(i_0_1902,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_1329]) ).
cnf(i_0_1903,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_1330]) ).
fof(i_0_1904,plain,
! [X4748,X4749] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4749)
| ~ 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),X4749),X4748)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4748)
| ~ 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),X4749),X4748)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4749)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4748)
| 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),X4749),X4748)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).
fof(i_0_1905,plain,
! [X5037,X5038] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5038)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5037)
| 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),X5038),X5037)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__order])]) ).
fof(i_0_1906,plain,
! [X5604,X5605] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5605)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5604)
| 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),X5605),X5604)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).
cnf(i_0_1907,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_1331]) ).
cnf(i_0_1908,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_1332]) ).
cnf(i_0_1909,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_1333]) ).
fof(i_0_1910,plain,
! [X4372] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4372,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4372),X4372))),
inference(variable_rename,[status(thm)],[fact_le__cube]) ).
fof(i_0_1911,plain,
! [X4276,X4277,X4278,X4279] :
( ~ class_Rings_Odivision__ring(X4279)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4279),X4278),c_Rings_Oinverse__class_Odivide(X4279,X4277,X4276)) = c_Rings_Oinverse__class_Odivide(X4279,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4279),X4278),X4277),X4276) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right])]) ).
cnf(i_0_1912,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_1334]) ).
cnf(i_0_1913,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_1335]) ).
fof(i_0_1914,plain,
! [X5737,X5738,X5739,X5740,X5741] :
( ( ~ c_Orderings_Oord__class_Oless(X5741,X5740,X5739)
| c_Orderings_Oord__class_Oless(X5741,X5738,X5737)
| c_Groups_Ominus__class_Ominus(X5741,X5740,X5739) != c_Groups_Ominus__class_Ominus(X5741,X5738,X5737)
| ~ class_Groups_Oordered__ab__group__add(X5741) )
& ( ~ c_Orderings_Oord__class_Oless(X5741,X5738,X5737)
| c_Orderings_Oord__class_Oless(X5741,X5740,X5739)
| c_Groups_Ominus__class_Ominus(X5741,X5740,X5739) != c_Groups_Ominus__class_Ominus(X5741,X5738,X5737)
| ~ class_Groups_Oordered__ab__group__add(X5741) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).
fof(i_0_1915,plain,
! [X5680,X5681,X5682,X5683,X5684] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5684,X5683,X5682)
| c_Orderings_Oord__class_Oless__eq(X5684,X5681,X5680)
| c_Groups_Ominus__class_Ominus(X5684,X5683,X5682) != c_Groups_Ominus__class_Ominus(X5684,X5681,X5680)
| ~ class_Groups_Oordered__ab__group__add(X5684) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5684,X5681,X5680)
| c_Orderings_Oord__class_Oless__eq(X5684,X5683,X5682)
| c_Groups_Ominus__class_Ominus(X5684,X5683,X5682) != c_Groups_Ominus__class_Ominus(X5684,X5681,X5680)
| ~ class_Groups_Oordered__ab__group__add(X5684) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).
fof(i_0_1916,plain,
! [X4373,X4374,X4375] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4375,X4374)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4375),X4373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4374),X4373)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).
fof(i_0_1917,plain,
! [X4376,X4377,X4378] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4378,X4377)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4376),X4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4376),X4377)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).
fof(i_0_1918,plain,
! [X2955,X2956] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2956),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2956)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2955)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2955,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096])]) ).
fof(i_0_1919,plain,
! [X4202,X4203,X4204,X4205] :
( ~ class_Rings_Ocomm__semiring__1(X4205)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4205),X4204),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4205),X4203),X4202)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4205),X4203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4205),X4204),X4202)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).
fof(i_0_1920,plain,
! [X5718,X5719,X5720] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5720,X5719),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5720,X5718)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5719,X5718),
inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).
fof(i_0_1921,plain,
! [X5715,X5716,X5717] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5717,X5716),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5715,X5716)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5717,X5715),
inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).
fof(i_0_1922,plain,
! [X5721,X5722,X5723] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5723,X5722),X5721) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5723,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5722,X5721)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
fof(i_0_1923,plain,
! [X5529,X5530,X5531] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5531,X5530),X5529) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5531,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5530,X5529)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
fof(i_0_1924,plain,
! [X3580,X3581,X3582] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3582,X3581),X3580) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3582,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3581,X3580)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_1925,plain,
! [X5532,X5533,X5534] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5534,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5533,X5532)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5533,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5534,X5532)),
inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).
fof(i_0_1926,plain,
! [X3585,X3586,X3587] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3587,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3586,X3585)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3586,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3587,X3585)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_1927,plain,
! [X5475,X5476] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5476,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5475,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5476,X5475)
| X5476 = X5475 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5476,X5475)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5476,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5475,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( X5476 != X5475
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5476,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5475,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_1928,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_1336]) ).
cnf(i_0_1929,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_1337]) ).
cnf(i_0_1930,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_1338]) ).
cnf(i_0_1931,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_1339]) ).
fof(i_0_1932,plain,
! [X2981,X2982] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2982),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2982)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2981)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2981,esk10_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mth2])])])]) ).
fof(i_0_1933,plain,
! [X5469,X5470] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5470,c_Groups_Oone__class_Oone(tc_Int_Oint)),X5469)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5470,X5469) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5470,X5469)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5470,c_Groups_Oone__class_Oone(tc_Int_Oint)),X5469) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).
cnf(i_0_1934,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_1340]) ).
cnf(i_0_1935,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_1341]) ).
cnf(i_0_1936,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_1342]) ).
cnf(i_0_1937,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_1343]) ).
cnf(i_0_1938,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_1344]) ).
fof(i_0_1939,plain,
! [X5467,X5468] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5468,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5467,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5468,X5467) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5468,X5467)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5468,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5467,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_1940,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_1345]) ).
cnf(i_0_1941,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_1346]) ).
fof(i_0_1942,plain,
! [X5796,X5797] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5797,X5796))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5796,X5797) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5796,X5797)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5797,X5796)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).
cnf(i_0_1943,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_1347]) ).
fof(i_0_1944,plain,
! [X3665,X3666,X3667,X3668] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3668,X3667)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3666,X3667) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3668,X3665)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3666,X3665) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_1945,plain,
! [X4039,X4040] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4040)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4040,c_RealDef_Oreal(tc_Nat_Onat,X4039))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X4040),X4039) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add])]) ).
fof(i_0_1946,plain,
! [X4011,X4012] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4012)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4012,c_RealDef_Oreal(tc_Nat_Onat,X4011))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X4012),X4011) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__add])]) ).
fof(i_0_1947,plain,
! [X3662,X3663,X3664] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3664,X3663),X3662)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3664,X3662) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_1948,plain,
! [X3547,X3548,X3549] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3549,X3547)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3549,X3548),X3547) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3548,X3547)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3549,X3548),X3547) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1348])])]) ).
fof(i_0_1949,plain,
! [X3550,X3551,X3552] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3552,X3551),X3550)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3552,X3550) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_1950,plain,
! [X3553,X3554,X3555] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3555,X3554),X3553)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3554,X3553) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_1951,plain,
! [X4144,X4145,X4146] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4146,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4145),X4144)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4146,X4145),X4144),
inference(variable_rename,[status(thm)],[fact_div__mult2__eq]) ).
cnf(i_0_1952,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_1349]) ).
cnf(i_0_1953,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))),
inference(split_conjunct,[status(thm)],[i_0_1350]) ).
cnf(i_0_1954,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_1351]) ).
cnf(i_0_1955,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_1352]) ).
cnf(i_0_1956,plain,
( X2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk20_2(X2,X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1346]) ).
fof(i_0_1957,plain,
! [X3373,X3374,X3375] :
( ( X3374 = c_Groups_Ozero__class_Ozero(X3375)
| c_Groups_Oplus__class_Oplus(X3375,X3374,X3373) != c_Groups_Ozero__class_Ozero(X3375)
| ~ c_Orderings_Oord__class_Oless__eq(X3375,c_Groups_Ozero__class_Ozero(X3375),X3373)
| ~ c_Orderings_Oord__class_Oless__eq(X3375,c_Groups_Ozero__class_Ozero(X3375),X3374)
| ~ class_Groups_Oordered__comm__monoid__add(X3375) )
& ( X3373 = c_Groups_Ozero__class_Ozero(X3375)
| c_Groups_Oplus__class_Oplus(X3375,X3374,X3373) != c_Groups_Ozero__class_Ozero(X3375)
| ~ c_Orderings_Oord__class_Oless__eq(X3375,c_Groups_Ozero__class_Ozero(X3375),X3373)
| ~ c_Orderings_Oord__class_Oless__eq(X3375,c_Groups_Ozero__class_Ozero(X3375),X3374)
| ~ class_Groups_Oordered__comm__monoid__add(X3375) )
& ( X3374 != c_Groups_Ozero__class_Ozero(X3375)
| X3373 != c_Groups_Ozero__class_Ozero(X3375)
| c_Groups_Oplus__class_Oplus(X3375,X3374,X3373) = c_Groups_Ozero__class_Ozero(X3375)
| ~ c_Orderings_Oord__class_Oless__eq(X3375,c_Groups_Ozero__class_Ozero(X3375),X3373)
| ~ c_Orderings_Oord__class_Oless__eq(X3375,c_Groups_Ozero__class_Ozero(X3375),X3374)
| ~ class_Groups_Oordered__comm__monoid__add(X3375) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_1958,plain,
! [X3950,X3951,X3952,X3953] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3952,X3953),X3951,X3950)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3952,X3953),X3951,X3950)
| ~ class_Orderings_Oord(X3953) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3952,X3953),X3950,X3951)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3952,X3953),X3951,X3950)
| ~ class_Orderings_Oord(X3953) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3952,X3953),X3951,X3950)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3952,X3953),X3950,X3951)
| c_Orderings_Oord__class_Oless(tc_fun(X3952,X3953),X3951,X3950)
| ~ class_Orderings_Oord(X3953) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1353])])]) ).
cnf(i_0_1959,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_1354]) ).
fof(i_0_1960,plain,
! [X4688,X4689,X4690,X4691,X4692] :
( ( c_Rings_Oinverse__class_Odivide(X4692,X4689,X4691) != c_Rings_Oinverse__class_Odivide(X4692,X4688,X4690)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4692),X4689),X4690) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4692),X4688),X4691)
| X4690 = c_Groups_Ozero__class_Ozero(X4692)
| X4691 = c_Groups_Ozero__class_Ozero(X4692)
| ~ class_Fields_Ofield(X4692) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4692),X4689),X4690) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4692),X4688),X4691)
| c_Rings_Oinverse__class_Odivide(X4692,X4689,X4691) = c_Rings_Oinverse__class_Odivide(X4692,X4688,X4690)
| X4690 = c_Groups_Ozero__class_Ozero(X4692)
| X4691 = c_Groups_Ozero__class_Ozero(X4692)
| ~ class_Fields_Ofield(X4692) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__eq__eq])])]) ).
fof(i_0_1961,plain,
! [X5665,X5666] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5666,X5665)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5665,X5666) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5665,X5666),X5666) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mod__geq])]) ).
fof(i_0_1962,plain,
! [X5173,X5174] :
( ( ~ 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),X5174),X5173))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5174)
| X5173 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5174)
| 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),X5174),X5173)) )
& ( X5173 != 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),X5174),X5173)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).
fof(i_0_1963,plain,
! [X5167,X5168] :
( ( ~ 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),X5168),X5167))
| X5167 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5168) )
& ( X5167 != 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),X5168),X5167)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5168)
| 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),X5168),X5167)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq])])]) ).
fof(i_0_1964,plain,
! [X4991,X4992,X4993] :
( ( X4993 != 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),X4993),X4992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4993),X4991)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4993 = 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),X4993),X4992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4993),X4991)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4992,X4991) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel__disj])]) ).
fof(i_0_1965,plain,
! [X5079,X5080] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5080),X5079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5080),X5080)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X5079,X5080),
inference(variable_rename,[status(thm)],[fact_real__divide__square__eq]) ).
fof(i_0_1966,plain,
! [X5460,X5461] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk74_2(X5460,X5461))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5460)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5461) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk74_2(X5460,X5461)),X5461) = X5460
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5460)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5461) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__pos__nth])])])]) ).
cnf(i_0_1967,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_1355]) ).
fof(i_0_1968,plain,
! [X5221,X5222,X5223,X5224] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X5224),X5223),X5222) != hAPP(hAPP(c_Power_Opower__class_Opower(X5224),X5223),X5221)
| X5222 = X5221
| ~ c_Orderings_Oord__class_Oless(X5224,c_Groups_Oone__class_Oone(X5224),X5223)
| ~ class_Rings_Olinordered__semidom(X5224) )
& ( X5222 != X5221
| hAPP(hAPP(c_Power_Opower__class_Opower(X5224),X5223),X5222) = hAPP(hAPP(c_Power_Opower__class_Opower(X5224),X5223),X5221)
| ~ c_Orderings_Oord__class_Oless(X5224,c_Groups_Oone__class_Oone(X5224),X5223)
| ~ class_Rings_Olinordered__semidom(X5224) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).
fof(i_0_1969,plain,
! [X4037,X4038] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4038)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4038,c_RealDef_Oreal(tc_Nat_Onat,X4037))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X4038),X4037) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__natfloor])]) ).
fof(i_0_1970,plain,
! [X4008,X4009] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X4009),X4008)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4009,c_RealDef_Oreal(tc_Nat_Onat,X4008))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4009) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4009,c_RealDef_Oreal(tc_Nat_Onat,X4008))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X4009),X4008)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4009) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq])])]) ).
fof(i_0_1971,plain,
! [X4033,X4034] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4033,c_RComplete_Onatfloor(X4034))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4033),X4034)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4034) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4033),X4034)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4033,c_RComplete_Onatfloor(X4034))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4034) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq])])]) ).
cnf(i_0_1972,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_1356]) ).
fof(i_0_1973,plain,
! [X5212,X5213,X5214] :
( ~ class_Rings_Olinordered__semidom(X5214)
| ~ c_Orderings_Oord__class_Oless(X5214,c_Groups_Ozero__class_Ozero(X5214),X5213)
| c_Orderings_Oord__class_Oless(X5214,c_Groups_Ozero__class_Ozero(X5214),hAPP(hAPP(c_Power_Opower__class_Opower(X5214),X5213),X5212)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).
fof(i_0_1974,plain,
! [X5215,X5216,X5217] :
( ~ class_Rings_Olinordered__semidom(X5217)
| ~ c_Orderings_Oord__class_Oless__eq(X5217,c_Groups_Oone__class_Oone(X5217),X5216)
| c_Orderings_Oord__class_Oless__eq(X5217,c_Groups_Oone__class_Oone(X5217),hAPP(hAPP(c_Power_Opower__class_Opower(X5217),X5216),X5215)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).
fof(i_0_1975,plain,
! [X5205,X5206,X5207] :
( ~ class_Rings_Olinordered__semidom(X5207)
| ~ c_Orderings_Oord__class_Oless__eq(X5207,c_Groups_Ozero__class_Ozero(X5207),X5206)
| c_Orderings_Oord__class_Oless__eq(X5207,c_Groups_Ozero__class_Ozero(X5207),hAPP(hAPP(c_Power_Opower__class_Opower(X5207),X5206),X5205)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).
fof(i_0_1976,plain,
! [X4014] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4014)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4014,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X4014),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_1977,plain,
! [X4013] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4013)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4013,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X4013),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_1978,plain,
! [X4593,X4594] :
( ~ class_Rings_Olinordered__ring(X4594)
| ~ c_Orderings_Oord__class_Oless(X4594,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4594),X4593),X4593),c_Groups_Ozero__class_Ozero(X4594)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1357])]) ).
fof(i_0_1979,plain,
! [X5663,X5664] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5664,X5663)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5664,X5663) = X5664 )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5664,X5663)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5664,X5663) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5664,X5663),X5663) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1358])]) ).
fof(i_0_1980,plain,
! [X5661,X5662] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5662,X5661)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5662,X5661) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5662,X5661),X5661) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1359])]) ).
fof(i_0_1981,plain,
! [X5477] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5477),X5477) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).
fof(i_0_1982,plain,
! [X5448,X5449,X5450,X5451] : hAPP(hAPP(c_Power_Opower_Opower(X5451,X5450,X5449),X5448),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X5450,
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).
cnf(i_0_1983,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_1360]) ).
fof(i_0_1984,plain,
! [X5471] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5471)
| 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),X5471)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).
cnf(i_0_1985,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_1320]) ).
cnf(i_0_1986,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_1324]) ).
fof(i_0_1987,plain,
! [X5506,X5507] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5506,X5507),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5507,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5507,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5506,X5507))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5507,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__conj])])]) ).
fof(i_0_1988,plain,
! [X5508,X5509] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5509,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5508,X5509),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__sign])]) ).
fof(i_0_1989,plain,
! [X5514,X5515] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5514,X5515))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5515) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5514,X5515),X5515)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5515) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__conj])])]) ).
fof(i_0_1990,plain,
! [X5516,X5517] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5517)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5516,X5517)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__sign])]) ).
fof(i_0_1991,plain,
! [X4293,X4294,X4295] :
( ~ class_RealVector_Oreal__normed__div__algebra(X4295)
| c_RealVector_Onorm__class_Onorm(X4295,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4295),X4294),X4293)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4295,X4294)),c_RealVector_Onorm__class_Onorm(X4295,X4293)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult])]) ).
fof(i_0_1992,plain,
! [X5472,X5473] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5473,X5472)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5473,c_Groups_Oone__class_Oone(tc_Int_Oint)),X5472) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).
cnf(i_0_1993,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_1361]) ).
cnf(i_0_1994,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_1342]) ).
cnf(i_0_1995,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_1343]) ).
cnf(i_0_1996,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_1336]) ).
cnf(i_0_1997,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_1362]) ).
cnf(i_0_1998,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_1363]) ).
cnf(i_0_1999,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_1345]) ).
cnf(i_0_2000,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_1320]) ).
cnf(i_0_2001,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_1364]) ).
fof(i_0_2002,plain,
! [X3689,X3690] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3690,X3689),X3690),
inference(variable_rename,[status(thm)],[i_0_1365]) ).
fof(i_0_2003,plain,
! [X3687,X3688] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3688,X3687),X3687),
inference(variable_rename,[status(thm)],[i_0_1366]) ).
fof(i_0_2004,plain,
! [X5494,X5495] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5495)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5494,X5495),X5495) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__bound])]) ).
fof(i_0_2005,plain,
! [X4532,X4533] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4533)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4532,X4533),X4533) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less__divisor])]) ).
fof(i_0_2006,plain,
! [X5484,X5485] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5485)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5485,X5484),X5485) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend])]) ).
fof(i_0_2007,plain,
! [X4762,X4763] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4763)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4762,X4763),X4763) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__le__divisor])]) ).
fof(i_0_2008,plain,
! [X5496,X5497] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5497,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5497,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5496,X5497)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__bound])]) ).
fof(i_0_2009,plain,
! [X5004,X5005,X5006] :
( ~ class_Fields_Ofield(X5006)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5006),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5006),X5005),X5004) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5006),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5006),X5005,X5004)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mod__minus__left])]) ).
fof(i_0_2010,plain,
! [X4082,X4083,X4084] :
( ~ class_Fields_Ofield(X4084)
| c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X4084),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4084),X4083),X4082) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4084),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X4084),X4083,X4082)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__div__minus__left])]) ).
fof(i_0_2011,plain,
! [X4085,X4086,X4087] :
( ~ class_Fields_Ofield(X4087)
| c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X4087),X4086,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4087),X4085)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4087),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X4087),X4086,X4085)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__div__minus__right])]) ).
fof(i_0_2012,plain,
! [X5754,X5755] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5755,X5754)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5754,X5755),X5755) = X5754 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).
fof(i_0_2013,plain,
! [X5705,X5706] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5706,X5705)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5705,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5705,X5706)) = X5706 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).
fof(i_0_2014,plain,
! [X5762,X5763] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5763,X5762)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5763,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5762,X5763)) = X5762 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).
fof(i_0_2015,plain,
! [X3768,X3769,X3770,X3771,X3772] :
( ~ class_Orderings_Oord(X3772)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3771,X3772),X3770,X3769)
| c_Orderings_Oord__class_Oless__eq(X3772,hAPP(X3770,X3768),hAPP(X3769,X3768)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_2016,plain,
! [X3730,X3731,X3732,X3733,X3734] :
( ~ class_Orderings_Oord(X3734)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3733,X3734),X3732,X3731)
| c_Orderings_Oord__class_Oless__eq(X3734,hAPP(X3732,X3730),hAPP(X3731,X3730)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_2017,plain,
! [X5728,X5729,X5730] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5730,X5729)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5730,X5728),X5729) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).
fof(i_0_2018,plain,
! [X3916,X3917,X3918] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3918,X3917)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3918,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3917,X3916)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_2019,plain,
! [X3679,X3680,X3681] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3681,X3680)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3681,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3680,X3679)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_2020,plain,
! [X3919,X3920,X3921] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3921,X3920)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3921,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3919,X3920)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_2021,plain,
! [X3676,X3677,X3678] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3678,X3677)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3678,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3676,X3677)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_2022,plain,
! [X3924,X3925,X3926] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3926,X3925)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3926,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3925,X3924)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_2023,plain,
! [X3568,X3569,X3570] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3570,X3569)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3570,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3569,X3568)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_2024,plain,
! [X3707,X3708,X3709] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3709,X3708)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3709,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3707,X3708)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_2025,plain,
! [X3565,X3566,X3567] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3567,X3566)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3567,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3565,X3566)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
cnf(i_0_2026,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_1351]) ).
cnf(i_0_2027,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_1351]) ).
cnf(i_0_2028,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_1352]) ).
cnf(i_0_2029,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_1352]) ).
fof(i_0_2030,plain,
! [X3142,X3143,X3144] :
( ~ class_Fields_Ofield__inverse__zero(X3144)
| ~ class_RealVector_Oreal__normed__field(X3144)
| c_RealVector_Onorm__class_Onorm(X3144,c_Rings_Oinverse__class_Odivide(X3144,X3143,X3142)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3144,X3143),c_RealVector_Onorm__class_Onorm(X3144,X3142)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__divide])]) ).
fof(i_0_2031,plain,
! [X3093,X3094,X3095] :
( ~ class_RealVector_Oreal__normed__field(X3095)
| X3094 = c_Groups_Ozero__class_Ozero(X3095)
| c_RealVector_Onorm__class_Onorm(X3095,c_Rings_Oinverse__class_Odivide(X3095,X3093,X3094)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3095,X3093),c_RealVector_Onorm__class_Onorm(X3095,X3094)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__norm__divide])]) ).
fof(i_0_2032,plain,
! [X5498,X5499] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X5499,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5498)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5499),X5498)),
inference(variable_rename,[status(thm)],[fact_zmod__zminus2]) ).
fof(i_0_2033,plain,
! [X5070] :
( ( 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),X5070),X5070))
| X5070 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X5070 != 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),X5070),X5070)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1367])]) ).
fof(i_0_2034,plain,
! [X5067,X5068,X5069] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5069),X5068) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5069),X5067)
| X5068 = X5067
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5069) )
& ( X5068 != X5067
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5069),X5068) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5069),X5067)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5069) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).
fof(i_0_2035,plain,
! [X5602,X5603] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5603)
| 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),X5603),X5602)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).
fof(i_0_2036,plain,
! [X3830,X3831,X3832,X3833] :
( ~ class_Orderings_Opreorder(X3833)
| ~ c_Orderings_Oord__class_Oless(X3833,X3832,X3831)
| ~ c_Orderings_Oord__class_Oless(X3833,X3831,X3830)
| c_Orderings_Oord__class_Oless(X3833,X3832,X3830) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_2037,plain,
! [X3908,X3909,X3910,X3911] :
( ~ class_Orderings_Opreorder(X3911)
| ~ c_Orderings_Oord__class_Oless__eq(X3911,X3910,X3909)
| ~ c_Orderings_Oord__class_Oless(X3911,X3909,X3908)
| c_Orderings_Oord__class_Oless(X3911,X3910,X3908) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_2038,plain,
! [X3900,X3901,X3902,X3903] :
( ~ class_Orderings_Opreorder(X3903)
| ~ c_Orderings_Oord__class_Oless(X3903,X3902,X3901)
| ~ c_Orderings_Oord__class_Oless__eq(X3903,X3901,X3900)
| c_Orderings_Oord__class_Oless(X3903,X3902,X3900) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_2039,plain,
! [X3834,X3835,X3836,X3837] :
( ~ class_Orderings_Oorder(X3837)
| ~ c_Orderings_Oord__class_Oless(X3837,X3836,X3835)
| ~ c_Orderings_Oord__class_Oless(X3837,X3834,X3836)
| c_Orderings_Oord__class_Oless(X3837,X3834,X3835) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_2040,plain,
! [X3912,X3913,X3914,X3915] :
( ~ class_Orderings_Oorder(X3915)
| ~ c_Orderings_Oord__class_Oless__eq(X3915,X3914,X3913)
| ~ c_Orderings_Oord__class_Oless(X3915,X3912,X3914)
| c_Orderings_Oord__class_Oless(X3915,X3912,X3913) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_2041,plain,
! [X3904,X3905,X3906,X3907] :
( ~ class_Orderings_Oorder(X3907)
| ~ c_Orderings_Oord__class_Oless(X3907,X3906,X3905)
| ~ c_Orderings_Oord__class_Oless__eq(X3907,X3904,X3906)
| c_Orderings_Oord__class_Oless(X3907,X3904,X3905) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_2042,plain,
! [X3757,X3758,X3759,X3760] :
( ~ class_Orderings_Opreorder(X3760)
| ~ c_Orderings_Oord__class_Oless__eq(X3760,X3759,X3758)
| ~ c_Orderings_Oord__class_Oless__eq(X3760,X3758,X3757)
| c_Orderings_Oord__class_Oless__eq(X3760,X3759,X3757) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_2043,plain,
! [X3764,X3765,X3766,X3767] :
( ~ class_Orderings_Oorder(X3767)
| ~ c_Orderings_Oord__class_Oless__eq(X3767,X3766,X3765)
| ~ c_Orderings_Oord__class_Oless__eq(X3767,X3764,X3766)
| c_Orderings_Oord__class_Oless__eq(X3767,X3764,X3765) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_2044,plain,
! [X3345,X3346,X3347] :
( ~ class_Groups_Oab__group__add(X3347)
| c_Groups_Ouminus__class_Ouminus(X3347,c_Groups_Oplus__class_Oplus(X3347,X3346,X3345)) = c_Groups_Oplus__class_Oplus(X3347,c_Groups_Ouminus__class_Ouminus(X3347,X3346),c_Groups_Ouminus__class_Ouminus(X3347,X3345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).
fof(i_0_2045,plain,
! [X3348,X3349,X3350] :
( ~ class_Groups_Ogroup__add(X3350)
| c_Groups_Ouminus__class_Ouminus(X3350,c_Groups_Oplus__class_Oplus(X3350,X3349,X3348)) = c_Groups_Oplus__class_Oplus(X3350,c_Groups_Ouminus__class_Ouminus(X3350,X3348),c_Groups_Ouminus__class_Ouminus(X3350,X3349)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).
fof(i_0_2046,plain,
! [X4036] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4036,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X4036)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__add__one__gt]) ).
fof(i_0_2047,plain,
! [X4917,X4918] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4918)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4918),X4917),X4918) = X4917 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m])]) ).
fof(i_0_2048,plain,
! [X4919,X4920] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4920)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4919),X4920),X4920) = X4919 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m])]) ).
fof(i_0_2049,plain,
! [X5610,X5611] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5611)
| c_SMT_Oz3div(X5610,X5611) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5610,X5611) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5611)
| c_SMT_Oz3div(X5610,X5611) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5610,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5611))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1368])]) ).
fof(i_0_2050,plain,
! [X3338,X3339,X3340] :
( ( ~ c_Orderings_Oord__class_Oless(X3340,c_Groups_Ouminus__class_Ouminus(X3340,X3339),c_Groups_Ouminus__class_Ouminus(X3340,X3338))
| c_Orderings_Oord__class_Oless(X3340,X3338,X3339)
| ~ class_Groups_Oordered__ab__group__add(X3340) )
& ( ~ c_Orderings_Oord__class_Oless(X3340,X3338,X3339)
| c_Orderings_Oord__class_Oless(X3340,c_Groups_Ouminus__class_Ouminus(X3340,X3339),c_Groups_Ouminus__class_Ouminus(X3340,X3338))
| ~ class_Groups_Oordered__ab__group__add(X3340) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).
fof(i_0_2051,plain,
! [X3944,X3945,X3946] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3946,c_Groups_Ouminus__class_Ouminus(X3946,X3945),c_Groups_Ouminus__class_Ouminus(X3946,X3944))
| c_Orderings_Oord__class_Oless__eq(X3946,X3944,X3945)
| ~ class_Lattices_Oboolean__algebra(X3946) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3946,X3944,X3945)
| c_Orderings_Oord__class_Oless__eq(X3946,c_Groups_Ouminus__class_Ouminus(X3946,X3945),c_Groups_Ouminus__class_Ouminus(X3946,X3944))
| ~ class_Lattices_Oboolean__algebra(X3946) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])]) ).
fof(i_0_2052,plain,
! [X3326,X3327,X3328] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3328,c_Groups_Ouminus__class_Ouminus(X3328,X3327),c_Groups_Ouminus__class_Ouminus(X3328,X3326))
| c_Orderings_Oord__class_Oless__eq(X3328,X3326,X3327)
| ~ class_Groups_Oordered__ab__group__add(X3328) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3328,X3326,X3327)
| c_Orderings_Oord__class_Oless__eq(X3328,c_Groups_Ouminus__class_Ouminus(X3328,X3327),c_Groups_Ouminus__class_Ouminus(X3328,X3326))
| ~ class_Groups_Oordered__ab__group__add(X3328) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).
cnf(i_0_2053,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_1369]) ).
fof(i_0_2054,plain,
! [X5567,X5568] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5568)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5568,X5567)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5568,X5567) = 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_2055,plain,
! [X5554,X5555] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5555,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),X5555)
| X5554 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5555,X5554) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5554,X5555)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5555)
| X5554 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5555,X5554) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5555,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5555,X5554)
| X5554 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5555,X5554) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5554,X5555)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5555,X5554)
| X5554 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5555,X5554) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X5554 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5555,X5554) = 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),X5555)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5555,X5554)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5555,X5554) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5555,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5554,X5555)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5555,X5554) = 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_2056,plain,
! [X5576,X5577] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5577,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5576,X5577)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5577,X5576) = 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_2057,plain,
! [X4263,X4264,X4265] :
( ~ class_RealVector_Oreal__normed__algebra(X4265)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4265),c_Groups_Ouminus__class_Ouminus(X4265,X4264)),X4263) = c_Groups_Ouminus__class_Ouminus(X4265,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4265),X4264),X4263)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus])]) ).
fof(i_0_2058,plain,
! [X4260,X4261,X4262] :
( ~ class_RealVector_Oreal__normed__algebra(X4262)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4262),c_Groups_Ouminus__class_Ouminus(X4262,X4261)),X4260) = c_Groups_Ouminus__class_Ouminus(X4262,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4262),X4261),X4260)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left])]) ).
fof(i_0_2059,plain,
! [X4242,X4243,X4244] :
( ~ class_Rings_Oring(X4244)
| c_Groups_Ouminus__class_Ouminus(X4244,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4244),X4243),X4242)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4244),c_Groups_Ouminus__class_Ouminus(X4244,X4243)),X4242) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).
fof(i_0_2060,plain,
! [X5512,X5513] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5513)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5513,X5512)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5513,X5512) = X5513 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial])]) ).
fof(i_0_2061,plain,
! [X5504,X5505] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5505,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5504,X5505)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5505,X5504) = X5505 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg__trivial])]) ).
cnf(i_0_2062,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_1354]) ).
cnf(i_0_2063,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_1354]) ).
fof(i_0_2064,plain,
! [X5751,X5752,X5753] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5752,X5753) != X5751
| X5752 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5751,X5753)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5753,X5752) )
& ( X5752 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5751,X5753)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5752,X5753) = X5751
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5753,X5752) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).
fof(i_0_2065,plain,
! [X4429,X4430,X4431] :
( ~ class_Divides_Osemiring__div(X4431)
| c_Divides_Odiv__class_Omod(X4431,c_Divides_Odiv__class_Omod(X4431,X4430,X4429),X4429) = c_Divides_Odiv__class_Omod(X4431,X4430,X4429) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial])]) ).
fof(i_0_2066,plain,
! [X4449,X4450,X4451] :
( ~ class_Divides_Osemiring__div(X4451)
| c_Divides_Odiv__class_Omod(X4451,c_Groups_Oplus__class_Oplus(X4451,X4450,X4449),X4450) = c_Divides_Odiv__class_Omod(X4451,X4449,X4450) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])]) ).
fof(i_0_2067,plain,
! [X4446,X4447,X4448] :
( ~ class_Divides_Osemiring__div(X4448)
| c_Divides_Odiv__class_Omod(X4448,c_Groups_Oplus__class_Oplus(X4448,X4447,X4446),X4446) = c_Divides_Odiv__class_Omod(X4448,X4447,X4446) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self2])]) ).
fof(i_0_2068,plain,
! [X5140,X5141,X5142] :
( ~ class_RealVector_Oreal__normed__div__algebra(X5142)
| c_RealVector_Onorm__class_Onorm(X5142,hAPP(hAPP(c_Power_Opower__class_Opower(X5142),X5141),X5140)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5142,X5141)),X5140) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power])]) ).
fof(i_0_2069,plain,
! [X3351,X3352,X3353] :
( ~ class_Groups_Ogroup__add(X3353)
| c_Groups_Oplus__class_Oplus(X3353,X3352,c_Groups_Oplus__class_Oplus(X3353,c_Groups_Ouminus__class_Ouminus(X3353,X3352),X3351)) = X3351 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).
fof(i_0_2070,plain,
! [X5524,X5525,X5526] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5526,X5525)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5525,X5524)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5526,X5524) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).
fof(i_0_2071,plain,
! [X3485,X3486,X3487] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3487,X3486)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3486,X3485)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3487,X3485) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_2072,plain,
! [X3111,X3112,X3113] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3113,X3112)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3112,X3111)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3113,X3111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
cnf(i_0_2073,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_1337]) ).
fof(i_0_2074,plain,
! [X5046,X5047] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5047),X5046)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5047)),c_RealDef_Oreal(tc_Nat_Onat,X5046)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__mult]) ).
cnf(i_0_2075,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_1325]) ).
cnf(i_0_2076,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_1326]) ).
fof(i_0_2077,plain,
! [X3696,X3697,X3698] :
( ~ class_Rings_Ocomm__ring(X3698)
| hAPP(c_Polynomial_Opoly(X3698,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3698),X3697)),X3696) = c_Groups_Ouminus__class_Ouminus(X3698,hAPP(c_Polynomial_Opoly(X3698,X3697),X3696)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__minus])]) ).
fof(i_0_2078,plain,
! [X3335,X3336,X3337] :
( ( ~ c_Orderings_Oord__class_Oless(X3337,c_Groups_Ouminus__class_Ouminus(X3337,X3336),X3335)
| c_Orderings_Oord__class_Oless(X3337,c_Groups_Ouminus__class_Ouminus(X3337,X3335),X3336)
| ~ class_Groups_Oordered__ab__group__add(X3337) )
& ( ~ c_Orderings_Oord__class_Oless(X3337,c_Groups_Ouminus__class_Ouminus(X3337,X3335),X3336)
| c_Orderings_Oord__class_Oless(X3337,c_Groups_Ouminus__class_Ouminus(X3337,X3336),X3335)
| ~ class_Groups_Oordered__ab__group__add(X3337) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).
fof(i_0_2079,plain,
! [X3323,X3324,X3325] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3325,c_Groups_Ouminus__class_Ouminus(X3325,X3324),X3323)
| c_Orderings_Oord__class_Oless__eq(X3325,c_Groups_Ouminus__class_Ouminus(X3325,X3323),X3324)
| ~ class_Groups_Oordered__ab__group__add(X3325) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3325,c_Groups_Ouminus__class_Ouminus(X3325,X3323),X3324)
| c_Orderings_Oord__class_Oless__eq(X3325,c_Groups_Ouminus__class_Ouminus(X3325,X3324),X3323)
| ~ class_Groups_Oordered__ab__group__add(X3325) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).
fof(i_0_2080,plain,
! [X3332,X3333,X3334] :
( ( ~ c_Orderings_Oord__class_Oless(X3334,X3333,c_Groups_Ouminus__class_Ouminus(X3334,X3332))
| c_Orderings_Oord__class_Oless(X3334,X3332,c_Groups_Ouminus__class_Ouminus(X3334,X3333))
| ~ class_Groups_Oordered__ab__group__add(X3334) )
& ( ~ c_Orderings_Oord__class_Oless(X3334,X3332,c_Groups_Ouminus__class_Ouminus(X3334,X3333))
| c_Orderings_Oord__class_Oless(X3334,X3333,c_Groups_Ouminus__class_Ouminus(X3334,X3332))
| ~ class_Groups_Oordered__ab__group__add(X3334) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).
fof(i_0_2081,plain,
! [X3320,X3321,X3322] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3322,X3321,c_Groups_Ouminus__class_Ouminus(X3322,X3320))
| c_Orderings_Oord__class_Oless__eq(X3322,X3320,c_Groups_Ouminus__class_Ouminus(X3322,X3321))
| ~ class_Groups_Oordered__ab__group__add(X3322) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3322,X3320,c_Groups_Ouminus__class_Ouminus(X3322,X3321))
| c_Orderings_Oord__class_Oless__eq(X3322,X3321,c_Groups_Ouminus__class_Ouminus(X3322,X3320))
| ~ class_Groups_Oordered__ab__group__add(X3322) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).
fof(i_0_2082,plain,
! [X5500,X5501] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5501),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5500)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5501,X5500)),
inference(variable_rename,[status(thm)],[fact_zmod__zminus__zminus]) ).
fof(i_0_2083,plain,
! [X3053,X3054] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3054,X3053)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3054),c_RealDef_Oreal(tc_Nat_Onat,X3053)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__add]) ).
fof(i_0_2084,plain,
! [X5539,X5540] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5540,X5539)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5540),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5539)),
inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(i_0_2085,plain,
! [X3452,X3453,X3454] :
( ~ class_Rings_Odivision__ring(X3454)
| X3453 = c_Groups_Ozero__class_Ozero(X3454)
| c_Groups_Ouminus__class_Ouminus(X3454,c_Rings_Oinverse__class_Odivide(X3454,X3452,X3453)) = c_Rings_Oinverse__class_Odivide(X3454,X3452,c_Groups_Ouminus__class_Ouminus(X3454,X3453)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right])]) ).
fof(i_0_2086,plain,
! [X4358,X4359,X4360] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X4360)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4360),X4359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4360),X4359),X4358)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4360),X4359),X4358) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])]) ).
cnf(i_0_2087,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_1351]) ).
cnf(i_0_2088,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_1351]) ).
cnf(i_0_2089,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_1352]) ).
cnf(i_0_2090,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_1352]) ).
fof(i_0_2091,plain,
! [X5779,X5780] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5780,X5779)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5779,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5780,X5779)) = X5780 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1370])]) ).
fof(i_0_2092,plain,
! [X3051,X3052] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3052),c_RealDef_Oreal(tc_Nat_Onat,X3051))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3052,X3051) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3052,X3051)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3052),c_RealDef_Oreal(tc_Nat_Onat,X3051)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff])]) ).
fof(i_0_2093,plain,
! [X3192,X3193] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3193),c_RealDef_Oreal(tc_Nat_Onat,X3192))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3193,X3192) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3193,X3192)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3193),c_RealDef_Oreal(tc_Nat_Onat,X3192)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff])]) ).
fof(i_0_2094,plain,
! [X3130,X3131,X3132] :
( ~ class_RealVector_Oreal__normed__field(X3132)
| c_Rings_Oinverse__class_Odivide(X3132,c_Groups_Ouminus__class_Ouminus(X3132,X3131),X3130) = c_Groups_Ouminus__class_Ouminus(X3132,c_Rings_Oinverse__class_Odivide(X3132,X3131,X3130)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Ominus])]) ).
fof(i_0_2095,plain,
! [X3363,X3364,X3365] :
( ~ class_Rings_Odivision__ring(X3365)
| c_Groups_Ouminus__class_Ouminus(X3365,c_Rings_Oinverse__class_Odivide(X3365,X3364,X3363)) = c_Rings_Oinverse__class_Odivide(X3365,c_Groups_Ouminus__class_Ouminus(X3365,X3364),X3363) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__left])]) ).
fof(i_0_2096,plain,
! [X3133,X3134,X3135] :
( ~ class_Fields_Ofield__inverse__zero(X3135)
| c_Groups_Ouminus__class_Ouminus(X3135,c_Rings_Oinverse__class_Odivide(X3135,X3134,X3133)) = c_Rings_Oinverse__class_Odivide(X3135,X3134,c_Groups_Ouminus__class_Ouminus(X3135,X3133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])]) ).
fof(i_0_2097,plain,
! [X3427,X3428] :
( ( ~ c_Orderings_Oord__class_Oless(X3428,c_Groups_Ouminus__class_Ouminus(X3428,X3427),c_Groups_Ozero__class_Ozero(X3428))
| c_Orderings_Oord__class_Oless(X3428,c_Groups_Ozero__class_Ozero(X3428),X3427)
| ~ class_Groups_Oordered__ab__group__add(X3428) )
& ( ~ c_Orderings_Oord__class_Oless(X3428,c_Groups_Ozero__class_Ozero(X3428),X3427)
| c_Orderings_Oord__class_Oless(X3428,c_Groups_Ouminus__class_Ouminus(X3428,X3427),c_Groups_Ozero__class_Ozero(X3428))
| ~ class_Groups_Oordered__ab__group__add(X3428) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).
fof(i_0_2098,plain,
! [X3419,X3420] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3420,c_Groups_Ouminus__class_Ouminus(X3420,X3419),c_Groups_Ozero__class_Ozero(X3420))
| c_Orderings_Oord__class_Oless__eq(X3420,c_Groups_Ozero__class_Ozero(X3420),X3419)
| ~ class_Groups_Oordered__ab__group__add(X3420) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3420,c_Groups_Ozero__class_Ozero(X3420),X3419)
| c_Orderings_Oord__class_Oless__eq(X3420,c_Groups_Ouminus__class_Ouminus(X3420,X3419),c_Groups_Ozero__class_Ozero(X3420))
| ~ class_Groups_Oordered__ab__group__add(X3420) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).
fof(i_0_2099,plain,
! [X3423,X3424] :
( ( ~ c_Orderings_Oord__class_Oless(X3424,c_Groups_Ozero__class_Ozero(X3424),c_Groups_Ouminus__class_Ouminus(X3424,X3423))
| c_Orderings_Oord__class_Oless(X3424,X3423,c_Groups_Ozero__class_Ozero(X3424))
| ~ class_Groups_Oordered__ab__group__add(X3424) )
& ( ~ c_Orderings_Oord__class_Oless(X3424,X3423,c_Groups_Ozero__class_Ozero(X3424))
| c_Orderings_Oord__class_Oless(X3424,c_Groups_Ozero__class_Ozero(X3424),c_Groups_Ouminus__class_Ouminus(X3424,X3423))
| ~ class_Groups_Oordered__ab__group__add(X3424) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).
fof(i_0_2100,plain,
! [X3415,X3416] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3416,c_Groups_Ozero__class_Ozero(X3416),c_Groups_Ouminus__class_Ouminus(X3416,X3415))
| c_Orderings_Oord__class_Oless__eq(X3416,X3415,c_Groups_Ozero__class_Ozero(X3416))
| ~ class_Groups_Oordered__ab__group__add(X3416) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3416,X3415,c_Groups_Ozero__class_Ozero(X3416))
| c_Orderings_Oord__class_Oless__eq(X3416,c_Groups_Ozero__class_Ozero(X3416),c_Groups_Ouminus__class_Ouminus(X3416,X3415))
| ~ class_Groups_Oordered__ab__group__add(X3416) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).
fof(i_0_2101,plain,
! [X3861,X3862,X3863] :
( ( c_Orderings_Oord__class_Oless__eq(X3863,X3862,X3861)
| ~ c_Orderings_Oord__class_Oless(X3863,X3862,X3861)
| ~ class_Orderings_Opreorder(X3863) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3863,X3861,X3862)
| ~ c_Orderings_Oord__class_Oless(X3863,X3862,X3861)
| ~ class_Orderings_Opreorder(X3863) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3863,X3862,X3861)
| c_Orderings_Oord__class_Oless__eq(X3863,X3861,X3862)
| c_Orderings_Oord__class_Oless(X3863,X3862,X3861)
| ~ class_Orderings_Opreorder(X3863) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1371])])]) ).
fof(i_0_2102,plain,
! [X4257,X4258,X4259] :
( ~ class_RealVector_Oreal__normed__algebra(X4259)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4259),X4258),c_Groups_Ouminus__class_Ouminus(X4259,X4257)) = c_Groups_Ouminus__class_Ouminus(X4259,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4259),X4258),X4257)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus])]) ).
fof(i_0_2103,plain,
! [X4254,X4255,X4256] :
( ~ class_RealVector_Oreal__normed__algebra(X4256)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4256),X4255),c_Groups_Ouminus__class_Ouminus(X4256,X4254)) = c_Groups_Ouminus__class_Ouminus(X4256,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4256),X4255),X4254)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right])]) ).
fof(i_0_2104,plain,
! [X4239,X4240,X4241] :
( ~ class_Rings_Oring(X4241)
| c_Groups_Ouminus__class_Ouminus(X4241,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4241),X4240),X4239)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4241),X4240),c_Groups_Ouminus__class_Ouminus(X4241,X4239)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).
cnf(i_0_2105,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[i_0_1372]) ).
fof(i_0_2106,plain,
! [X3947,X3948,X3949] :
( ~ class_Lattices_Oboolean__algebra(X3949)
| ~ c_Orderings_Oord__class_Oless__eq(X3949,X3948,X3947)
| c_Orderings_Oord__class_Oless__eq(X3949,c_Groups_Ouminus__class_Ouminus(X3949,X3947),c_Groups_Ouminus__class_Ouminus(X3949,X3948)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])]) ).
fof(i_0_2107,plain,
! [X3329,X3330,X3331] :
( ~ class_Groups_Oordered__ab__group__add(X3331)
| ~ c_Orderings_Oord__class_Oless__eq(X3331,X3330,X3329)
| c_Orderings_Oord__class_Oless__eq(X3331,c_Groups_Ouminus__class_Ouminus(X3331,X3329),c_Groups_Ouminus__class_Ouminus(X3331,X3330)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).
cnf(i_0_2108,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_1369]) ).
fof(i_0_2109,plain,
! [X3167] :
( ~ class_Rings_Olinordered__semidom(X3167)
| c_Orderings_Oord__class_Oless(X3167,c_Groups_Ozero__class_Ozero(X3167),c_Groups_Oplus__class_Oplus(X3167,c_Groups_Oone__class_Oone(X3167),c_Groups_Oone__class_Oone(X3167))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_2110,plain,
! [X3354,X3355,X3356] :
( ~ class_Groups_Ogroup__add(X3356)
| c_Groups_Oplus__class_Oplus(X3356,c_Groups_Ouminus__class_Ouminus(X3356,X3355),c_Groups_Oplus__class_Oplus(X3356,X3355,X3354)) = X3354 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).
fof(i_0_2111,plain,
! [X3429,X3430] :
( ( ~ c_Orderings_Oord__class_Oless(X3430,c_Groups_Ouminus__class_Ouminus(X3430,X3429),X3429)
| c_Orderings_Oord__class_Oless(X3430,c_Groups_Ozero__class_Ozero(X3430),X3429)
| ~ class_Groups_Olinordered__ab__group__add(X3430) )
& ( ~ c_Orderings_Oord__class_Oless(X3430,c_Groups_Ozero__class_Ozero(X3430),X3429)
| c_Orderings_Oord__class_Oless(X3430,c_Groups_Ouminus__class_Ouminus(X3430,X3429),X3429)
| ~ class_Groups_Olinordered__ab__group__add(X3430) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).
fof(i_0_2112,plain,
! [X3421,X3422] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3422,c_Groups_Ouminus__class_Ouminus(X3422,X3421),X3421)
| c_Orderings_Oord__class_Oless__eq(X3422,c_Groups_Ozero__class_Ozero(X3422),X3421)
| ~ class_Groups_Olinordered__ab__group__add(X3422) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3422,c_Groups_Ozero__class_Ozero(X3422),X3421)
| c_Orderings_Oord__class_Oless__eq(X3422,c_Groups_Ouminus__class_Ouminus(X3422,X3421),X3421)
| ~ class_Groups_Olinordered__ab__group__add(X3422) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).
fof(i_0_2113,plain,
! [X3425,X3426] :
( ( ~ c_Orderings_Oord__class_Oless(X3426,X3425,c_Groups_Ouminus__class_Ouminus(X3426,X3425))
| c_Orderings_Oord__class_Oless(X3426,X3425,c_Groups_Ozero__class_Ozero(X3426))
| ~ class_Rings_Olinordered__idom(X3426) )
& ( ~ c_Orderings_Oord__class_Oless(X3426,X3425,c_Groups_Ozero__class_Ozero(X3426))
| c_Orderings_Oord__class_Oless(X3426,X3425,c_Groups_Ouminus__class_Ouminus(X3426,X3425))
| ~ class_Rings_Olinordered__idom(X3426) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).
fof(i_0_2114,plain,
! [X3417,X3418] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3418,X3417,c_Groups_Ouminus__class_Ouminus(X3418,X3417))
| c_Orderings_Oord__class_Oless__eq(X3418,X3417,c_Groups_Ozero__class_Ozero(X3418))
| ~ class_Groups_Olinordered__ab__group__add(X3418) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3418,X3417,c_Groups_Ozero__class_Ozero(X3418))
| c_Orderings_Oord__class_Oless__eq(X3418,X3417,c_Groups_Ouminus__class_Ouminus(X3418,X3417))
| ~ class_Groups_Olinordered__ab__group__add(X3418) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).
fof(i_0_2115,plain,
! [X5169,X5170] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5170)),X5169) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5170),X5169)),
inference(variable_rename,[status(thm)],[fact_power__real__of__nat]) ).
fof(i_0_2116,plain,
! [X5331,X5332] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5332)),X5331) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5332),X5331)),
inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).
fof(i_0_2117,plain,
! [X5171,X5172] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5172),X5171)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5172)),X5171),
inference(variable_rename,[status(thm)],[fact_real__of__nat__power]) ).
cnf(i_0_2118,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_1373]) ).
fof(i_0_2119,plain,
! [X3518,X3519,X3520] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3519,X3520)
| hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| X3520 = X3519
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3520,X3519) )
& ( ~ hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| X3520 = X3519
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3520,X3519) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3519,X3520)
| hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| ~ hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3520,X3519) )
& ( ~ hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| ~ hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3520,X3519) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3519,X3520)
| hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| X3520 = X3519
| ~ hBOOL(hAPP(hAPP(X3518,X3519),X3520)) )
& ( ~ hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| X3520 = X3519
| ~ hBOOL(hAPP(hAPP(X3518,X3519),X3520)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3519,X3520)
| hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| ~ hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| ~ hBOOL(hAPP(hAPP(X3518,X3519),X3520)) )
& ( ~ hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| ~ hBOOL(hAPP(hAPP(X3518,X3519),X3520))
| ~ hBOOL(hAPP(hAPP(X3518,X3519),X3520)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_2120,plain,
! [X4248,X4249,X4250] :
( ~ class_Rings_Oring(X4250)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4250),c_Groups_Ouminus__class_Ouminus(X4250,X4249)),c_Groups_Ouminus__class_Ouminus(X4250,X4248)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4250),X4249),X4248) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).
fof(i_0_2121,plain,
! [X4245,X4246,X4247] :
( ~ class_Rings_Oring(X4247)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4247),c_Groups_Ouminus__class_Ouminus(X4247,X4246)),X4245) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4247),X4246),c_Groups_Ouminus__class_Ouminus(X4247,X4245)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).
fof(i_0_2122,plain,
! [X4251,X4252,X4253] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4253),X4252),X4252) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4253),X4251),X4251)
| X4252 = X4251
| X4252 = c_Groups_Ouminus__class_Ouminus(X4253,X4251)
| ~ class_Rings_Oidom(X4253) )
& ( X4252 != X4251
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4253),X4252),X4252) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4253),X4251),X4251)
| ~ class_Rings_Oidom(X4253) )
& ( X4252 != c_Groups_Ouminus__class_Ouminus(X4253,X4251)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4253),X4252),X4252) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4253),X4251),X4251)
| ~ class_Rings_Oidom(X4253) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).
fof(i_0_2123,plain,
! [X4122,X4123,X4125] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk51_2(X4122,X4123))
| ~ c_SEQ_OBseq(X4123,X4122)
| ~ class_RealVector_Oreal__normed__vector(X4123) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4123,hAPP(X4122,X4125)),esk51_2(X4122,X4123))
| ~ c_SEQ_OBseq(X4123,X4122)
| ~ class_RealVector_Oreal__normed__vector(X4123) ) ),
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])])])])]) ).
cnf(i_0_2124,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_1351]) ).
cnf(i_0_2125,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_1352]) ).
fof(i_0_2126,plain,
! [X5181,X5182] :
( X5182 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5182))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5182),X5181)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X5182)),X5181) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__power])]) ).
fof(i_0_2127,plain,
! [X3888,X3889,X3890] :
( ( c_Orderings_Oord__class_Oless(X3890,X3889,X3888)
| X3889 = X3888
| ~ c_Orderings_Oord__class_Oless__eq(X3890,X3889,X3888)
| ~ class_Orderings_Olinorder(X3890) )
& ( X3889 != X3888
| ~ c_Orderings_Oord__class_Oless(X3890,X3889,X3888)
| ~ c_Orderings_Oord__class_Oless__eq(X3890,X3889,X3888)
| ~ class_Orderings_Olinorder(X3890) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1374])])]) ).
fof(i_0_2128,plain,
! [X5734,X5735,X5736] :
( ~ class_Groups_Oab__group__add(X5736)
| c_Groups_Ouminus__class_Ouminus(X5736,c_Groups_Ominus__class_Ominus(X5736,X5735,X5734)) = c_Groups_Ominus__class_Ominus(X5736,X5734,X5735) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).
fof(i_0_2129,plain,
! [X3761,X3762,X3763] :
( ~ class_Orderings_Oorder(X3763)
| ~ c_Orderings_Oord__class_Oless__eq(X3763,X3762,X3761)
| ~ c_Orderings_Oord__class_Oless__eq(X3763,X3761,X3762)
| X3761 = X3762 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_2130,plain,
! [X3754,X3755,X3756] :
( ~ class_Orderings_Oorder(X3756)
| ~ c_Orderings_Oord__class_Oless__eq(X3756,X3755,X3754)
| ~ c_Orderings_Oord__class_Oless__eq(X3756,X3754,X3755)
| X3755 = X3754 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_2131,plain,
! [X3735,X3736,X3737] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3737,X3735,X3736)
| X3735 = X3736
| ~ c_Orderings_Oord__class_Oless__eq(X3737,X3736,X3735)
| ~ class_Orderings_Oorder(X3737) )
& ( X3735 != X3736
| c_Orderings_Oord__class_Oless__eq(X3737,X3735,X3736)
| ~ c_Orderings_Oord__class_Oless__eq(X3737,X3736,X3735)
| ~ class_Orderings_Oorder(X3737) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_2132,plain,
! [X3724,X3725,X3726] :
( ( c_Orderings_Oord__class_Oless__eq(X3726,X3725,X3724)
| X3725 != X3724
| ~ class_Orderings_Oorder(X3726) )
& ( c_Orderings_Oord__class_Oless__eq(X3726,X3724,X3725)
| X3725 != X3724
| ~ class_Orderings_Oorder(X3726) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3726,X3725,X3724)
| ~ c_Orderings_Oord__class_Oless__eq(X3726,X3724,X3725)
| X3725 = X3724
| ~ class_Orderings_Oorder(X3726) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_2133,plain,
! [X3238] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X3238))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3238) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3238)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X3238)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff])]) ).
fof(i_0_2134,plain,
! [X3431,X3432] :
( ~ class_Rings_Olinordered__semidom(X3432)
| c_Orderings_Oord__class_Oless(X3432,X3431,c_Groups_Oplus__class_Oplus(X3432,X3431,c_Groups_Oone__class_Oone(X3432))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_2135,plain,
! [X3220,X3221,X3222,X3223] :
( ~ class_Groups_Ocancel__semigroup__add(X3223)
| c_Groups_Oplus__class_Oplus(X3223,X3222,X3221) != c_Groups_Oplus__class_Oplus(X3223,X3220,X3221)
| X3222 = X3220 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_2136,plain,
! [X3208,X3209,X3210,X3211] :
( ( c_Groups_Oplus__class_Oplus(X3211,X3210,X3209) != c_Groups_Oplus__class_Oplus(X3211,X3208,X3209)
| X3210 = X3208
| ~ class_Groups_Ocancel__semigroup__add(X3211) )
& ( X3210 != X3208
| c_Groups_Oplus__class_Oplus(X3211,X3210,X3209) = c_Groups_Oplus__class_Oplus(X3211,X3208,X3209)
| ~ class_Groups_Ocancel__semigroup__add(X3211) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_2137,plain,
! [X3216,X3217,X3218,X3219] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X3219)
| c_Groups_Oplus__class_Oplus(X3219,X3218,X3217) != c_Groups_Oplus__class_Oplus(X3219,X3218,X3216)
| X3217 = X3216 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_2138,plain,
! [X3212,X3213,X3214,X3215] :
( ~ class_Groups_Ocancel__semigroup__add(X3215)
| c_Groups_Oplus__class_Oplus(X3215,X3214,X3213) != c_Groups_Oplus__class_Oplus(X3215,X3214,X3212)
| X3213 = X3212 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_2139,plain,
! [X3204,X3205,X3206,X3207] :
( ( c_Groups_Oplus__class_Oplus(X3207,X3206,X3205) != c_Groups_Oplus__class_Oplus(X3207,X3206,X3204)
| X3205 = X3204
| ~ class_Groups_Ocancel__semigroup__add(X3207) )
& ( X3205 != X3204
| c_Groups_Oplus__class_Oplus(X3207,X3206,X3205) = c_Groups_Oplus__class_Oplus(X3207,X3206,X3204)
| ~ class_Groups_Ocancel__semigroup__add(X3207) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_2140,plain,
! [X3811,X3812,X3813] :
( ~ class_Orderings_Oorder(X3813)
| ~ c_Orderings_Oord__class_Oless(X3813,X3812,X3811)
| ~ c_Orderings_Oord__class_Oless(X3813,X3811,X3812) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1375])]) ).
fof(i_0_2141,plain,
! [X3781,X3782,X3783] :
( ( c_Orderings_Oord__class_Oless(X3783,X3782,X3781)
| c_Orderings_Oord__class_Oless(X3783,X3781,X3782)
| X3782 = X3781
| ~ class_Orderings_Olinorder(X3783) )
& ( ~ c_Orderings_Oord__class_Oless(X3783,X3781,X3782)
| ~ c_Orderings_Oord__class_Oless(X3783,X3782,X3781)
| ~ class_Orderings_Olinorder(X3783) )
& ( X3782 != X3781
| ~ c_Orderings_Oord__class_Oless(X3783,X3782,X3781)
| ~ class_Orderings_Olinorder(X3783) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1376])])]) ).
fof(i_0_2142,plain,
! [X3882,X3883,X3884] :
( ~ class_Orderings_Olinorder(X3884)
| ~ c_Orderings_Oord__class_Oless__eq(X3884,X3883,X3882)
| ~ c_Orderings_Oord__class_Oless(X3884,X3882,X3883) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1377])]) ).
fof(i_0_2143,plain,
! [X3849,X3850,X3851] :
( ( c_Orderings_Oord__class_Oless(X3851,X3850,X3849)
| c_Orderings_Oord__class_Oless__eq(X3851,X3849,X3850)
| ~ class_Orderings_Olinorder(X3851) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3851,X3849,X3850)
| ~ c_Orderings_Oord__class_Oless(X3851,X3850,X3849)
| ~ class_Orderings_Olinorder(X3851) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1378])])]) ).
fof(i_0_2144,plain,
! [X3852,X3853,X3854] :
( ( c_Orderings_Oord__class_Oless__eq(X3854,X3853,X3852)
| c_Orderings_Oord__class_Oless(X3854,X3852,X3853)
| ~ class_Orderings_Olinorder(X3854) )
& ( ~ c_Orderings_Oord__class_Oless(X3854,X3852,X3853)
| ~ c_Orderings_Oord__class_Oless__eq(X3854,X3853,X3852)
| ~ class_Orderings_Olinorder(X3854) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1379])])]) ).
fof(i_0_2145,plain,
! [X3838,X3839,X3840] :
( ~ class_Orderings_Opreorder(X3840)
| ~ c_Orderings_Oord__class_Oless(X3840,X3839,X3838)
| ~ c_Orderings_Oord__class_Oless(X3840,X3838,X3839) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1380])]) ).
fof(i_0_2146,plain,
! [X3808,X3809,X3810] :
( ~ class_Orderings_Opreorder(X3810)
| ~ c_Orderings_Oord__class_Oless(X3810,X3809,X3808)
| ~ c_Orderings_Oord__class_Oless(X3810,X3808,X3809) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1381])]) ).
fof(i_0_2147,plain,
! [X3799,X3800,X3801] :
( ~ class_Orderings_Opreorder(X3801)
| ~ c_Orderings_Oord__class_Oless(X3801,X3800,X3799)
| ~ c_Orderings_Oord__class_Oless(X3801,X3799,X3800) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1382])]) ).
fof(i_0_2148,plain,
! [X3796,X3797,X3798] :
( ~ class_Orderings_Opreorder(X3798)
| ~ c_Orderings_Oord__class_Oless(X3798,X3797,X3796)
| ~ c_Orderings_Oord__class_Oless(X3798,X3796,X3797) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1383])]) ).
fof(i_0_2149,plain,
! [X3982,X3983] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3983,c_RealDef_Oreal(tc_Nat_Onat,X3982))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3983),X3982) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le])]) ).
fof(i_0_2150,plain,
! [X4031,X4032] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4032),X4031)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4032,c_RComplete_Onatfloor(X4031)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor])]) ).
cnf(i_0_2151,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1384]) ).
cnf(i_0_2152,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1385]) ).
fof(i_0_2153,plain,
! [X3929,X3930,X3931] :
( ( hAPP(c_Polynomial_Opoly(X3931,X3930),X3929) != c_Groups_Ozero__class_Ozero(X3931)
| X3930 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3931))
| c_Polynomial_Oorder(X3931,X3929,X3930) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X3931) )
& ( X3930 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3931))
| hAPP(c_Polynomial_Opoly(X3931,X3930),X3929) = c_Groups_Ozero__class_Ozero(X3931)
| ~ class_Rings_Oidom(X3931) )
& ( c_Polynomial_Oorder(X3931,X3929,X3930) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(X3931,X3930),X3929) = c_Groups_Ozero__class_Ozero(X3931)
| ~ class_Rings_Oidom(X3931) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__root])])]) ).
fof(i_0_2154,plain,
! [X5694,X5695] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5695,X5694) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5694,X5695) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X5695 = X5694 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).
fof(i_0_2155,plain,
! [X4030] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4030)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X4030)),X4030) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__natfloor__le])]) ).
cnf(i_0_2156,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_1355]) ).
fof(i_0_2157,plain,
! [X3189,X3190,X3191] :
( ~ class_Rings_Odivision__ring(X3191)
| X3190 = c_Groups_Ozero__class_Ozero(X3191)
| c_Rings_Oinverse__class_Odivide(X3191,c_Groups_Ouminus__class_Ouminus(X3191,X3189),c_Groups_Ouminus__class_Ouminus(X3191,X3190)) = c_Rings_Oinverse__class_Odivide(X3191,X3189,X3190) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide])]) ).
fof(i_0_2158,plain,
! [X4526,X4527,X4528] :
( ~ class_Divides_Osemiring__div(X4528)
| c_Divides_Odiv__class_Odiv(X4528,c_Divides_Odiv__class_Omod(X4528,X4527,X4526),X4526) = c_Groups_Ozero__class_Ozero(X4528) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__trivial])]) ).
cnf(i_0_2159,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1386]) ).
fof(i_0_2160,plain,
! [X4723,X4724,X4725] :
( ~ class_Divides_Osemiring__div(X4725)
| X4724 = c_Groups_Ozero__class_Ozero(X4725)
| c_Divides_Odiv__class_Odiv(X4725,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4725),X4724),X4723),X4724) = X4723 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id])]) ).
fof(i_0_2161,plain,
! [X4720,X4721,X4722] :
( ~ class_Divides_Osemiring__div(X4722)
| X4721 = c_Groups_Ozero__class_Ozero(X4722)
| c_Divides_Odiv__class_Odiv(X4722,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4722),X4720),X4721),X4721) = X4720 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id])]) ).
fof(i_0_2162,plain,
! [X4534,X4535] :
( ~ class_Rings_Olinordered__ring(X4535)
| c_Orderings_Oord__class_Oless__eq(X4535,c_Groups_Ozero__class_Ozero(X4535),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4535),X4534),X4534)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).
fof(i_0_2163,plain,
! [X5527,X5528] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5528,X5527)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5527,X5528)
| X5528 = X5527 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).
fof(i_0_2164,plain,
! [X3483,X3484] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3484,X3483)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3483,X3484)
| X3484 = X3483 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_2165,plain,
! [X3109,X3110] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3110,X3109)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3109,X3110)
| X3110 = X3109 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).
cnf(i_0_2166,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_1387]) ).
fof(i_0_2167,plain,
! [X5685,X5686,X5687] :
( ~ class_Groups_Ogroup__add(X5687)
| c_Groups_Ominus__class_Ominus(X5687,c_Groups_Oplus__class_Oplus(X5687,X5686,X5685),X5685) = X5686 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(i_0_2168,plain,
! [X5688,X5689,X5690] :
( ~ class_Groups_Ogroup__add(X5690)
| c_Groups_Oplus__class_Oplus(X5690,c_Groups_Ominus__class_Ominus(X5690,X5689,X5688),X5688) = X5689 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
fof(i_0_2169,plain,
! [X5336,X5337] :
( ( X5337 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5337),X5336) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5337) )
& ( X5336 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5337),X5336) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5337) )
& ( X5337 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X5336 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5337),X5336) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5337) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).
cnf(i_0_2170,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_1323]) ).
fof(i_0_2171,plain,
! [X3574,X3575,X3576] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3576,X3575) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3574,X3575)
| X3576 = X3574 )
& ( X3576 != X3574
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3576,X3575) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3574,X3575) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_2172,plain,
! [X3577,X3578,X3579] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3579,X3578) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3579,X3577)
| X3578 = X3577 )
& ( X3578 != X3577
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3579,X3578) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3579,X3577) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_2173,plain,
! [X4487,X4488,X4489] :
( ~ class_Divides_Osemiring__div(X4489)
| c_Divides_Odiv__class_Omod(X4489,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4489),X4488),X4487),X4488) = c_Groups_Ozero__class_Ozero(X4489) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0])]) ).
fof(i_0_2174,plain,
! [X4490,X4491,X4492] :
( ~ class_Divides_Osemiring__div(X4492)
| c_Divides_Odiv__class_Omod(X4492,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4492),X4491),X4490),X4490) = c_Groups_Ozero__class_Ozero(X4492) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0])]) ).
fof(i_0_2175,plain,
! [X3127,X3128,X3129] :
( ~ class_Fields_Ofield__inverse__zero(X3129)
| c_Rings_Oinverse__class_Odivide(X3129,c_Groups_Ouminus__class_Ouminus(X3129,X3128),c_Groups_Ouminus__class_Ouminus(X3129,X3127)) = c_Rings_Oinverse__class_Odivide(X3129,X3128,X3127) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__divide])]) ).
cnf(i_0_2176,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_1388]) ).
cnf(i_0_2177,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1336]) ).
fof(i_0_2178,plain,
! [X5001,X5002,X5003] :
( ~ class_Fields_Ofield(X5003)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5003),X5002,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5003),X5001)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5003),X5002,X5001) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mod__minus__right])]) ).
cnf(i_0_2179,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_1389]) ).
fof(i_0_2180,plain,
! [X5492,X5493] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5493),X5492) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5493,X5492) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__not__zero])]) ).
fof(i_0_2181,plain,
! [X5490,X5491] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X5491,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5490)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5491,X5490) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__not__zero])]) ).
fof(i_0_2182,plain,
! [X3932,X3933,X3935,X3936,X3937] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3933,X3932)
| X3932 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3933,esk30_2(X3932,X3933)) )
& ( X3935 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3936,X3937)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3936,X3935) ) ),
inference(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_2183,plain,
! [X3590,X3591,X3593,X3594,X3595] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3591,X3590)
| X3590 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3591,esk24_2(X3590,X3591)) )
& ( X3593 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3594,X3595)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3594,X3593) ) ),
inference(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_2184,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[i_0_1390]) ).
fof(i_0_2185,plain,
! [X5408,X5409,X5411,X5412,X5413] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X5409,X5408) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X5409 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5408),esk69_2(X5408,X5409)) )
& ( X5412 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5411),X5413)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5412,X5411) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__eq__0__iff])])])])]) ).
fof(i_0_2186,plain,
! [X4493,X4494,X4496,X4497,X4498] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4494,X4493) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4494 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4493),esk54_2(X4493,X4494)) )
& ( X4497 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4496),X4498)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4497,X4496) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq__0__iff])])])])]) ).
fof(i_0_2187,plain,
! [X5481,X5482] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5482,X5481),X5481) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__zdiv__trivial]) ).
fof(i_0_2188,plain,
! [X5790,X5791] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5791,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5791,X5790)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).
fof(i_0_2189,plain,
! [X5724,X5725] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5725,X5724),X5725) = X5724,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).
fof(i_0_2190,plain,
! [X5726,X5727] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5727,X5726),X5726) = X5727,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).
fof(i_0_2191,plain,
! [X5713,X5714] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5714,X5713),X5714),
inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).
fof(i_0_2192,plain,
! [X4392,X4393] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4393,X4392),X4393),
inference(variable_rename,[status(thm)],[fact_mod__less__eq__dividend]) ).
fof(i_0_2193,plain,
! [X4097,X4098] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4098,X4097),X4098),
inference(variable_rename,[status(thm)],[fact_div__le__dividend]) ).
fof(i_0_2194,plain,
! [X3598,X3599] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3599,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3599,X3598)),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_2195,plain,
! [X3600,X3601] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3601,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3600,X3601)),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_2196,plain,
! [X5608,X5609] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5609)
| c_SMT_Oz3mod(X5608,X5609) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X5608,X5609) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5609)
| c_SMT_Oz3mod(X5608,X5609) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X5608,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5609)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1391])]) ).
fof(i_0_2197,plain,
! [X4676,X4677,X4678,X4679] :
( ( X4677 = c_Groups_Ozero__class_Ozero(X4679)
| X4678 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4679),X4676),X4677)
| c_Rings_Oinverse__class_Odivide(X4679,X4678,X4677) != X4676
| ~ class_Fields_Ofield__inverse__zero(X4679) )
& ( X4677 != c_Groups_Ozero__class_Ozero(X4679)
| X4676 = c_Groups_Ozero__class_Ozero(X4679)
| c_Rings_Oinverse__class_Odivide(X4679,X4678,X4677) != X4676
| ~ class_Fields_Ofield__inverse__zero(X4679) )
& ( X4677 = c_Groups_Ozero__class_Ozero(X4679)
| X4677 != c_Groups_Ozero__class_Ozero(X4679)
| c_Rings_Oinverse__class_Odivide(X4679,X4678,X4677) = X4676
| ~ class_Fields_Ofield__inverse__zero(X4679) )
& ( X4676 != c_Groups_Ozero__class_Ozero(X4679)
| X4677 != c_Groups_Ozero__class_Ozero(X4679)
| c_Rings_Oinverse__class_Odivide(X4679,X4678,X4677) = X4676
| ~ class_Fields_Ofield__inverse__zero(X4679) )
& ( X4677 = c_Groups_Ozero__class_Ozero(X4679)
| X4678 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4679),X4676),X4677)
| c_Rings_Oinverse__class_Odivide(X4679,X4678,X4677) = X4676
| ~ class_Fields_Ofield__inverse__zero(X4679) )
& ( X4676 != c_Groups_Ozero__class_Ozero(X4679)
| X4678 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4679),X4676),X4677)
| c_Rings_Oinverse__class_Odivide(X4679,X4678,X4677) = X4676
| ~ class_Fields_Ofield__inverse__zero(X4679) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq])])]) ).
fof(i_0_2198,plain,
! [X4672,X4673,X4674,X4675] :
( ( X4672 = c_Groups_Ozero__class_Ozero(X4675)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4675),X4674),X4672) = X4673
| X4674 != c_Rings_Oinverse__class_Odivide(X4675,X4673,X4672)
| ~ class_Fields_Ofield__inverse__zero(X4675) )
& ( X4672 != c_Groups_Ozero__class_Ozero(X4675)
| X4674 = c_Groups_Ozero__class_Ozero(X4675)
| X4674 != c_Rings_Oinverse__class_Odivide(X4675,X4673,X4672)
| ~ class_Fields_Ofield__inverse__zero(X4675) )
& ( X4672 = c_Groups_Ozero__class_Ozero(X4675)
| X4672 != c_Groups_Ozero__class_Ozero(X4675)
| X4674 = c_Rings_Oinverse__class_Odivide(X4675,X4673,X4672)
| ~ class_Fields_Ofield__inverse__zero(X4675) )
& ( X4674 != c_Groups_Ozero__class_Ozero(X4675)
| X4672 != c_Groups_Ozero__class_Ozero(X4675)
| X4674 = c_Rings_Oinverse__class_Odivide(X4675,X4673,X4672)
| ~ class_Fields_Ofield__inverse__zero(X4675) )
& ( X4672 = c_Groups_Ozero__class_Ozero(X4675)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4675),X4674),X4672) != X4673
| X4674 = c_Rings_Oinverse__class_Odivide(X4675,X4673,X4672)
| ~ class_Fields_Ofield__inverse__zero(X4675) )
& ( X4674 != c_Groups_Ozero__class_Ozero(X4675)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4675),X4674),X4672) != X4673
| X4674 = c_Rings_Oinverse__class_Odivide(X4675,X4673,X4672)
| ~ class_Fields_Ofield__inverse__zero(X4675) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq])])]) ).
fof(i_0_2199,plain,
! [X4035] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X4035))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4035) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4035)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X4035)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one])]) ).
fof(i_0_2200,plain,
! [X4010] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X4010),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4010,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4010,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X4010),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_2201,plain,
! [X4693,X4694,X4695,X4696] :
( ( X4694 != c_Rings_Oinverse__class_Odivide(X4696,X4693,X4695)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4694),X4695) = X4693
| X4695 = c_Groups_Ozero__class_Ozero(X4696)
| ~ class_Rings_Odivision__ring(X4696) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4694),X4695) != X4693
| X4694 = c_Rings_Oinverse__class_Odivide(X4696,X4693,X4695)
| X4695 = c_Groups_Ozero__class_Ozero(X4696)
| ~ class_Rings_Odivision__ring(X4696) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq])])]) ).
fof(i_0_2202,plain,
! [X4697,X4698,X4699,X4700] :
( ( c_Rings_Oinverse__class_Odivide(X4700,X4698,X4699) != X4697
| X4698 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4700),X4697),X4699)
| X4699 = c_Groups_Ozero__class_Ozero(X4700)
| ~ class_Rings_Odivision__ring(X4700) )
& ( X4698 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4700),X4697),X4699)
| c_Rings_Oinverse__class_Odivide(X4700,X4698,X4699) = X4697
| X4699 = c_Groups_Ozero__class_Ozero(X4700)
| ~ class_Rings_Odivision__ring(X4700) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq])])]) ).
fof(i_0_2203,plain,
! [X4701,X4702,X4703,X4704] :
( ~ class_Rings_Odivision__ring(X4704)
| X4703 = c_Groups_Ozero__class_Ozero(X4704)
| X4702 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4704),X4701),X4703)
| c_Rings_Oinverse__class_Odivide(X4704,X4702,X4703) = X4701 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__imp])]) ).
fof(i_0_2204,plain,
! [X4705,X4706,X4707,X4708] :
( ~ class_Rings_Odivision__ring(X4708)
| X4707 = c_Groups_Ozero__class_Ozero(X4708)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4708),X4706),X4707) != X4705
| X4706 = c_Rings_Oinverse__class_Odivide(X4708,X4705,X4707) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__imp])]) ).
cnf(i_0_2205,plain,
( X1 = c_Nat_OSuc(esk25_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_1392]) ).
fof(i_0_2206,plain,
! [X5584,X5585] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5585),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5584)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5585,X5584),
inference(variable_rename,[status(thm)],[fact_zdiv__zminus__zminus]) ).
fof(i_0_2207,plain,
! [X5586,X5587] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5587,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5586)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5587),X5586),
inference(variable_rename,[status(thm)],[fact_zdiv__zminus2]) ).
fof(i_0_2208,plain,
! [X4266,X4267,X4268] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4268),X4267) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4266),X4267)
| X4268 = X4266
| X4267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4268 != X4266
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4268),X4267) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4266),X4267) )
& ( X4267 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4268),X4267) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4266),X4267) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).
fof(i_0_2209,plain,
! [X5023,X5024,X5025] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5024),X5025) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5023),X5025)
| X5024 = X5023
| X5025 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X5024 != X5023
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5024),X5025) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5023),X5025)
| X5025 = 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_2210,plain,
! [X5060,X5061,X5062] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5062),X5061) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5062),X5060)
| X5062 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X5061 = X5060 )
& ( X5062 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5062),X5061) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5062),X5060) )
& ( X5061 != X5060
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5062),X5061) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5062),X5060) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_2211,plain,
! [X4269,X4270,X4271] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4271),X4270) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4271),X4269)
| X4270 = X4269
| X4271 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4270 != X4269
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4271),X4270) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4271),X4269) )
& ( X4271 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4271),X4270) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4271),X4269) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).
fof(i_0_2212,plain,
! [X5020,X5021,X5022] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5022),X5021) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5022),X5020)
| X5021 = X5020
| X5022 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X5021 != X5020
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5022),X5021) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5022),X5020)
| X5022 = 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_2213,plain,
! [X3897,X3898,X3899] :
( ~ class_Orderings_Oorder(X3899)
| ~ c_Orderings_Oord__class_Oless__eq(X3899,X3898,X3897)
| X3897 = X3898
| c_Orderings_Oord__class_Oless(X3899,X3898,X3897) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_2214,plain,
! [X3894,X3895,X3896] :
( ~ class_Orderings_Oorder(X3896)
| ~ c_Orderings_Oord__class_Oless__eq(X3896,X3895,X3894)
| X3895 = X3894
| c_Orderings_Oord__class_Oless(X3896,X3895,X3894) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_2215,plain,
! [X3891,X3892,X3893] :
( ~ class_Orderings_Oorder(X3893)
| ~ c_Orderings_Oord__class_Oless__eq(X3893,X3892,X3891)
| c_Orderings_Oord__class_Oless(X3893,X3892,X3891)
| X3892 = X3891 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_2216,plain,
! [X3876,X3877,X3878] :
( ~ class_Orderings_Oorder(X3878)
| X3877 = X3876
| ~ c_Orderings_Oord__class_Oless__eq(X3878,X3877,X3876)
| c_Orderings_Oord__class_Oless(X3878,X3877,X3876) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_2217,plain,
! [X3864,X3865,X3866] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3866,X3865,X3864)
| c_Orderings_Oord__class_Oless(X3866,X3865,X3864)
| X3865 = X3864
| ~ class_Orderings_Oorder(X3866) )
& ( ~ c_Orderings_Oord__class_Oless(X3866,X3865,X3864)
| c_Orderings_Oord__class_Oless__eq(X3866,X3865,X3864)
| ~ class_Orderings_Oorder(X3866) )
& ( X3865 != X3864
| c_Orderings_Oord__class_Oless__eq(X3866,X3865,X3864)
| ~ class_Orderings_Oorder(X3866) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_2218,plain,
! [X3858,X3859,X3860] :
( ( c_Orderings_Oord__class_Oless__eq(X3860,X3859,X3858)
| ~ c_Orderings_Oord__class_Oless(X3860,X3859,X3858)
| ~ class_Orderings_Oorder(X3860) )
& ( X3859 != X3858
| ~ c_Orderings_Oord__class_Oless(X3860,X3859,X3858)
| ~ class_Orderings_Oorder(X3860) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3860,X3859,X3858)
| X3859 = X3858
| c_Orderings_Oord__class_Oless(X3860,X3859,X3858)
| ~ class_Orderings_Oorder(X3860) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_2219,plain,
! [X3873,X3874,X3875] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3875,X3874,X3873)
| X3874 = X3873
| c_Orderings_Oord__class_Oless(X3875,X3874,X3873)
| ~ class_Orderings_Olinorder(X3875) )
& ( X3874 != X3873
| c_Orderings_Oord__class_Oless__eq(X3875,X3874,X3873)
| c_Orderings_Oord__class_Oless(X3875,X3874,X3873)
| ~ class_Orderings_Olinorder(X3875) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1393])])]) ).
fof(i_0_2220,plain,
! [X3879,X3880,X3881] :
( ~ class_Orderings_Oorder(X3881)
| X3880 = X3879
| ~ c_Orderings_Oord__class_Oless__eq(X3881,X3879,X3880)
| c_Orderings_Oord__class_Oless(X3881,X3879,X3880) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_2221,plain,
! [X4714,X4715] :
( ~ class_Rings_Ocomm__ring__1(X4715)
| c_Groups_Ouminus__class_Ouminus(X4715,X4714) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4715),c_Groups_Ouminus__class_Ouminus(X4715,c_Groups_Oone__class_Oone(X4715))),X4714) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).
fof(i_0_2222,plain,
! [X4027,X4028] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4028,X4027)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X4028),c_RComplete_Onatfloor(X4027)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__mono])]) ).
fof(i_0_2223,plain,
! [X3978,X3979] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3979,X3978)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3979),c_RComplete_Onatceiling(X3978)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__mono])]) ).
fof(i_0_2224,plain,
! [X3885,X3886,X3887] :
( ~ class_Orderings_Opreorder(X3887)
| ~ c_Orderings_Oord__class_Oless(X3887,X3886,X3885)
| c_Orderings_Oord__class_Oless__eq(X3887,X3886,X3885) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
cnf(i_0_2225,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_1392]) ).
fof(i_0_2226,plain,
! [X5466] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5466)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5466) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5466)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5466) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).
fof(i_0_2227,plain,
! [X3006,X3007] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3007,X3006))
| X3006 != c_Groups_Ozero__class_Ozero(X3007)
| ~ class_RealVector_Oreal__normed__vector(X3007) )
& ( X3006 = c_Groups_Ozero__class_Ozero(X3007)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3007,X3006))
| ~ class_RealVector_Oreal__normed__vector(X3007) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).
fof(i_0_2228,plain,
! [X3188] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3188)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3188)),
inference(variable_rename,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).
fof(i_0_2229,plain,
! [X4371] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4371,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4371),X4371)),
inference(variable_rename,[status(thm)],[fact_le__square]) ).
fof(i_0_2230,plain,
! [X5798,X5799,X5800] :
( ~ class_Groups_Ogroup__add(X5800)
| c_Groups_Ominus__class_Ominus(X5800,X5799,c_Groups_Ouminus__class_Ouminus(X5800,X5798)) = c_Groups_Oplus__class_Oplus(X5800,X5799,X5798) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).
fof(i_0_2231,plain,
! [X3004,X3005] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3005,X3004),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X3004 = c_Groups_Ozero__class_Ozero(X3005)
| ~ class_RealVector_Oreal__normed__vector(X3005) )
& ( X3004 != c_Groups_Ozero__class_Ozero(X3005)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3005,X3004),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X3005) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])]) ).
fof(i_0_2232,plain,
! [X5786,X5787] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5787,X5786) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5787,X5786) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5787,X5786)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5787,X5786) = 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_2233,plain,
! [X5548,X5549] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5549,X5548)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5549,X5548) )
& ( X5549 != X5548
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5549,X5548) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5549,X5548)
| X5549 = X5548
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5549,X5548) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).
fof(i_0_2234,plain,
! [X3539,X3540] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3540,X3539)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3540,X3539) )
& ( X3540 != X3539
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3540,X3539) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3540,X3539)
| X3540 = X3539
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3540,X3539) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_2235,plain,
! [X3537,X3538] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3538,X3537)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3538,X3537)
| X3538 = X3537 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3538,X3537)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3538,X3537) )
& ( X3538 != X3537
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3538,X3537) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_2236,plain,
! [X3524,X3525] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3525,X3524)
| X3525 = X3524
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3525,X3524) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_2237,plain,
! [X3125,X3126] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3126,X3125)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3126,X3125) )
& ( X3126 != X3125
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3126,X3125) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3126,X3125)
| X3126 = X3125
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3126,X3125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).
fof(i_0_2238,plain,
! [X3123,X3124] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3124,X3123)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3124,X3123)
| X3124 = X3123 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3124,X3123)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3124,X3123) )
& ( X3124 != X3123
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3124,X3123) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
fof(i_0_2239,plain,
! [X5788,X5789] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5789,X5788)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5789,X5788) = 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_2240,plain,
! [X4080,X4081] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4081,X4080)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4081,X4080) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less])]) ).
fof(i_0_2241,plain,
! [X3957,X3958,X3959,X3960] :
( ~ class_Groups_Ouminus(X3960)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3959,X3960),X3958),X3957) = c_Groups_Ouminus__class_Ouminus(X3960,hAPP(X3958,X3957)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).
fof(i_0_2242,plain,
! [X4506,X4507] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4507,X4506)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4507,X4506) = X4507 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less])]) ).
fof(i_0_2243,plain,
! [X3922,X3923] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3923,X3922)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3923,X3922) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_2244,plain,
! [X3526,X3527] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3527,X3526)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3527,X3526) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_2245,plain,
! [X3522,X3523] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3523,X3522)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3523,X3522) )
& ( X3523 != X3522
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3523,X3522) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_2246,plain,
! [X3057,X3058] :
( ~ class_RealVector_Oreal__normed__vector(X3058)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3058,X3057),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1394])]) ).
cnf(i_0_2247,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__one]) ).
fof(i_0_2248,plain,
! [X5012,X5013] :
( ~ class_Rings_Ocomm__semiring__0(X5013)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5013)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5013))),X5012) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5013)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__0__left])]) ).
fof(i_0_2249,plain,
! [X3237] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3237),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X3237 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3237 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3237),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_2250,plain,
! [X2952,X2953] :
( hAPP(X2953,esk1_2(X2952,X2953)) != hAPP(X2952,esk1_2(X2952,X2953))
| X2953 = X2952 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_2251,plain,
! [X3062,X3063] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3063,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3062)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3063 = X3062 )
& ( X3063 != X3062
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3063,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3062)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__minus__iff])]) ).
fof(i_0_2252,plain,
! [X3061] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3061),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[i_0_1395]) ).
fof(i_0_2253,plain,
! [X5218,X5219,X5220] :
( ( X5219 = c_Groups_Ozero__class_Ozero(X5220)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5220),X5219),X5218) != c_Groups_Ozero__class_Ozero(X5220)
| ~ class_Power_Opower(X5220)
| ~ class_Rings_Omult__zero(X5220)
| ~ class_Rings_Ono__zero__divisors(X5220)
| ~ class_Rings_Ozero__neq__one(X5220) )
& ( X5218 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5220),X5219),X5218) != c_Groups_Ozero__class_Ozero(X5220)
| ~ class_Power_Opower(X5220)
| ~ class_Rings_Omult__zero(X5220)
| ~ class_Rings_Ono__zero__divisors(X5220)
| ~ class_Rings_Ozero__neq__one(X5220) )
& ( X5219 != c_Groups_Ozero__class_Ozero(X5220)
| X5218 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5220),X5219),X5218) = c_Groups_Ozero__class_Ozero(X5220)
| ~ class_Power_Opower(X5220)
| ~ class_Rings_Omult__zero(X5220)
| ~ class_Rings_Ono__zero__divisors(X5220)
| ~ class_Rings_Ozero__neq__one(X5220) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).
fof(i_0_2254,plain,
! [X4712,X4713] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4713),X4712),X4712) != c_Groups_Oone__class_Oone(X4713)
| X4712 = c_Groups_Oone__class_Oone(X4713)
| X4712 = c_Groups_Ouminus__class_Ouminus(X4713,c_Groups_Oone__class_Oone(X4713))
| ~ class_Rings_Oring__1__no__zero__divisors(X4713) )
& ( X4712 != c_Groups_Oone__class_Oone(X4713)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4713),X4712),X4712) = c_Groups_Oone__class_Oone(X4713)
| ~ class_Rings_Oring__1__no__zero__divisors(X4713) )
& ( X4712 != c_Groups_Ouminus__class_Ouminus(X4713,c_Groups_Oone__class_Oone(X4713))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4713),X4712),X4712) = c_Groups_Oone__class_Oone(X4713)
| ~ class_Rings_Oring__1__no__zero__divisors(X4713) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).
fof(i_0_2255,plain,
! [X3778,X3779,X3780] :
( ( X3779 = X3778
| c_Orderings_Oord__class_Oless(X3780,X3779,X3778)
| c_Orderings_Oord__class_Oless(X3780,X3778,X3779)
| ~ class_Orderings_Olinorder(X3780) )
& ( ~ c_Orderings_Oord__class_Oless(X3780,X3779,X3778)
| X3779 != X3778
| ~ class_Orderings_Olinorder(X3780) )
& ( ~ c_Orderings_Oord__class_Oless(X3780,X3778,X3779)
| X3779 != X3778
| ~ class_Orderings_Olinorder(X3780) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_2256,plain,
! [X3841,X3842,X3843] :
( ~ class_Orderings_Olinorder(X3843)
| c_Orderings_Oord__class_Oless(X3843,X3842,X3841)
| X3842 = X3841
| c_Orderings_Oord__class_Oless(X3843,X3841,X3842) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1396])]) ).
fof(i_0_2257,plain,
! [X3790,X3791,X3792] :
( ~ class_Orderings_Olinorder(X3792)
| X3791 = X3790
| c_Orderings_Oord__class_Oless(X3792,X3791,X3790)
| c_Orderings_Oord__class_Oless(X3792,X3790,X3791) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1397])]) ).
fof(i_0_2258,plain,
! [X3787,X3788,X3789] :
( ( c_Orderings_Oord__class_Oless(X3789,X3787,X3788)
| X3787 = X3788
| c_Orderings_Oord__class_Oless(X3789,X3788,X3787)
| ~ class_Orderings_Olinorder(X3789) )
& ( X3787 != X3788
| ~ c_Orderings_Oord__class_Oless(X3789,X3787,X3788)
| c_Orderings_Oord__class_Oless(X3789,X3788,X3787)
| ~ class_Orderings_Olinorder(X3789) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1398])])]) ).
fof(i_0_2259,plain,
! [X3784,X3785,X3786] :
( ~ class_Orderings_Olinorder(X3786)
| c_Orderings_Oord__class_Oless(X3786,X3785,X3784)
| X3785 = X3784
| c_Orderings_Oord__class_Oless(X3786,X3784,X3785) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_2260,plain,
! [X3197,X3198,X3199] :
( ~ class_Rings_Olinordered__idom(X3199)
| X3198 = X3197
| c_Orderings_Oord__class_Oless(X3199,X3198,X3197)
| c_Orderings_Oord__class_Oless(X3199,X3197,X3198) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1399])]) ).
fof(i_0_2261,plain,
! [X3870,X3871,X3872] :
( ~ class_Orderings_Olinorder(X3872)
| c_Orderings_Oord__class_Oless__eq(X3872,X3871,X3870)
| c_Orderings_Oord__class_Oless(X3872,X3870,X3871) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1400])]) ).
fof(i_0_2262,plain,
! [X3855,X3856,X3857] :
( ~ class_Orderings_Olinorder(X3857)
| c_Orderings_Oord__class_Oless__eq(X3857,X3856,X3855)
| c_Orderings_Oord__class_Oless(X3857,X3855,X3856) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_2263,plain,
! [X3867,X3868,X3869] :
( ~ class_Orderings_Olinorder(X3869)
| c_Orderings_Oord__class_Oless(X3869,X3868,X3867)
| c_Orderings_Oord__class_Oless__eq(X3869,X3867,X3868) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1401])]) ).
fof(i_0_2264,plain,
! [X3773,X3774,X3775] :
( ~ class_Orderings_Olinorder(X3775)
| c_Orderings_Oord__class_Oless__eq(X3775,X3774,X3773)
| c_Orderings_Oord__class_Oless__eq(X3775,X3773,X3774) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1402])]) ).
fof(i_0_2265,plain,
! [X3721,X3722,X3723] :
( ~ class_Orderings_Olinorder(X3723)
| c_Orderings_Oord__class_Oless__eq(X3723,X3722,X3721)
| c_Orderings_Oord__class_Oless__eq(X3723,X3721,X3722) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_2266,plain,
! [X3984,X3985,X3986] :
( ~ class_Rings_Ocomm__semiring__1(X3986)
| c_Groups_Oplus__class_Oplus(X3986,X3985,X3984) = c_Groups_Oplus__class_Oplus(X3986,X3984,X3985) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_2267,plain,
! [X3442,X3443,X3444] :
( ~ class_Groups_Ogroup__add(X3444)
| c_Groups_Oplus__class_Oplus(X3444,X3443,X3442) != c_Groups_Ozero__class_Ozero(X3444)
| c_Groups_Ouminus__class_Ouminus(X3444,X3443) = X3442 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).
fof(i_0_2268,plain,
! [X3435,X3436,X3437] :
( ( X3436 != c_Groups_Ouminus__class_Ouminus(X3437,X3435)
| c_Groups_Oplus__class_Oplus(X3437,X3436,X3435) = c_Groups_Ozero__class_Ozero(X3437)
| ~ class_Groups_Ogroup__add(X3437) )
& ( c_Groups_Oplus__class_Oplus(X3437,X3436,X3435) != c_Groups_Ozero__class_Ozero(X3437)
| X3436 = c_Groups_Ouminus__class_Ouminus(X3437,X3435)
| ~ class_Groups_Ogroup__add(X3437) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).
fof(i_0_2269,plain,
! [X3022,X3023,X3024] :
( ( c_Groups_Oplus__class_Oplus(X3024,X3023,X3022) != c_Groups_Ozero__class_Ozero(X3024)
| X3022 = c_Groups_Ouminus__class_Ouminus(X3024,X3023)
| ~ class_Groups_Ogroup__add(X3024) )
& ( X3022 != c_Groups_Ouminus__class_Ouminus(X3024,X3023)
| c_Groups_Oplus__class_Oplus(X3024,X3023,X3022) = c_Groups_Ozero__class_Ozero(X3024)
| ~ class_Groups_Ogroup__add(X3024) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff])])]) ).
fof(i_0_2270,plain,
! [X3413] :
( ~ class_Rings_Olinordered__semidom(X3413)
| ~ c_Orderings_Oord__class_Oless(X3413,c_Groups_Oone__class_Oone(X3413),c_Groups_Ozero__class_Ozero(X3413)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1403])]) ).
fof(i_0_2271,plain,
! [X3411] :
( ~ class_Rings_Olinordered__semidom(X3411)
| ~ c_Orderings_Oord__class_Oless__eq(X3411,c_Groups_Oone__class_Oone(X3411),c_Groups_Ozero__class_Ozero(X3411)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1404])]) ).
fof(i_0_2272,plain,
! [X5014,X5015] :
( ~ class_Rings_Ocomm__semiring__0(X5015)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5015)),X5014),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5015))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5015)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__0__right])]) ).
cnf(i_0_2273,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_1405]) ).
fof(i_0_2274,plain,
! [X4206,X4207,X4208] :
( ~ class_Rings_Ocomm__semiring__1(X4208)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4208),X4207),X4206) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4208),X4206),X4207) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
cnf(i_0_2275,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_1369]) ).
fof(i_0_2276,plain,
! [X5546,X5547] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5547,X5546)
| X5547 = X5546
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5546,X5547) ),
inference(variable_rename,[status(thm)],[fact_zless__linear]) ).
fof(i_0_2277,plain,
! [X3542,X3543] :
( ( X3543 = X3542
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3543,X3542)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3542,X3543) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3543,X3542)
| X3543 != X3542 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3542,X3543)
| X3543 != X3542 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_2278,plain,
! [X3535,X3536] :
( X3536 = X3535
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3536,X3535)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3535,X3536) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1406])]) ).
fof(i_0_2279,plain,
! [X3449,X3450,X3451] :
( ( c_Rings_Oinverse__class_Odivide(X3451,X3449,X3450) != c_Groups_Oone__class_Oone(X3451)
| X3449 = X3450
| X3450 = c_Groups_Ozero__class_Ozero(X3451)
| ~ class_Rings_Odivision__ring(X3451) )
& ( X3449 != X3450
| c_Rings_Oinverse__class_Odivide(X3451,X3449,X3450) = c_Groups_Oone__class_Oone(X3451)
| X3450 = c_Groups_Ozero__class_Ozero(X3451)
| ~ class_Rings_Odivision__ring(X3451) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])]) ).
fof(i_0_2280,plain,
! [X5522,X5523] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5523,X5522)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5522,X5523) ),
inference(variable_rename,[status(thm)],[fact_zle__linear]) ).
fof(i_0_2281,plain,
! [X3490,X3491] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3491,X3490)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3490,X3491) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_2282,plain,
! [X3114,X3115] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3115,X3114)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3114,X3115) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(i_0_2283,plain,
! [X4340,X4341,X4342] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4342),X4341),X4340) != c_Groups_Ozero__class_Ozero(X4342)
| X4341 = c_Groups_Ozero__class_Ozero(X4342)
| X4340 = c_Groups_Ozero__class_Ozero(X4342)
| ~ class_Rings_Oring__no__zero__divisors(X4342) )
& ( X4341 != c_Groups_Ozero__class_Ozero(X4342)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4342),X4341),X4340) = c_Groups_Ozero__class_Ozero(X4342)
| ~ class_Rings_Oring__no__zero__divisors(X4342) )
& ( X4340 != c_Groups_Ozero__class_Ozero(X4342)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4342),X4341),X4340) = c_Groups_Ozero__class_Ozero(X4342)
| ~ class_Rings_Oring__no__zero__divisors(X4342) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).
fof(i_0_2284,plain,
! [X4337,X4338,X4339] :
( ~ class_Rings_Ono__zero__divisors(X4339)
| X4338 = c_Groups_Ozero__class_Ozero(X4339)
| X4337 = c_Groups_Ozero__class_Ozero(X4339)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4339),X4338),X4337) != c_Groups_Ozero__class_Ozero(X4339) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).
fof(i_0_2285,plain,
! [X4334,X4335,X4336] :
( ~ class_Rings_Ono__zero__divisors(X4336)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4336),X4335),X4334) != c_Groups_Ozero__class_Ozero(X4336)
| X4335 = c_Groups_Ozero__class_Ozero(X4336)
| X4334 = c_Groups_Ozero__class_Ozero(X4336) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).
fof(i_0_2286,plain,
! [X5535,X5536] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5536,X5535) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5535,X5536),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(i_0_2287,plain,
! [X3588,X3589] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3589,X3588) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3588,X3589),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_2288,plain,
! [X3602,X3603] :
( ( c_Groups_Oplus__class_Oplus(X3603,X3602,X3602) != c_Groups_Ozero__class_Ozero(X3603)
| X3602 = c_Groups_Ozero__class_Ozero(X3603)
| ~ class_Groups_Olinordered__ab__group__add(X3603) )
& ( X3602 != c_Groups_Ozero__class_Ozero(X3603)
| c_Groups_Oplus__class_Oplus(X3603,X3602,X3602) = c_Groups_Ozero__class_Ozero(X3603)
| ~ class_Groups_Olinordered__ab__group__add(X3603) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_2289,plain,
! [X3245,X3246] :
( ( c_Groups_Ozero__class_Ozero(X3246) != c_Groups_Oplus__class_Oplus(X3246,X3245,X3245)
| X3245 = c_Groups_Ozero__class_Ozero(X3246)
| ~ class_Groups_Olinordered__ab__group__add(X3246) )
& ( X3245 != c_Groups_Ozero__class_Ozero(X3246)
| c_Groups_Ozero__class_Ozero(X3246) = c_Groups_Oplus__class_Oplus(X3246,X3245,X3245)
| ~ class_Groups_Olinordered__ab__group__add(X3246) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_2290,plain,
! [X5674,X5675,X5676] :
( ( X5675 != X5674
| c_Groups_Ominus__class_Ominus(X5676,X5675,X5674) = c_Groups_Ozero__class_Ozero(X5676)
| ~ class_Groups_Oab__group__add(X5676) )
& ( c_Groups_Ominus__class_Ominus(X5676,X5675,X5674) != c_Groups_Ozero__class_Ozero(X5676)
| X5675 = X5674
| ~ class_Groups_Oab__group__add(X5676) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).
fof(i_0_2291,plain,
! [X5677,X5678,X5679] :
( ( c_Groups_Ominus__class_Ominus(X5679,X5678,X5677) != c_Groups_Ozero__class_Ozero(X5679)
| X5678 = X5677
| ~ class_Groups_Ogroup__add(X5679) )
& ( X5678 != X5677
| c_Groups_Ominus__class_Ominus(X5679,X5678,X5677) = c_Groups_Ozero__class_Ozero(X5679)
| ~ class_Groups_Ogroup__add(X5679) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).
fof(i_0_2292,plain,
! [X5183,X5184,X5185] :
( ~ class_Rings_Oring__1__no__zero__divisors(X5185)
| X5184 = c_Groups_Ozero__class_Ozero(X5185)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5185),X5184),X5183) != c_Groups_Ozero__class_Ozero(X5185) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).
fof(i_0_2293,plain,
! [X3064,X3065] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3065,X3064) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3064 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3065) )
& ( X3064 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3065)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3065,X3064) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__eq__0__iff])]) ).
fof(i_0_2294,plain,
! [X3963,X3964,X3965] :
( ( X3964 != c_Groups_Oplus__class_Oplus(X3965,X3964,X3963)
| X3963 = c_Groups_Ozero__class_Ozero(X3965)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3965) )
& ( X3963 != c_Groups_Ozero__class_Ozero(X3965)
| X3964 = c_Groups_Oplus__class_Oplus(X3965,X3964,X3963)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3965) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_2295,plain,
! [X3844,X3845] :
( ( c_Polynomial_Opoly(X3845,X3844) != c_Polynomial_Opoly(X3845,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3845)))
| X3844 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3845))
| ~ class_Int_Oring__char__0(X3845)
| ~ class_Rings_Oidom(X3845) )
& ( X3844 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3845))
| c_Polynomial_Opoly(X3845,X3844) = c_Polynomial_Opoly(X3845,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3845)))
| ~ class_Int_Oring__char__0(X3845)
| ~ class_Rings_Oidom(X3845) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__zero])])]) ).
fof(i_0_2296,plain,
! [X3805,X3806,X3807] :
( ~ class_Orderings_Oorder(X3807)
| ~ c_Orderings_Oord__class_Oless(X3807,X3806,X3805)
| X3805 != X3806 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_2297,plain,
! [X3802,X3803,X3804] :
( ~ class_Orderings_Oorder(X3804)
| ~ c_Orderings_Oord__class_Oless(X3804,X3803,X3802)
| X3803 != X3802 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_2298,plain,
! [X3793,X3794,X3795] :
( ~ class_Orderings_Oorder(X3795)
| ~ c_Orderings_Oord__class_Oless(X3795,X3794,X3793)
| X3794 != X3793 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_2299,plain,
! [X4029] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4029,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(X4029) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__neg])]) ).
fof(i_0_2300,plain,
! [X3981] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3981,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatceiling(X3981) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__neg])]) ).
fof(i_0_2301,plain,
! [X3544] :
( ( X3544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3544) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3544)
| X3544 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_2302,plain,
! [X3776,X3777] :
( ~ class_Orderings_Opreorder(X3777)
| ~ c_Orderings_Oord__class_Oless(X3777,X3776,X3776) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1407])]) ).
fof(i_0_2303,plain,
! [X3482] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3482,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3482 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3482,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_2304,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1408]) ).
cnf(i_0_2305,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1409]) ).
cnf(i_0_2306,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1410]) ).
cnf(i_0_2307,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1411]) ).
cnf(i_0_2308,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1412]) ).
cnf(i_0_2309,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1413]) ).
fof(i_0_2310,plain,
! [X5349,X5350] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5350),X5349) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5349),X5350),
inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).
fof(i_0_2311,plain,
! [X4299,X4300] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4300),X4299) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4299),X4300),
inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).
fof(i_0_2312,plain,
! [X5010,X5011] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5011),X5010) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5010),X5011),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
fof(i_0_2313,plain,
! [X3440,X3441] :
( ~ class_Groups_Oab__group__add(X3441)
| c_Groups_Oplus__class_Oplus(X3441,c_Groups_Ouminus__class_Ouminus(X3441,X3440),X3440) = c_Groups_Ozero__class_Ozero(X3441) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).
fof(i_0_2314,plain,
! [X3438,X3439] :
( ~ class_Groups_Ogroup__add(X3439)
| c_Groups_Oplus__class_Oplus(X3439,c_Groups_Ouminus__class_Ouminus(X3439,X3438),X3438) = c_Groups_Ozero__class_Ozero(X3439) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).
fof(i_0_2315,plain,
! [X3433,X3434] :
( ~ class_Groups_Ogroup__add(X3434)
| c_Groups_Oplus__class_Oplus(X3434,X3433,c_Groups_Ouminus__class_Ouminus(X3434,X3433)) = c_Groups_Ozero__class_Ozero(X3434) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).
fof(i_0_2316,plain,
! [X3583,X3584] :
( ( X3584 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3584,X3583) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3583 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3584,X3583) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3584 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3583 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3584,X3583) = 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_2317,plain,
! [X3532,X3533] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3533,X3532)
| X3532 != 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_2318,plain,
c_Nat_OSuc(X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1414]) ).
cnf(i_0_2319,plain,
X1 != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1415]) ).
fof(i_0_2320,plain,
! [X3055,X3056] :
( ~ class_RealVector_Oreal__normed__vector(X3056)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3056,X3055)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).
fof(i_0_2321,plain,
! [X5264,X5265] :
( ( X5264 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5265),c_Groups_Ozero__class_Ozero(X5265)),X5264) = c_Groups_Oone__class_Oone(X5265)
| ~ class_Power_Opower(X5265)
| ~ class_Rings_Osemiring__0(X5265) )
& ( X5264 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5265),c_Groups_Ozero__class_Ozero(X5265)),X5264) = c_Groups_Ozero__class_Ozero(X5265)
| ~ class_Power_Opower(X5265)
| ~ class_Rings_Osemiring__0(X5265) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).
fof(i_0_2322,plain,
! [X3556,X3557] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3557,X3556) != X3557
| X3556 = 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_2323,plain,
! [X3546] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3546,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1416]) ).
fof(i_0_2324,plain,
! [X3541] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3541,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1417]) ).
fof(i_0_2325,plain,
! [X3479] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3479,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1418]) ).
fof(i_0_2326,plain,
! [X3980] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3980,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X3980))),
inference(variable_rename,[status(thm)],[fact_real__natceiling__ge]) ).
fof(i_0_2327,plain,
! [X3699,X3700] :
( ~ class_Rings_Ocomm__semiring__1(X3700)
| hAPP(c_Polynomial_Opoly(X3700,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X3700))),X3699) = c_Groups_Oone__class_Oone(X3700) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__1])]) ).
fof(i_0_2328,plain,
! [X3705,X3706] :
( ~ class_Rings_Ocomm__semiring__0(X3706)
| hAPP(c_Polynomial_Opoly(X3706,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3706))),X3705) = c_Groups_Ozero__class_Ozero(X3706) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])]) ).
fof(i_0_2329,plain,
! [X3530,X3531] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3531,X3530)
| X3530 != X3531 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_2330,plain,
! [X3528,X3529] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3529,X3528)
| X3529 != X3528 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_2331,plain,
! [X3711,X3712] :
( ~ class_Groups_Ocomm__monoid__add(X3712)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3712),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3712)),X3711) = X3711 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J])]) ).
fof(i_0_2332,plain,
! [X3713,X3714] :
( ~ class_Groups_Ocomm__monoid__add(X3714)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3714),X3713,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3714))) = X3713 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J])]) ).
fof(i_0_2333,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk28_0),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk28_0)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,esk27_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_mth1])]) ).
fof(i_0_2334,plain,
! [X4272,X4273] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4273),X4272) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4272 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4273 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4273),X4272) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4272 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4273),X4272) = 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_2335,plain,
! [X3545] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3545,X3545),
inference(variable_rename,[status(thm)],[i_0_1419]) ).
fof(i_0_2336,plain,
! [X3534] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3534,X3534),
inference(variable_rename,[status(thm)],[i_0_1420]) ).
fof(i_0_2337,plain,
! [X4760,X4761] :
( X4761 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4761),X4760)
| X4760 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4761 = 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_2338,plain,
! [X4369,X4370] :
( ( X4370 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4370),X4369) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4369 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4370),X4369) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4370 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4369 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4370),X4369) = 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_2339,plain,
! [X4366,X4367] :
( ( X4367 = 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),X4367),X4366) )
& ( X4366 = 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),X4367),X4366) )
& ( X4367 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4366 != 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),X4367),X4366) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).
fof(i_0_2340,plain,
! [X2998] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2998)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__ge__zero]) ).
fof(i_0_2341,plain,
! [X5541] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5541),X5541) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).
fof(i_0_2342,plain,
! [X5317] :
( ~ class_Power_Opower(X5317)
| c_Power_Opower__class_Opower(X5317) = c_Power_Opower_Opower(X5317,c_Groups_Oone__class_Oone(X5317),c_Groups_Otimes__class_Otimes(X5317)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).
fof(i_0_2343,plain,
! [X5193,X5194] :
( ~ class_Groups_Omonoid__mult(X5194)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5194),c_Groups_Oone__class_Oone(X5194)),X5193) = c_Groups_Oone__class_Oone(X5194) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(i_0_2344,plain,
! [X4345,X4346] :
( ~ class_Rings_Omult__zero(X4346)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4346),c_Groups_Ozero__class_Ozero(X4346)),X4345) = c_Groups_Ozero__class_Ozero(X4346) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).
fof(i_0_2345,plain,
! [X4353,X4354] :
( ~ class_RealVector_Oreal__normed__algebra(X4354)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4354),c_Groups_Ozero__class_Ozero(X4354)),X4353) = c_Groups_Ozero__class_Ozero(X4354) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])]) ).
fof(i_0_2346,plain,
! [X4351,X4352] :
( ~ class_RealVector_Oreal__normed__algebra(X4352)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4352),c_Groups_Ozero__class_Ozero(X4352)),X4351) = c_Groups_Ozero__class_Ozero(X4352) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])]) ).
fof(i_0_2347,plain,
! [X4237,X4238] :
( ~ class_Rings_Ocomm__semiring__1(X4238)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4238),c_Groups_Ozero__class_Ozero(X4238)),X4237) = c_Groups_Ozero__class_Ozero(X4238) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
fof(i_0_2348,plain,
! [X3445,X3446] :
( ( X3445 != c_Groups_Ozero__class_Ozero(X3446)
| c_Rings_Oinverse__class_Odivide(X3446,X3445,X3445) = c_Groups_Ozero__class_Ozero(X3446)
| ~ class_Rings_Odivision__ring__inverse__zero(X3446) )
& ( X3445 = c_Groups_Ozero__class_Ozero(X3446)
| c_Rings_Oinverse__class_Odivide(X3446,X3445,X3445) = c_Groups_Oone__class_Oone(X3446)
| ~ class_Rings_Odivision__ring__inverse__zero(X3446) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self__if])])]) ).
fof(i_0_2349,plain,
! [X3414] :
( ~ class_Rings_Olinordered__semidom(X3414)
| c_Orderings_Oord__class_Oless(X3414,c_Groups_Ozero__class_Ozero(X3414),c_Groups_Oone__class_Oone(X3414)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_2350,plain,
! [X3412] :
( ~ class_Rings_Olinordered__semidom(X3412)
| c_Orderings_Oord__class_Oless__eq(X3412,c_Groups_Ozero__class_Ozero(X3412),c_Groups_Oone__class_Oone(X3412)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_2351,plain,
! [X4303,X4304] :
( ~ class_Groups_Ocomm__monoid__mult(X4304)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4304),c_Groups_Oone__class_Oone(X4304)),X4303) = X4303 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).
fof(i_0_2352,plain,
! [X4301,X4302] :
( ~ class_Groups_Omonoid__mult(X4302)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4302),c_Groups_Oone__class_Oone(X4302)),X4301) = X4301 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).
fof(i_0_2353,plain,
! [X4209,X4210] :
( ~ class_Rings_Ocomm__semiring__1(X4210)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4210),c_Groups_Oone__class_Oone(X4210)),X4209) = X4209 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).
fof(i_0_2354,plain,
! [X4481,X4482] :
( ~ class_Divides_Osemiring__div(X4482)
| c_Divides_Odiv__class_Omod(X4482,c_Groups_Ozero__class_Ozero(X4482),X4481) = c_Groups_Ozero__class_Ozero(X4482) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__0])]) ).
fof(i_0_2355,plain,
! [X4088,X4089] :
( ~ class_Divides_Osemiring__div(X4089)
| c_Divides_Odiv__class_Odiv(X4089,c_Groups_Ozero__class_Ozero(X4089),X4088) = c_Groups_Ozero__class_Ozero(X4089) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])]) ).
fof(i_0_2356,plain,
! [X3341,X3342] :
( ~ class_Rings_Odivision__ring(X3342)
| c_Rings_Oinverse__class_Odivide(X3342,c_Groups_Ozero__class_Ozero(X3342),X3341) = c_Groups_Ozero__class_Ozero(X3342) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])]) ).
fof(i_0_2357,plain,
! [X3002,X3003] :
( ~ class_RealVector_Oreal__normed__field(X3003)
| c_Rings_Oinverse__class_Odivide(X3003,c_Groups_Ozero__class_Ozero(X3003),X3002) = c_Groups_Ozero__class_Ozero(X3003) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Ozero])]) ).
fof(i_0_2358,plain,
! [X4524,X4525] :
( ~ class_Divides_Osemiring__div(X4525)
| c_Divides_Odiv__class_Omod(X4525,X4524,c_Groups_Oone__class_Oone(X4525)) = c_Groups_Ozero__class_Ozero(X4525) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__1])]) ).
fof(i_0_2359,plain,
! [X4090,X4091] :
( ~ class_Divides_Osemiring__div(X4091)
| c_Divides_Odiv__class_Odiv(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_div__by__0])]) ).
fof(i_0_2360,plain,
! [X3343,X3344] :
( ~ class_Rings_Odivision__ring__inverse__zero(X3344)
| c_Rings_Oinverse__class_Odivide(X3344,X3343,c_Groups_Ozero__class_Ozero(X3344)) = c_Groups_Ozero__class_Ozero(X3344) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])]) ).
fof(i_0_2361,plain,
! [X4099,X4100] :
( ~ class_Divides_Osemiring__div(X4100)
| X4099 = c_Groups_Ozero__class_Ozero(X4100)
| c_Divides_Odiv__class_Odiv(X4100,X4099,X4099) = c_Groups_Oone__class_Oone(X4100) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__self])]) ).
fof(i_0_2362,plain,
! [X3447,X3448] :
( ~ class_Rings_Odivision__ring(X3448)
| X3447 = c_Groups_Ozero__class_Ozero(X3448)
| c_Rings_Oinverse__class_Odivide(X3448,X3447,X3447) = c_Groups_Oone__class_Oone(X3448) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])]) ).
fof(i_0_2363,plain,
! [X4343,X4344] :
( ~ class_Rings_Omult__zero(X4344)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4344),X4343),c_Groups_Ozero__class_Ozero(X4344)) = c_Groups_Ozero__class_Ozero(X4344) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).
fof(i_0_2364,plain,
! [X4349,X4350] :
( ~ class_RealVector_Oreal__normed__algebra(X4350)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4350),X4349),c_Groups_Ozero__class_Ozero(X4350)) = c_Groups_Ozero__class_Ozero(X4350) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).
fof(i_0_2365,plain,
! [X4347,X4348] :
( ~ class_RealVector_Oreal__normed__algebra(X4348)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4348),X4347),c_Groups_Ozero__class_Ozero(X4348)) = c_Groups_Ozero__class_Ozero(X4348) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero])]) ).
fof(i_0_2366,plain,
! [X4235,X4236] :
( ~ class_Rings_Ocomm__semiring__1(X4236)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4236),X4235),c_Groups_Ozero__class_Ozero(X4236)) = c_Groups_Ozero__class_Ozero(X4236) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).
fof(i_0_2367,plain,
! [X3968,X3969] :
( ~ class_Rings_Ocomm__semiring__1(X3969)
| c_Groups_Oplus__class_Oplus(X3969,c_Groups_Ozero__class_Ozero(X3969),X3968) = X3968 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_2368,plain,
! [X3243,X3244] :
( ~ class_Groups_Ocomm__monoid__add(X3244)
| c_Groups_Oplus__class_Oplus(X3244,c_Groups_Ozero__class_Ozero(X3244),X3243) = X3243 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_2369,plain,
! [X3241,X3242] :
( ~ class_Groups_Omonoid__add(X3242)
| c_Groups_Oplus__class_Oplus(X3242,c_Groups_Ozero__class_Ozero(X3242),X3241) = X3241 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_2370,plain,
! [X5670,X5671] :
( ~ class_Groups_Ogroup__add(X5671)
| c_Groups_Ominus__class_Ominus(X5671,X5670,c_Groups_Ozero__class_Ozero(X5671)) = X5670 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).
fof(i_0_2371,plain,
! [X4483,X4484] :
( ~ class_Divides_Osemiring__div(X4484)
| c_Divides_Odiv__class_Omod(X4484,X4483,c_Groups_Ozero__class_Ozero(X4484)) = X4483 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__0])]) ).
fof(i_0_2372,plain,
! [X4092,X4093] :
( ~ class_Divides_Osemiring__div(X4093)
| c_Divides_Odiv__class_Odiv(X4093,X4092,c_Groups_Oone__class_Oone(X4093)) = X4092 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])]) ).
fof(i_0_2373,plain,
! [X3966,X3967] :
( ~ class_Rings_Ocomm__semiring__1(X3967)
| c_Groups_Oplus__class_Oplus(X3967,X3966,c_Groups_Ozero__class_Ozero(X3967)) = X3966 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_2374,plain,
! [X3249,X3250] :
( ~ class_Groups_Ocomm__monoid__add(X3250)
| c_Groups_Oplus__class_Oplus(X3250,X3249,c_Groups_Ozero__class_Ozero(X3250)) = X3249 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_2375,plain,
! [X3247,X3248] :
( ~ class_Groups_Omonoid__add(X3248)
| c_Groups_Oplus__class_Oplus(X3248,X3247,c_Groups_Ozero__class_Ozero(X3248)) = X3247 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_2376,plain,
! [X3361,X3362] :
( ~ class_Rings_Odivision__ring(X3362)
| c_Rings_Oinverse__class_Odivide(X3362,X3361,c_Groups_Oone__class_Oone(X3362)) = X3361 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])]) ).
fof(i_0_2377,plain,
! [X5237,X5238] :
( ~ class_Power_Opower(X5238)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5238),X5237),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X5238) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).
fof(i_0_2378,plain,
! [X5128,X5129] :
( ~ class_Rings_Ocomm__semiring__1(X5129)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5129),X5128),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X5129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).
fof(i_0_2379,plain,
! [X4307,X4308] :
( ~ class_Groups_Ocomm__monoid__mult(X4308)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4308),X4307),c_Groups_Oone__class_Oone(X4308)) = X4307 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).
fof(i_0_2380,plain,
! [X4305,X4306] :
( ~ class_Groups_Omonoid__mult(X4306)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4306),X4305),c_Groups_Oone__class_Oone(X4306)) = X4305 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).
fof(i_0_2381,plain,
! [X4211,X4212] :
( ~ class_Rings_Ocomm__semiring__1(X4212)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4212),X4211),c_Groups_Oone__class_Oone(X4212)) = X4211 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).
fof(i_0_2382,plain,
! [X5672,X5673] :
( ~ class_Groups_Ogroup__add(X5673)
| c_Groups_Ominus__class_Ominus(X5673,X5672,X5672) = c_Groups_Ozero__class_Ozero(X5673) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).
fof(i_0_2383,plain,
! [X4485,X4486] :
( ~ class_Divides_Osemiring__div(X4486)
| c_Divides_Odiv__class_Omod(X4486,X4485,X4485) = c_Groups_Ozero__class_Ozero(X4486) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__self])]) ).
fof(i_0_2384,plain,
! [X3727,X3728,X3729] :
( ~ class_Orderings_Opreorder(X3729)
| X3728 != X3727
| c_Orderings_Oord__class_Oless__eq(X3729,X3728,X3727) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_2385,plain,
! [X5203,X5204] :
( ~ class_Groups_Omonoid__mult(X5204)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5204),X5203),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X5203 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).
fof(i_0_2386,plain,
! [X5134,X5135] :
( ~ class_Rings_Ocomm__semiring__1(X5135)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5135),X5134),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X5134 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).
fof(i_0_2387,plain,
! [X4026] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X4026)),
inference(variable_rename,[status(thm)],[fact_zero__le__natfloor]) ).
fof(i_0_2388,plain,
! [X3977] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X3977)),
inference(variable_rename,[status(thm)],[fact_zero__le__natceiling]) ).
fof(i_0_2389,plain,
! [X3692,X3693] :
( ~ class_Orderings_Opreorder(X3693)
| c_Orderings_Oord__class_Oless__eq(X3693,X3692,X3692) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
cnf(i_0_2390,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_2391,plain,
! [X3136,X3137] :
( ~ class_RealVector_Oreal__normed__vector(X3137)
| c_RealVector_Onorm__class_Onorm(X3137,c_Groups_Ouminus__class_Ouminus(X3137,X3136)) = c_RealVector_Onorm__class_Onorm(X3137,X3136) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__cancel])]) ).
fof(i_0_2392,plain,
! [X3846,X3847,X3848] :
( ( c_Polynomial_Opoly(X3848,X3847) != c_Polynomial_Opoly(X3848,X3846)
| X3847 = X3846
| ~ class_Int_Oring__char__0(X3848)
| ~ class_Rings_Oidom(X3848) )
& ( X3847 != X3846
| c_Polynomial_Opoly(X3848,X3847) = c_Polynomial_Opoly(X3848,X3846)
| ~ class_Int_Oring__char__0(X3848)
| ~ class_Rings_Oidom(X3848) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__iff])])]) ).
fof(i_0_2393,plain,
! [X4363,X4364] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X4364)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4364),X4363),X4363) = X4363 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])]) ).
fof(i_0_2394,plain,
! [X4361,X4362] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X4362)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4362),X4361),X4361) = X4361 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__idem])]) ).
fof(i_0_2395,plain,
! [X3521] :
( X3521 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3521) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_2396,plain,
! [X5463] :
( X5463 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5463,X5463) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__self])]) ).
fof(i_0_2397,plain,
! [X5691] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5691) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).
fof(i_0_2398,plain,
! [X5489] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5489) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__zero]) ).
fof(i_0_2399,plain,
! [X5594] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5594) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zdiv__zero]) ).
fof(i_0_2400,plain,
! [X5483] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5483,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& c_Divides_Odiv__class_Omod(tc_Int_Oint,X5483,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X5483 ),
inference(variable_rename,[status(thm)],[fact_DIVISION__BY__ZERO]) ).
fof(i_0_2401,plain,
! [X5538] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5538) = X5538,
inference(variable_rename,[status(thm)],[fact_zadd__0]) ).
fof(i_0_2402,plain,
! [X3597] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3597) = X3597,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_2403,plain,
! [X5692] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5692,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X5692,
inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(i_0_2404,plain,
! [X5537] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5537,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X5537,
inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).
fof(i_0_2405,plain,
! [X3596] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3596,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3596,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_2406,plain,
! [X3488,X3489] :
( X3489 != X3488
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3489,X3488) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_2407,plain,
! [X3481] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3481),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_2408,plain,
! [X3480] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3480),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_2409,plain,
! [X3710] :
( ~ class_Groups_Oab__group__add(X3710)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3710),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3710))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3710)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J])]) ).
fof(i_0_2410,plain,
! [X5693] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5693,X5693) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).
fof(i_0_2411,plain,
! [X5488] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X5488,X5488) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__self]) ).
fof(i_0_2412,plain,
! [X4275] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4275) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0]) ).
fof(i_0_2413,plain,
! [X3954,X3955,X3956] :
( ( c_Groups_Ouminus__class_Ouminus(X3956,X3955) != c_Groups_Ouminus__class_Ouminus(X3956,X3954)
| X3955 = X3954
| ~ class_Lattices_Oboolean__algebra(X3956) )
& ( X3955 != X3954
| c_Groups_Ouminus__class_Ouminus(X3956,X3955) = c_Groups_Ouminus__class_Ouminus(X3956,X3954)
| ~ class_Lattices_Oboolean__algebra(X3956) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).
fof(i_0_2414,plain,
! [X3234,X3235,X3236] :
( ( c_Groups_Ouminus__class_Ouminus(X3236,X3235) != c_Groups_Ouminus__class_Ouminus(X3236,X3234)
| X3235 = X3234
| ~ class_Groups_Ogroup__add(X3236) )
& ( X3235 != X3234
| c_Groups_Ouminus__class_Ouminus(X3236,X3235) = c_Groups_Ouminus__class_Ouminus(X3236,X3234)
| ~ class_Groups_Ogroup__add(X3236) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).
fof(i_0_2415,plain,
! [X5338] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X5338) = X5338,
inference(variable_rename,[status(thm)],[fact_zmult__1]) ).
fof(i_0_2416,plain,
! [X4365] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4365) = X4365,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(i_0_2417,plain,
! [X5019] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X5019) = X5019,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(i_0_2418,plain,
! [X5521] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5521,X5521),
inference(variable_rename,[status(thm)],[fact_zle__refl]) ).
fof(i_0_2419,plain,
! [X3492] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3492,X3492),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_2420,plain,
! [X3116] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3116,X3116),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(i_0_2421,plain,
! [X4274] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4274),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_2422,plain,
! [X5339] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5339),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X5339,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(i_0_2423,plain,
! [X4368] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4368),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4368,
inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).
fof(i_0_2424,plain,
! [X3961,X3962] :
( ~ class_Lattices_Oboolean__algebra(X3962)
| c_Groups_Ouminus__class_Ouminus(X3962,c_Groups_Ouminus__class_Ouminus(X3962,X3961)) = X3961 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).
fof(i_0_2425,plain,
! [X3226,X3227] :
( ~ class_Groups_Ogroup__add(X3227)
| c_Groups_Ouminus__class_Ouminus(X3227,c_Groups_Ouminus__class_Ouminus(X3227,X3226)) = X3226 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).
fof(i_0_2426,plain,
! [X3231,X3232,X3233] :
( ( c_Groups_Ouminus__class_Ouminus(X3233,X3232) != X3231
| c_Groups_Ouminus__class_Ouminus(X3233,X3231) = X3232
| ~ class_Groups_Ogroup__add(X3233) )
& ( c_Groups_Ouminus__class_Ouminus(X3233,X3231) != X3232
| c_Groups_Ouminus__class_Ouminus(X3233,X3232) = X3231
| ~ class_Groups_Ogroup__add(X3233) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).
fof(i_0_2427,plain,
! [X3228,X3229,X3230] :
( ( X3229 != c_Groups_Ouminus__class_Ouminus(X3230,X3228)
| X3228 = c_Groups_Ouminus__class_Ouminus(X3230,X3229)
| ~ class_Groups_Ogroup__add(X3230) )
& ( X3228 != c_Groups_Ouminus__class_Ouminus(X3230,X3229)
| X3229 = c_Groups_Ouminus__class_Ouminus(X3230,X3228)
| ~ class_Groups_Ogroup__add(X3230) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).
fof(i_0_2428,plain,
! [X3927,X3928] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3928,X3927) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3927 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3928))
| ~ class_Groups_Ozero(X3928) )
& ( X3927 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3928))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3928,X3927) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X3928) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psize__eq__0__iff])])]) ).
fof(i_0_2429,plain,
! [X3117,X3118] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X3118) != c_RealDef_Oreal(tc_Nat_Onat,X3117)
| X3118 = X3117 )
& ( X3118 != X3117
| c_RealDef_Oreal(tc_Nat_Onat,X3118) = c_RealDef_Oreal(tc_Nat_Onat,X3117) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject])]) ).
fof(i_0_2430,plain,
! [X3312,X3313] :
( ( c_Groups_Ozero__class_Ozero(X3313) != c_Groups_Ouminus__class_Ouminus(X3313,X3312)
| c_Groups_Ozero__class_Ozero(X3313) = X3312
| ~ class_Groups_Ogroup__add(X3313) )
& ( c_Groups_Ozero__class_Ozero(X3313) != X3312
| c_Groups_Ozero__class_Ozero(X3313) = c_Groups_Ouminus__class_Ouminus(X3313,X3312)
| ~ class_Groups_Ogroup__add(X3313) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])]) ).
fof(i_0_2431,plain,
! [X3316,X3317] :
( ( c_Groups_Ouminus__class_Ouminus(X3317,X3316) != c_Groups_Ozero__class_Ozero(X3317)
| X3316 = c_Groups_Ozero__class_Ozero(X3317)
| ~ class_Groups_Ogroup__add(X3317) )
& ( X3316 != c_Groups_Ozero__class_Ozero(X3317)
| c_Groups_Ouminus__class_Ouminus(X3317,X3316) = c_Groups_Ozero__class_Ozero(X3317)
| ~ class_Groups_Ogroup__add(X3317) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).
fof(i_0_2432,plain,
! [X3000,X3001] :
( ( c_RealVector_Onorm__class_Onorm(X3001,X3000) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3000 = c_Groups_Ozero__class_Ozero(X3001)
| ~ class_RealVector_Oreal__normed__vector(X3001) )
& ( X3000 != c_Groups_Ozero__class_Ozero(X3001)
| c_RealVector_Onorm__class_Onorm(X3001,X3000) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X3001) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])]) ).
fof(i_0_2433,plain,
! [X5810,X5811] :
( ~ class_Groups_Ouminus(X5811)
| class_Groups_Ouminus(tc_fun(X5810,X5811)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).
fof(i_0_2434,plain,
! [X5802,X5803] :
( ~ class_Lattices_Oboolean__algebra(X5803)
| class_Lattices_Oboolean__algebra(tc_fun(X5802,X5803)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).
fof(i_0_2435,plain,
! [X5806,X5807] :
( ~ class_Orderings_Oorder(X5807)
| class_Orderings_Oorder(tc_fun(X5806,X5807)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_2436,plain,
! [X5808,X5809] :
( ~ class_Orderings_Oord(X5809)
| class_Orderings_Oord(tc_fun(X5808,X5809)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_2437,plain,
! [X5804,X5805] :
( ~ class_Orderings_Opreorder(X5805)
| class_Orderings_Opreorder(tc_fun(X5804,X5805)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_2438,plain,
! [X5545] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5545)) = X5545,
inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).
fof(i_0_2439,plain,
! [X3318,X3319] :
( ( c_Groups_Ouminus__class_Ouminus(X3319,X3318) != X3318
| X3318 = c_Groups_Ozero__class_Ozero(X3319)
| ~ class_Groups_Olinordered__ab__group__add(X3319) )
& ( X3318 != c_Groups_Ozero__class_Ozero(X3319)
| c_Groups_Ouminus__class_Ouminus(X3319,X3318) = X3318
| ~ class_Groups_Olinordered__ab__group__add(X3319) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).
fof(i_0_2440,plain,
! [X3314,X3315] :
( ( X3314 != c_Groups_Ouminus__class_Ouminus(X3315,X3314)
| X3314 = c_Groups_Ozero__class_Ozero(X3315)
| ~ class_Groups_Olinordered__ab__group__add(X3315) )
& ( X3314 != c_Groups_Ozero__class_Ozero(X3315)
| X3314 = c_Groups_Ouminus__class_Ouminus(X3315,X3314)
| ~ class_Groups_Olinordered__ab__group__add(X3315) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).
fof(i_0_2441,plain,
! [X3311] :
( ~ class_Groups_Ogroup__add(X3311)
| c_Groups_Ouminus__class_Ouminus(X3311,c_Groups_Ozero__class_Ozero(X3311)) = c_Groups_Ozero__class_Ozero(X3311) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).
fof(i_0_2442,plain,
! [X3141] :
( ~ class_RealVector_Oreal__normed__algebra__1(X3141)
| c_RealVector_Onorm__class_Onorm(X3141,c_Groups_Oone__class_Oone(X3141)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__one])]) ).
fof(i_0_2443,plain,
! [X2999] :
( ~ class_RealVector_Oreal__normed__vector(X2999)
| c_RealVector_Onorm__class_Onorm(X2999,c_Groups_Ozero__class_Ozero(X2999)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__zero])]) ).
fof(i_0_2444,plain,
! [X4025] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X4025)) = X4025,
inference(variable_rename,[status(thm)],[fact_natfloor__real__of__nat]) ).
fof(i_0_2445,plain,
! [X3976] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X3976)) = X3976,
inference(variable_rename,[status(thm)],[fact_natceiling__real__of__nat]) ).
fof(i_0_2446,plain,
! [X3194] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X3194) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3194 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3194 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X3194) = 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_2447,plain,
! [X3310] :
( ~ class_Rings_Ozero__neq__one(X3310)
| c_Groups_Ozero__class_Ozero(X3310) != c_Groups_Oone__class_Oone(X3310) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_2448,plain,
! [X3309] :
( ~ class_Rings_Ozero__neq__one(X3309)
| c_Groups_Oone__class_Oone(X3309) != c_Groups_Ozero__class_Ozero(X3309) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_2449,plain,
! [X5597] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5597) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(variable_rename,[status(thm)],[fact_rcis__zero__mod]) ).
fof(i_0_2450,plain,
! [X5801] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5801)
| class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X5801)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add])]) ).
fof(i_0_2451,plain,
! [X5862] :
( ~ class_Rings_Ocomm__ring__1(X5862)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X5862)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1])]) ).
fof(i_0_2452,plain,
! [X5852] :
( ~ class_Rings_Ocomm__semiring__0(X5852)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X5852)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__0])]) ).
fof(i_0_2453,plain,
! [X5863] :
( ~ class_Rings_Ocomm__semiring__1(X5863)
| class_Power_Opower(tc_Polynomial_Opoly(X5863)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower])]) ).
fof(i_0_2454,plain,
! [X5816] :
( ~ class_Rings_Olinordered__idom(X5816)
| class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X5816)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict])]) ).
fof(i_0_2455,plain,
! [X5827] :
( ~ class_Rings_Olinordered__idom(X5827)
| class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X5827)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1])]) ).
fof(i_0_2456,plain,
! [X5830] :
( ~ class_Rings_Olinordered__idom(X5830)
| class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X5830)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring])]) ).
fof(i_0_2457,plain,
! [X5850] :
( ~ class_Rings_Ocomm__ring__1(X5850)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X5850)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1])]) ).
fof(i_0_2458,plain,
! [X5822] :
( ~ class_Rings_Oidom(X5822)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X5822)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors])]) ).
fof(i_0_2459,plain,
! [X5815] :
( ~ class_Rings_Olinordered__idom(X5815)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X5815)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict])]) ).
fof(i_0_2460,plain,
! [X5817] :
( ~ class_Rings_Olinordered__idom(X5817)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X5817)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict])]) ).
fof(i_0_2461,plain,
! [X5826] :
( ~ class_Rings_Olinordered__idom(X5826)
| class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X5826)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__comm__semiring])]) ).
fof(i_0_2462,plain,
! [X5835] :
( ~ class_Rings_Olinordered__idom(X5835)
| class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X5835)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__semiring])]) ).
fof(i_0_2463,plain,
! [X5846] :
( ~ class_Rings_Olinordered__idom(X5846)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X5846)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring])]) ).
fof(i_0_2464,plain,
! [X5823] :
( ~ class_Rings_Olinordered__idom(X5823)
| class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X5823)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring])]) ).
fof(i_0_2465,plain,
! [X5824] :
( ~ class_Rings_Olinordered__idom(X5824)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X5824)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict])]) ).
fof(i_0_2466,plain,
! [X5838] :
( ~ class_Rings_Olinordered__idom(X5838)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X5838)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring])]) ).
fof(i_0_2467,plain,
! [X5854] :
( ~ class_Fields_Ofield(X5854)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X5854)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Oring__div])]) ).
fof(i_0_2468,plain,
! [X5855] :
( ~ class_Rings_Ocomm__semiring__0(X5855)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X5855)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero])]) ).
fof(i_0_2469,plain,
! [X5825] :
( ~ class_Rings_Oidom(X5825)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X5825)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors])]) ).
fof(i_0_2470,plain,
! [X5836] :
( ~ class_Rings_Oidom(X5836)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X5836)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors])]) ).
fof(i_0_2471,plain,
! [X5859] :
( ~ class_Rings_Ocomm__semiring__0(X5859)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X5859)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring])]) ).
fof(i_0_2472,plain,
! [X5843] :
( ~ class_Rings_Ocomm__semiring__0(X5843)
| class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X5843)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring])]) ).
fof(i_0_2473,plain,
! [X5833] :
( ~ class_Rings_Ocomm__semiring__1(X5833)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X5833)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult])]) ).
fof(i_0_2474,plain,
! [X5849] :
( ~ class_Rings_Ocomm__semiring__1(X5849)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X5849)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult])]) ).
fof(i_0_2475,plain,
! [X5832] :
( ~ class_Rings_Ocomm__semiring__0(X5832)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X5832)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__mult])]) ).
fof(i_0_2476,plain,
! [X5865] :
( ~ class_Rings_Ocomm__ring(X5865)
| class_Rings_Oring(tc_Polynomial_Opoly(X5865)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring])]) ).
fof(i_0_2477,plain,
! [X5842] :
( ~ class_Fields_Ofield(X5842)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X5842)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Osemiring__div])]) ).
fof(i_0_2478,plain,
! [X5812] :
( ~ class_Rings_Oidom(X5812)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X5812)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct])]) ).
fof(i_0_2479,plain,
! [X5861] :
( ~ class_Groups_Oab__group__add(X5861)
| class_Groups_Ouminus(tc_Polynomial_Opoly(X5861)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ouminus])]) ).
fof(i_0_2480,plain,
! [X5866] :
( ~ class_Rings_Oidom(X5866)
| class_Rings_Oidom(tc_Polynomial_Opoly(X5866)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom])]) ).
fof(i_0_2481,plain,
! [X5858] :
( ~ class_Rings_Olinordered__idom(X5858)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X5858)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0])]) ).
fof(i_0_2482,plain,
! [X5857] :
( ~ class_Rings_Olinordered__idom(X5857)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X5857)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder])]) ).
fof(i_0_2483,plain,
! [X5848] :
( ~ class_Rings_Olinordered__idom(X5848)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X5848)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder])]) ).
fof(i_0_2484,plain,
! [X5860] :
( ~ class_Rings_Olinordered__idom(X5860)
| class_Orderings_Oord(tc_Polynomial_Opoly(X5860)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord])]) ).
fof(i_0_2485,plain,
! [X5841] :
( ~ class_Rings_Ocomm__semiring__0(X5841)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X5841)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0])]) ).
fof(i_0_2486,plain,
! [X5840] :
( ~ class_Rings_Ocomm__semiring__1(X5840)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X5840)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1])]) ).
fof(i_0_2487,plain,
! [X5856] :
( ~ class_Rings_Ocomm__ring(X5856)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X5856)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring])]) ).
fof(i_0_2488,plain,
! [X5847] :
( ~ class_Rings_Olinordered__idom(X5847)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X5847)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder])]) ).
fof(i_0_2489,plain,
! [X5844] :
( ~ class_Groups_Oab__group__add(X5844)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X5844)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add])]) ).
fof(i_0_2490,plain,
! [X5828] :
( ~ class_Rings_Olinordered__idom(X5828)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X5828)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add])]) ).
fof(i_0_2491,plain,
! [X5845] :
( ~ class_Rings_Ocomm__semiring__1(X5845)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X5845)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one])]) ).
fof(i_0_2492,plain,
! [X5813] :
( ~ class_Rings_Olinordered__idom(X5813)
| class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X5813)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add])]) ).
fof(i_0_2493,plain,
! [X5818] :
( ~ class_Rings_Olinordered__idom(X5818)
| class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X5818)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add])]) ).
fof(i_0_2494,plain,
! [X5814] :
( ~ class_Rings_Olinordered__idom(X5814)
| class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X5814)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le])]) ).
fof(i_0_2495,plain,
! [X5820] :
( ~ class_Rings_Olinordered__idom(X5820)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X5820)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add])]) ).
fof(i_0_2496,plain,
! [X5837] :
( ~ class_Groups_Ocomm__monoid__add(X5837)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X5837)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add])]) ).
fof(i_0_2497,plain,
! [X5851] :
( ~ class_Groups_Ocomm__monoid__add(X5851)
| class_Groups_Omonoid__add(tc_Polynomial_Opoly(X5851)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add])]) ).
fof(i_0_2498,plain,
! [X5867] :
( ~ class_Rings_Ocomm__semiring__1(X5867)
| class_Groups_Oone(tc_Polynomial_Opoly(X5867)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone])]) ).
fof(i_0_2499,plain,
! [X5821] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5821)
| class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X5821)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add])]) ).
fof(i_0_2500,plain,
! [X5829] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5829)
| class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X5829)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add])]) ).
fof(i_0_2501,plain,
! [X5834] :
( ~ class_Groups_Ocomm__monoid__add(X5834)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X5834)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add])]) ).
fof(i_0_2502,plain,
! [X5839] :
( ~ class_Rings_Olinordered__idom(X5839)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X5839)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom])]) ).
fof(i_0_2503,plain,
! [X5864] :
( ~ class_Groups_Ozero(X5864)
| class_Groups_Ozero(tc_Polynomial_Opoly(X5864)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero])]) ).
fof(i_0_2504,plain,
! [X5819] :
( ~ class_Rings_Olinordered__idom(X5819)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X5819)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add])]) ).
fof(i_0_2505,plain,
! [X5831] :
( ~ class_Rings_Olinordered__idom(X5831)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X5831)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semidom])]) ).
fof(i_0_2506,plain,
! [X5853] :
( ~ class_Groups_Oab__group__add(X5853)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X5853)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add])]) ).
fof(i_0_2507,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_1])]) ).
cnf(i_0_2508,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,c_Groups_Oplus__class_Oplus(X2,hAPP(X3,esk46_4(X3,X2,X1,X4)),c_Groups_Ouminus__class_Ouminus(X2,hAPP(X3,X4)))),X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1421]),
[final] ).
cnf(i_0_2509,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,c_Groups_Oplus__class_Oplus(X2,hAPP(X3,esk49_4(X3,X2,X1,X4)),c_Groups_Ouminus__class_Ouminus(X2,X4))),X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1422]),
[final] ).
cnf(i_0_2510,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk29_4(X3,X2,X4,X1)),hAPP(X3,esk29_4(X3,X2,X4,X1)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1423]),
[final] ).
cnf(i_0_2511,plain,
( c_SEQ_OBseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk52_4(X3,X2,X4,X1))),X3)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1424]),
[final] ).
cnf(i_0_2512,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_1425]),
[final] ).
cnf(i_0_2513,plain,
c_Divides_Odiv__class_Odiv(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,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),c_Divides_Odiv__class_Omod(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)),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1426,c_0_1427]),c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2514,hypothesis,
( v_thesis____
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X1,esk76_1(X1))),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X1,esk77_1(X1)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk77_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) ),
inference(rw,[status(thm)],[i_0_1428,c_0_1427]),
[final] ).
cnf(i_0_2515,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),esk68_2(X2,X1)),X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1429]),
[final] ).
cnf(i_0_2516,plain,
( hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ hBOOL(hAPP(hAPP(X1,esk70_3(X2,X1,X3)),esk71_3(X2,X1,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1430]),
[final] ).
cnf(i_0_2517,plain,
( hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ hBOOL(hAPP(hAPP(X1,esk72_3(X2,X1,X3)),esk73_3(X2,X1,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1431]),
[final] ).
cnf(i_0_2518,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)),
inference(split_conjunct,[status(thm)],[i_0_1432]),
[final] ).
cnf(i_0_2519,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X3),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X3),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)),X3)),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2520,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_1434,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2521,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_1435,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2522,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
| X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X5),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_1430]),
[final] ).
cnf(i_0_2523,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,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),X3),X5),X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1431]),
[final] ).
cnf(i_0_2524,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(esk2_0,X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(rw,[status(thm)],[i_0_1436,c_0_1427]),
[final] ).
cnf(i_0_2525,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk6_1(X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(rw,[status(thm)],[i_0_1437,c_0_1427]),
[final] ).
cnf(i_0_2526,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk5_1(X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(rw,[status(thm)],[i_0_1438,c_0_1427]),
[final] ).
cnf(i_0_2527,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),X3),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1439]),
[final] ).
cnf(i_0_2528,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk17_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,esk16_3(X3,X2,X1))),X1) ),
inference(rw,[status(thm)],[i_0_1440,c_0_1427]),
[final] ).
cnf(i_0_2529,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk13_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,esk12_3(X3,X2,X1))),X1) ),
inference(rw,[status(thm)],[i_0_1441,c_0_1427]),
[final] ).
cnf(i_0_2530,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3),
inference(split_conjunct,[status(thm)],[i_0_1442]),
[final] ).
cnf(i_0_2531,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk19_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,esk18_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1443,c_0_1427]),
[final] ).
cnf(i_0_2532,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk15_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,esk14_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1444,c_0_1427]),
[final] ).
cnf(i_0_2533,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_1445]),
[final] ).
cnf(i_0_2534,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_1446]),
[final] ).
cnf(i_0_2535,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))),esk64_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1447]),
[final] ).
cnf(i_0_2536,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))),esk60_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_2537,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1449]),
[final] ).
cnf(i_0_2538,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk19_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,esk18_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1450,c_0_1427]),
[final] ).
cnf(i_0_2539,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk15_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,esk14_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1451,c_0_1427]),
[final] ).
cnf(i_0_2540,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_1452]),
[final] ).
cnf(i_0_2541,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_1453]),
[final] ).
cnf(i_0_2542,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,esk37_3(X2,X1,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1454,c_0_1427]),
[final] ).
cnf(i_0_2543,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,esk39_3(X2,X1,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1455,c_0_1427]),
[final] ).
cnf(i_0_2544,plain,
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3),X4)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1456]),
[final] ).
cnf(i_0_2545,plain,
( X2 = X3
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Oidom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1457,c_0_1427]),c_0_1427]),c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2546,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk70_3(X1,X3,X2)),esk71_3(X1,X3,X2))
| hBOOL(hAPP(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Omod(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_1430]),
[final] ).
cnf(i_0_2547,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk72_3(X1,X3,X2)),esk73_3(X1,X3,X2))
| hBOOL(hAPP(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Omod(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_1431]),
[final] ).
cnf(i_0_2548,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_1458,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2549,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_1459]),
[final] ).
cnf(i_0_2550,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_1460]),
[final] ).
cnf(i_0_2551,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,esk53_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_1461,c_0_1427]),
[final] ).
cnf(i_0_2552,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_1462,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2553,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_1463,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2554,plain,
c_Divides_Odiv__class_Odiv(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),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)),
inference(split_conjunct,[status(thm)],[i_0_1464]),
[final] ).
cnf(i_0_2555,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)),X3)),
inference(split_conjunct,[status(thm)],[i_0_1465]),
[final] ).
cnf(i_0_2556,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(X2,X3),c_Groups_Ouminus__class_Ouminus(X1,hAPP(X2,esk45_2(X2,X1))))),esk44_2(X2,X1))
| ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1421]),
[final] ).
cnf(i_0_2557,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,esk53_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_1466,c_0_1427]),
[final] ).
cnf(i_0_2558,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_1467]),
[final] ).
cnf(i_0_2559,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_2560,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1))
| ~ 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,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1469]),
[final] ).
cnf(i_0_2561,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1)),X3))
| ~ c_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,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1470]),
[final] ).
cnf(i_0_2562,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,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_1471]),
[final] ).
cnf(i_0_2563,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_1459]),
[final] ).
cnf(i_0_2564,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_1460]),
[final] ).
cnf(i_0_2565,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_1472,c_0_1427]),
[final] ).
cnf(i_0_2566,plain,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_RealDef_Oreal(tc_Nat_Onat,X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)),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_1473]),
[final] ).
cnf(i_0_2567,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Odiv(X1,X3,X2)),c_Divides_Odiv__class_Omod(X1,X3,X2)),X4) = c_Groups_Oplus__class_Oplus(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1474]),
[final] ).
cnf(i_0_2568,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_1475]),
[final] ).
cnf(i_0_2569,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk80_3(X1,X2,X3)),esk81_3(X1,X2,X3))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk78_3(X1,X2,X3)),esk79_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_1476]),
[final] ).
cnf(i_0_2570,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_1477]),
[final] ).
cnf(i_0_2571,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_1478]),
[final] ).
cnf(i_0_2572,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk84_3(X1,X2,X3)),esk85_3(X1,X2,X3))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk82_3(X1,X2,X3)),esk83_3(X1,X2,X3))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2573,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1)),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),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1480]),
[final] ).
cnf(i_0_2574,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,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)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1481]),
[final] ).
cnf(i_0_2575,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),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4,X1)),X2),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_1482]),
[final] ).
cnf(i_0_2576,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1483]),
[final] ).
cnf(i_0_2577,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_1484]),
[final] ).
cnf(i_0_2578,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,esk50_3(X3,X2,X1))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1485]),
[final] ).
cnf(i_0_2579,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,esk41_3(X3,X2,X1))),X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1486]),
[final] ).
cnf(i_0_2580,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk84_3(X1,X2,X3)),esk85_3(X1,X2,X3))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk82_3(X1,X2,X3)),esk83_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2581,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk80_3(X1,X2,X3)),esk81_3(X1,X2,X3))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk78_3(X1,X2,X3)),esk79_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_1476]),
[final] ).
cnf(i_0_2582,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_1487]),
[final] ).
cnf(i_0_2583,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk67_3(X2,X3,X1)),X3),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1488]),
[final] ).
cnf(i_0_2584,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1489]),
[final] ).
cnf(i_0_2585,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk80_3(X1,X2,X3)),esk81_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk78_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2586,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk78_3(X2,X3,X1)),esk79_3(X2,X3,X1))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk80_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2587,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Rings_Oinverse__class_Odivide(X1,X5,X3)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1490]),
[final] ).
cnf(i_0_2588,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk73_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1431]),
[final] ).
cnf(i_0_2589,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk71_3(X1,X2,X3))
| hBOOL(hAPP(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1430]),
[final] ).
cnf(i_0_2590,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk71_3(X1,X2,X3),X3)
| hBOOL(hAPP(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1430]),
[final] ).
cnf(i_0_2591,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk73_3(X2,X3,X1))
| hBOOL(hAPP(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,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_1431]),
[final] ).
cnf(i_0_2592,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk7_1(X1))))),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1449]),
[final] ).
cnf(i_0_2593,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk84_3(X1,X2,X3)),esk85_3(X1,X2,X3))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk83_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2594,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk82_3(X2,X3,X1)),esk83_3(X2,X3,X1))
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk85_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2595,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_1491,c_0_1427]),
[final] ).
cnf(i_0_2596,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_1492]),
[final] ).
cnf(i_0_2597,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_1493]),
[final] ).
cnf(i_0_2598,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_1494]),
[final] ).
cnf(i_0_2599,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_1494]),
[final] ).
cnf(i_0_2600,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_1495]),
[final] ).
cnf(i_0_2601,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_1496,c_0_1427]),
[final] ).
cnf(i_0_2602,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk84_3(X1,X2,X3)),esk85_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk83_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2603,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk80_3(X1,X2,X3)),esk81_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk78_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2604,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk82_3(X2,X3,X1)),esk83_3(X2,X3,X1))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk85_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2605,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk78_3(X2,X3,X1)),esk79_3(X2,X3,X1))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk80_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2606,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1497,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2607,plain,
( epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk80_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk78_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2608,plain,
( epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk85_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk83_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2609,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_1498,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2610,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk85_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk83_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2611,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk80_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk78_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2612,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_1499]),
[final] ).
cnf(i_0_2613,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_1500]),
[final] ).
cnf(i_0_2614,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Rings_Oidom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1501,c_0_1427]),c_0_1427]),c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2615,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_1502,c_0_1427]),c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2616,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_1503,c_0_1427]),c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2617,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1504]),
[final] ).
cnf(i_0_2618,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_1505]),
[final] ).
cnf(i_0_2619,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk53_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_1280]),
[final] ).
cnf(i_0_2620,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(X2,X3),c_Groups_Ouminus__class_Ouminus(X1,esk48_2(X2,X1)))),esk47_2(X2,X1))
| ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1422]),
[final] ).
cnf(i_0_2621,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_1506]),
[final] ).
cnf(i_0_2622,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk57_3(X2,X1,X3)),esk58_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_1507]),
[final] ).
cnf(i_0_2623,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ 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),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2624,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ 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),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2625,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2626,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ c_Orderings_Oord__class_Oless(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),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2627,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2628,plain,
( c_Orderings_Oord__class_Oless(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2629,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1511]),
[final] ).
cnf(i_0_2630,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1511]),
[final] ).
cnf(i_0_2631,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1512]),
[final] ).
cnf(i_0_2632,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1513]),
[final] ).
cnf(i_0_2633,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk55_3(X2,X1,X3)),esk56_3(X2,X1,X3))
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_2634,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1515]),
[final] ).
cnf(i_0_2635,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1516]),
[final] ).
cnf(i_0_2636,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_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),esk78_3(X1,X2,X3)),esk79_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_1476]),
[final] ).
cnf(i_0_2637,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk80_3(X1,X2,X3)),esk81_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk79_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_1476]),
[final] ).
cnf(i_0_2638,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk80_3(X1,X2,X3)),esk81_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_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_1476]),
[final] ).
cnf(i_0_2639,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk81_3(X2,X1,X3))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk78_3(X2,X1,X3)),esk79_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_1476]),
[final] ).
cnf(i_0_2640,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk53_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_1280]),
[final] ).
cnf(i_0_2641,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1517]),
[final] ).
cnf(i_0_2642,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1518]),
[final] ).
cnf(i_0_2643,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_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),esk82_3(X1,X2,X3)),esk83_3(X1,X2,X3))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2644,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk84_3(X1,X2,X3)),esk85_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk83_3(X1,X2,X3))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2645,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk84_3(X1,X2,X3)),esk85_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X1,X2,X3),X2)
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2646,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk85_3(X2,X1,X3))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk82_3(X2,X1,X3)),esk83_3(X2,X1,X3))
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2647,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_1519]),
[final] ).
cnf(i_0_2648,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_1520]),
[final] ).
cnf(i_0_2649,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5,X2))
| ~ 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_Omod(tc_Nat_Onat,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_2650,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_1507]),
[final] ).
cnf(i_0_2651,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ 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,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1521]),
[final] ).
cnf(i_0_2652,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1522]),
[final] ).
cnf(i_0_2653,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1523]),
[final] ).
cnf(i_0_2654,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1524]),
[final] ).
cnf(i_0_2655,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_1525,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2656,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk57_3(X2,X1,X3)),esk58_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_1507]),
[final] ).
cnf(i_0_2657,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk55_3(X2,X1,X3)),esk56_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_2658,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_1526,c_0_1427]),
[final] ).
cnf(i_0_2659,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1527]),
[final] ).
cnf(i_0_2660,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),X3),c_Divides_Odiv__class_Omod(X1,X2,X3)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1528]),
[final] ).
cnf(i_0_2661,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),X3)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1529]),
[final] ).
cnf(i_0_2662,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_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),esk82_3(X1,X2,X3)),esk83_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2663,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_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),esk78_3(X1,X2,X3)),esk79_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_1476]),
[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),esk84_3(X1,X2,X3)),esk85_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk83_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2665,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk80_3(X1,X2,X3)),esk81_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk79_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_1476]),
[final] ).
cnf(i_0_2666,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_1530]),
[final] ).
cnf(i_0_2667,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_1531,c_0_1427]),c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2668,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1532]),
[final] ).
cnf(i_0_2669,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk84_3(X1,X2,X3)),esk85_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X1,X2,X3),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2670,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk80_3(X1,X2,X3)),esk81_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_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_1476]),
[final] ).
cnf(i_0_2671,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk85_3(X2,X1,X3))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk82_3(X2,X1,X3)),esk83_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2672,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk81_3(X2,X1,X3))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk78_3(X2,X1,X3)),esk79_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_1476]),
[final] ).
cnf(i_0_2673,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk57_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1507]),
[final] ).
cnf(i_0_2674,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_1533,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2675,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_1534,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2676,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X4,X6),X3)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1535]),
[final] ).
cnf(i_0_2677,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X5),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X4,X6),X3)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1536]),
[final] ).
cnf(i_0_2678,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk56_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_2679,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X6),X3)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1537]),
[final] ).
cnf(i_0_2680,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_1538]),
[final] ).
cnf(i_0_2681,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk78_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2682,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk79_3(X2,X3,X1))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk80_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2683,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_3(X2,X3,X1),X3)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk80_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2684,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk81_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk78_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2685,plain,
( hBOOL(hAPP(X1,esk53_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_1280]),
[final] ).
cnf(i_0_2686,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_1539]),
[final] ).
cnf(i_0_2687,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_1540]),
[final] ).
cnf(i_0_2688,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk83_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2689,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk83_3(X2,X3,X1))
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk85_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2690,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X2,X3,X1),X3)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk85_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2691,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk85_3(X2,X1,X3))
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk83_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2692,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X5),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_2693,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X5),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ 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__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1542]),
[final] ).
cnf(i_0_2694,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X5),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1543]),
[final] ).
cnf(i_0_2695,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3)),c_Rings_Oinverse__class_Odivide(X1,X4,X5)) = c_Rings_Oinverse__class_Odivide(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1544]),
[final] ).
cnf(i_0_2696,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1545]),
[final] ).
cnf(i_0_2697,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk80_3(X1,X2,X3)),esk81_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_1476]),
[final] ).
cnf(i_0_2698,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),esk78_3(X2,X1,X3)),esk79_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_1476]),
[final] ).
cnf(i_0_2699,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_1546]),
[final] ).
cnf(i_0_2700,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_1547]),
[final] ).
cnf(i_0_2701,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_1548]),
[final] ).
cnf(i_0_2702,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_1549]),
[final] ).
cnf(i_0_2703,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_1550]),
[final] ).
cnf(i_0_2704,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_1551]),
[final] ).
cnf(i_0_2705,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_1552]),
[final] ).
cnf(i_0_2706,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_1553]),
[final] ).
cnf(i_0_2707,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_1554]),
[final] ).
cnf(i_0_2708,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) = X2
| ~ 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_1555]),
[final] ).
cnf(i_0_2709,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_1556]),
[final] ).
cnf(i_0_2710,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk56_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_2711,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,esk57_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1507]),
[final] ).
cnf(i_0_2712,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk84_3(X1,X2,X3)),esk85_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2713,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),esk82_3(X2,X1,X3)),esk83_3(X2,X1,X3))
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2714,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_1557]),
[final] ).
cnf(i_0_2715,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_1558]),
[final] ).
cnf(i_0_2716,plain,
( hBOOL(hAPP(X1,esk53_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_1280]),
[final] ).
cnf(i_0_2717,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk83_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2718,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_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,esk78_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2719,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk83_3(X2,X3,X1))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk85_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2720,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk79_3(X2,X3,X1))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk80_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2721,plain,
( hBOOL(hAPP(X5,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)
| ~ 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)
| ~ epred2_3(X5,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2722,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_1476]),
[final] ).
cnf(i_0_2723,plain,
( hBOOL(hAPP(X5,X2))
| ~ 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)
| ~ epred2_3(X5,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2724,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_1476]),
[final] ).
cnf(i_0_2725,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X2,X3,X1),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk85_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2726,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_3(X2,X3,X1),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk80_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2727,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk85_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk83_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2728,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk81_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk78_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2729,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_1494]),
[final] ).
cnf(i_0_2730,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_1492]),
[final] ).
cnf(i_0_2731,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_1492]),
[final] ).
cnf(i_0_2732,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_1559]),
[final] ).
cnf(i_0_2733,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_1560,c_0_1427]),
[final] ).
cnf(i_0_2734,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk84_3(X1,X2,X3)),esk85_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)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2735,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk80_3(X1,X2,X3)),esk81_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_1476]),
[final] ).
cnf(i_0_2736,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),esk82_3(X2,X1,X3)),esk83_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2737,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),esk78_3(X2,X1,X3)),esk79_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_1476]),
[final] ).
cnf(i_0_2738,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_1561,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2739,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_1562,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2740,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_1563,c_0_1427]),
[final] ).
cnf(i_0_2741,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2742,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2743,plain,
( c_Orderings_Oord__class_Oless(X1,X3,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,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2744,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,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,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1511]),
[final] ).
cnf(i_0_2745,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ 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),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2746,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ 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),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2747,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2748,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ c_Orderings_Oord__class_Oless(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),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2749,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2750,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1511]),
[final] ).
cnf(i_0_2751,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2752,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1511]),
[final] ).
cnf(i_0_2753,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2754,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2755,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2756,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ 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),X2),X3),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1511]),
[final] ).
cnf(i_0_2757,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk52_4(X2,X3,X1,X4))
| c_SEQ_OBseq(X4,X3)
| ~ class_RealVector_Oreal__normed__vector(X4) ),
inference(split_conjunct,[status(thm)],[i_0_1424]),
[final] ).
cnf(i_0_2758,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
inference(split_conjunct,[status(thm)],[i_0_1564]),
[final] ).
cnf(i_0_2759,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_1565]),
[final] ).
cnf(i_0_2760,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_1566]),
[final] ).
cnf(i_0_2761,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_1567]),
[final] ).
cnf(i_0_2762,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_1568]),
[final] ).
cnf(i_0_2763,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_1569]),
[final] ).
cnf(i_0_2764,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_1570]),
[final] ).
cnf(i_0_2765,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_1571]),
[final] ).
cnf(i_0_2766,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_1572]),
[final] ).
cnf(i_0_2767,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_1573]),
[final] ).
cnf(i_0_2768,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_1574]),
[final] ).
cnf(i_0_2769,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_1575]),
[final] ).
cnf(i_0_2770,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_1576]),
[final] ).
cnf(i_0_2771,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_1577]),
[final] ).
cnf(i_0_2772,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_1578]),
[final] ).
cnf(i_0_2773,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_1579]),
[final] ).
cnf(i_0_2774,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_1580]),
[final] ).
cnf(i_0_2775,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_2776,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,esk80_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2777,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,esk78_3(X3,X1,X2)))
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2778,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,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)
| ~ 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_1555]),
[final] ).
cnf(i_0_2779,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_1556]),
[final] ).
cnf(i_0_2780,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk63_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_2781,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk59_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1583]),
[final] ).
cnf(i_0_2782,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_1584]),
[final] ).
cnf(i_0_2783,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_1585]),
[final] ).
cnf(i_0_2784,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_2785,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_2786,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1588]),
[final] ).
cnf(i_0_2787,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1589]),
[final] ).
cnf(i_0_2788,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1590]),
[final] ).
cnf(i_0_2789,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1591]),
[final] ).
cnf(i_0_2790,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk85_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2791,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| epred2_3(X2,X1,X3)
| ~ hBOOL(hAPP(X2,esk83_3(X3,X1,X2)))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2792,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_1592]),
[final] ).
cnf(i_0_2793,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_1593]),
[final] ).
cnf(i_0_2794,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_1594]),
[final] ).
cnf(i_0_2795,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_1595]),
[final] ).
cnf(i_0_2796,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1596]),
[final] ).
cnf(i_0_2797,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),X2)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1597]),
[final] ).
cnf(i_0_2798,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1598]),
[final] ).
cnf(i_0_2799,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1599]),
[final] ).
cnf(i_0_2800,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_1600]),
[final] ).
cnf(i_0_2801,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_1601]),
[final] ).
cnf(i_0_2802,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_1602,c_0_1427]),
[final] ).
cnf(i_0_2803,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_1603]),
[final] ).
cnf(i_0_2804,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_1604]),
[final] ).
cnf(i_0_2805,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)),esk65_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1605]),
[final] ).
cnf(i_0_2806,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_1606]),
[final] ).
cnf(i_0_2807,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_1607]),
[final] ).
cnf(i_0_2808,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)),esk66_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1608]),
[final] ).
cnf(i_0_2809,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)),esk62_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1609]),
[final] ).
cnf(i_0_2810,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1610]),
[final] ).
cnf(i_0_2811,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1611,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2812,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1612]),
[final] ).
cnf(i_0_2813,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_1613]),
[final] ).
cnf(i_0_2814,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3)),X4) = c_Rings_Oinverse__class_Odivide(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1614]),
[final] ).
cnf(i_0_2815,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_1615]),
[final] ).
cnf(i_0_2816,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_1616]),
[final] ).
cnf(i_0_2817,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_1617]),
[final] ).
cnf(i_0_2818,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_1618]),
[final] ).
cnf(i_0_2819,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_1604]),
[final] ).
cnf(i_0_2820,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_1603]),
[final] ).
cnf(i_0_2821,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_1603]),
[final] ).
cnf(i_0_2822,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_1604]),
[final] ).
cnf(i_0_2823,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_1500]),
[final] ).
cnf(i_0_2824,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_1499]),
[final] ).
cnf(i_0_2825,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk11_0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r) ),
inference(split_conjunct,[status(thm)],[i_0_1619]),
[final] ).
cnf(i_0_2826,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_1620,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2827,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_1604]),
[final] ).
cnf(i_0_2828,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_1603]),
[final] ).
cnf(i_0_2829,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_1621]),
[final] ).
cnf(i_0_2830,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_1622]),
[final] ).
cnf(i_0_2831,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_1623]),
[final] ).
cnf(i_0_2832,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_1624]),
[final] ).
cnf(i_0_2833,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_1625]),
[final] ).
cnf(i_0_2834,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_2835,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2836,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2837,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1628]),
[final] ).
cnf(i_0_2838,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1511]),
[final] ).
cnf(i_0_2839,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2840,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2841,plain,
( c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2842,plain,
( c_Orderings_Oord__class_Oless(X1,X3,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,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2843,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2844,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,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__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2845,plain,
( c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2846,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2847,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_Omod(tc_Int_Oint,X3,X1) = X2
| ~ 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_1555]),
[final] ).
cnf(i_0_2848,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_1556]),
[final] ).
cnf(i_0_2849,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_1546]),
[final] ).
cnf(i_0_2850,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_1547]),
[final] ).
cnf(i_0_2851,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2852,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2853,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2854,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2855,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2856,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2857,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2858,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2859,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2860,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ 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),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2861,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field(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),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1637]),
[final] ).
cnf(i_0_2862,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1628]),
[final] ).
cnf(i_0_2863,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1511]),
[final] ).
cnf(i_0_2864,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1638]),
[final] ).
cnf(i_0_2865,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2866,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2867,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_1639]),
[final] ).
cnf(i_0_2868,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_1640]),
[final] ).
cnf(i_0_2869,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_1641]),
[final] ).
cnf(i_0_2870,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_1642]),
[final] ).
cnf(i_0_2871,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_1643]),
[final] ).
cnf(i_0_2872,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_1644]),
[final] ).
cnf(i_0_2873,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_1645]),
[final] ).
cnf(i_0_2874,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_1646]),
[final] ).
cnf(i_0_2875,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_1647]),
[final] ).
cnf(i_0_2876,plain,
( c_RComplete_Onatceiling(X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[i_0_1648]),
[final] ).
cnf(i_0_2877,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_1649]),
[final] ).
cnf(i_0_2878,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_1650]),
[final] ).
cnf(i_0_2879,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk36_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_1651,c_0_1427]),
[final] ).
cnf(i_0_2880,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk38_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_1652,c_0_1427]),
[final] ).
cnf(i_0_2881,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)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk85_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2882,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,esk80_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2883,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)
| epred2_3(X2,X1,X3)
| ~ hBOOL(hAPP(X2,esk83_3(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2884,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,esk78_3(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2885,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_2886,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1654]),
[final] ).
cnf(i_0_2887,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3),
inference(split_conjunct,[status(thm)],[i_0_1655]),
[final] ).
cnf(i_0_2888,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_1656]),
[final] ).
cnf(i_0_2889,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_1656]),
[final] ).
cnf(i_0_2890,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_1657]),
[final] ).
cnf(i_0_2891,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X3) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1658]),
[final] ).
cnf(i_0_2892,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_1659]),
[final] ).
cnf(i_0_2893,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_1660]),
[final] ).
cnf(i_0_2894,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_1661,c_0_1427]),
[final] ).
cnf(i_0_2895,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Odiv(X1,X3,X2)),c_Divides_Odiv__class_Omod(X1,X3,X2)) = X3
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1662]),
[final] ).
cnf(i_0_2896,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_1663]),
[final] ).
cnf(i_0_2897,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_1664]),
[final] ).
cnf(i_0_2898,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_1665]),
[final] ).
cnf(i_0_2899,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_1666]),
[final] ).
cnf(i_0_2900,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_1667]),
[final] ).
cnf(i_0_2901,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_1668]),
[final] ).
cnf(i_0_2902,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_1669]),
[final] ).
cnf(i_0_2903,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_1670]),
[final] ).
cnf(i_0_2904,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_1671]),
[final] ).
cnf(i_0_2905,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| c_Divides_Odiv__class_Omod(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_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1672,c_0_1427]),c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2906,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_1673,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2907,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_1674,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2908,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_1675,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_2909,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_1676]),
[final] ).
cnf(i_0_2910,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))),
inference(split_conjunct,[status(thm)],[i_0_1677]),
[final] ).
cnf(i_0_2911,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_1678]),
[final] ).
cnf(i_0_2912,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_1539]),
[final] ).
cnf(i_0_2913,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_1679]),
[final] ).
cnf(i_0_2914,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_1680]),
[final] ).
cnf(i_0_2915,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_1681]),
[final] ).
cnf(i_0_2916,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_1682]),
[final] ).
cnf(i_0_2917,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),X2)),X3)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1683]),
[final] ).
cnf(i_0_2918,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_Fields_Olinordered__field(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_1684]),
[final] ).
cnf(i_0_2919,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_Fields_Olinordered__field__inverse__zero(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_1685]),
[final] ).
cnf(i_0_2920,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X4),c_Rings_Oinverse__class_Odivide(X1,X2,X4))
| ~ class_Fields_Olinordered__field(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_1686]),
[final] ).
cnf(i_0_2921,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X4),c_Rings_Oinverse__class_Odivide(X1,X2,X4))
| ~ class_Fields_Olinordered__field__inverse__zero(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_1687]),
[final] ).
cnf(i_0_2922,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk58_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_1507]),
[final] ).
cnf(i_0_2923,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_1688]),
[final] ).
cnf(i_0_2924,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_2925,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_1690]),
[final] ).
cnf(i_0_2926,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_1691]),
[final] ).
cnf(i_0_2927,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_1692]),
[final] ).
cnf(i_0_2928,plain,
( c_RComplete_Onatfloor(X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_2929,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
inference(split_conjunct,[status(thm)],[fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096]),
[final] ).
cnf(i_0_2930,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_1694]),
[final] ).
cnf(i_0_2931,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_1695]),
[final] ).
cnf(i_0_2932,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_1696]),
[final] ).
cnf(i_0_2933,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_1603]),
[final] ).
cnf(i_0_2934,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_1697]),
[final] ).
cnf(i_0_2935,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_1604]),
[final] ).
cnf(i_0_2936,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_1698]),
[final] ).
cnf(i_0_2937,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_1699]),
[final] ).
cnf(i_0_2938,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_1571]),
[final] ).
cnf(i_0_2939,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_1700]),
[final] ).
cnf(i_0_2940,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_1701]),
[final] ).
cnf(i_0_2941,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_1702]),
[final] ).
cnf(i_0_2942,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_1703]),
[final] ).
cnf(i_0_2943,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_1574]),
[final] ).
cnf(i_0_2944,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_1603]),
[final] ).
cnf(i_0_2945,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_1704]),
[final] ).
cnf(i_0_2946,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_1604]),
[final] ).
cnf(i_0_2947,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_1705]),
[final] ).
cnf(i_0_2948,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_1575]),
[final] ).
cnf(i_0_2949,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_1706]),
[final] ).
cnf(i_0_2950,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_1707]),
[final] ).
cnf(i_0_2951,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_1576]),
[final] ).
cnf(i_0_2952,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_1708]),
[final] ).
cnf(i_0_2953,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_1709]),
[final] ).
cnf(i_0_2954,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_1710]),
[final] ).
cnf(i_0_2955,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_1711]),
[final] ).
cnf(i_0_2956,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_1712]),
[final] ).
cnf(i_0_2957,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(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_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1713]),
[final] ).
cnf(i_0_2958,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_1714]),
[final] ).
cnf(i_0_2959,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_1577]),
[final] ).
cnf(i_0_2960,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_1715]),
[final] ).
cnf(i_0_2961,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_1580]),
[final] ).
cnf(i_0_2962,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk56_3(X1,X2,X3),X1)
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_2963,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),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2964,plain,
( c_Orderings_Oord__class_Oless(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(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2965,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2966,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1511]),
[final] ).
cnf(i_0_2967,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_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),esk79_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_1476]),
[final] ).
cnf(i_0_2968,plain,
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk34_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_1716]),
[final] ).
cnf(i_0_2969,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_2970,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1718]),
[final] ).
cnf(i_0_2971,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_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_1476]),
[final] ).
cnf(i_0_2972,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk81_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk79_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_1476]),
[final] ).
cnf(i_0_2973,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,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)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[i_0_1719,c_0_1427]),
[final] ).
cnf(i_0_2974,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_1720]),
[final] ).
cnf(i_0_2975,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_1721]),
[final] ).
cnf(i_0_2976,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_1722]),
[final] ).
cnf(i_0_2977,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk81_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_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_1476]),
[final] ).
cnf(i_0_2978,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_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),esk83_3(X1,X2,X3))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2979,plain,
( epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_2980,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_1724]),
[final] ).
cnf(i_0_2981,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_1725]),
[final] ).
cnf(i_0_2982,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_1726]),
[final] ).
cnf(i_0_2983,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_1727]),
[final] ).
cnf(i_0_2984,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_1728]),
[final] ).
cnf(i_0_2985,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_1729]),
[final] ).
cnf(i_0_2986,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1730]),
[final] ).
cnf(i_0_2987,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1731]),
[final] ).
cnf(i_0_2988,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X1,X2,X3),X2)
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2989,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk85_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk83_3(X2,X1,X3))
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2990,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_1732]),
[final] ).
cnf(i_0_2991,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_1732]),
[final] ).
cnf(i_0_2992,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_1733,c_0_1427]),
[final] ).
cnf(i_0_2993,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_1734,c_0_1427]),
[final] ).
cnf(i_0_2994,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_2995,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_1736]),
[final] ).
cnf(i_0_2996,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_1737]),
[final] ).
cnf(i_0_2997,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_1738]),
[final] ).
cnf(i_0_2998,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk85_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X2,X1,X3),X1)
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2999,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_1739]),
[final] ).
cnf(i_0_3000,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_1740]),
[final] ).
cnf(i_0_3001,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_1741]),
[final] ).
cnf(i_0_3002,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_1742]),
[final] ).
cnf(i_0_3003,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_1743]),
[final] ).
cnf(i_0_3004,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_1740]),
[final] ).
cnf(i_0_3005,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_1739]),
[final] ).
cnf(i_0_3006,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1744,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3007,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_1745]),
[final] ).
cnf(i_0_3008,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_1746]),
[final] ).
cnf(i_0_3009,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_1747]),
[final] ).
cnf(i_0_3010,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_1748]),
[final] ).
cnf(i_0_3011,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_3012,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[i_0_1750]),
[final] ).
cnf(i_0_3013,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_1507]),
[final] ).
cnf(i_0_3014,plain,
( hBOOL(hAPP(X2,X3))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_3015,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk35_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_1751,c_0_1427]),
[final] ).
cnf(i_0_3016,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_1752,c_0_1427]),
[final] ).
cnf(i_0_3017,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_1753,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3018,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_1754]),
[final] ).
cnf(i_0_3019,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_1755]),
[final] ).
cnf(i_0_3020,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_1756]),
[final] ).
cnf(i_0_3021,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_1739]),
[final] ).
cnf(i_0_3022,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_1757]),
[final] ).
cnf(i_0_3023,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_1740]),
[final] ).
cnf(i_0_3024,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_1641]),
[final] ).
cnf(i_0_3025,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_1758]),
[final] ).
cnf(i_0_3026,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_1759]),
[final] ).
cnf(i_0_3027,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_1642]),
[final] ).
cnf(i_0_3028,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_1644]),
[final] ).
cnf(i_0_3029,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_1646]),
[final] ).
cnf(i_0_3030,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_1647]),
[final] ).
cnf(i_0_3031,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_1760]),
[final] ).
cnf(i_0_3032,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_1761]),
[final] ).
cnf(i_0_3033,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_1760]),
[final] ).
cnf(i_0_3034,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_1761]),
[final] ).
cnf(i_0_3035,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk58_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_1507]),
[final] ).
cnf(i_0_3036,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk56_3(X1,X2,X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_3037,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_1762]),
[final] ).
cnf(i_0_3038,plain,
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3),X4)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1763]),
[final] ).
cnf(i_0_3039,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_1764]),
[final] ).
cnf(i_0_3040,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_1765]),
[final] ).
cnf(i_0_3041,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_1766]),
[final] ).
cnf(i_0_3042,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_1767]),
[final] ).
cnf(i_0_3043,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_1768]),
[final] ).
cnf(i_0_3044,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_1741]),
[final] ).
cnf(i_0_3045,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_1769]),
[final] ).
cnf(i_0_3046,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_1770]),
[final] ).
cnf(i_0_3047,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_1771]),
[final] ).
cnf(i_0_3048,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_1772]),
[final] ).
cnf(i_0_3049,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,esk21_0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_3050,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,v_s____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_3051,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_1741]),
[final] ).
cnf(i_0_3052,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_1775]),
[final] ).
cnf(i_0_3053,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3054,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,c_Rings_Oinverse__class_Odivide(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3055,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,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3056,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3057,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_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3058,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,c_Rings_Oinverse__class_Odivide(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3059,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,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1778]),
[final] ).
cnf(i_0_3060,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,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1778]),
[final] ).
cnf(i_0_3061,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),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1778]),
[final] ).
cnf(i_0_3062,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),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1778]),
[final] ).
cnf(i_0_3063,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),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_3064,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),c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_3065,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),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_3066,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),c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_3067,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3068,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3069,plain,
( c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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_1780]),
[final] ).
cnf(i_0_3070,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2),
inference(split_conjunct,[status(thm)],[i_0_1781]),
[final] ).
cnf(i_0_3071,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_1782]),
[final] ).
cnf(i_0_3072,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_3073,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_3074,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_3075,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1511]),
[final] ).
cnf(i_0_3076,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_1783]),
[final] ).
cnf(i_0_3077,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_1783]),
[final] ).
cnf(i_0_3078,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_1783]),
[final] ).
cnf(i_0_3079,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_1784]),
[final] ).
cnf(i_0_3080,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_1784]),
[final] ).
cnf(i_0_3081,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_1784]),
[final] ).
cnf(i_0_3082,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_1784]),
[final] ).
cnf(i_0_3083,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_1783]),
[final] ).
cnf(i_0_3084,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_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),esk83_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3085,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_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),esk79_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_1476]),
[final] ).
cnf(i_0_3086,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),c_RealDef_Oreal(tc_Nat_Onat,X3)),X2)),
inference(split_conjunct,[status(thm)],[i_0_1785]),
[final] ).
cnf(i_0_3087,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_1786]),
[final] ).
cnf(i_0_3088,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1787]),
[final] ).
cnf(i_0_3089,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_1788]),
[final] ).
cnf(i_0_3090,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X1,X2,X3),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3091,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_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_1476]),
[final] ).
cnf(i_0_3092,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk85_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk83_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3093,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk81_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk79_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_1476]),
[final] ).
cnf(i_0_3094,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ouminus__class_Ouminus(X1,c_Divides_Odiv__class_Omod(X1,X2,X3)),X3)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1789]),
[final] ).
cnf(i_0_3095,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk85_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk83_3(X2,X1,X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3096,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk81_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk79_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_1476]),
[final] ).
cnf(i_0_3097,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_1790]),
[final] ).
cnf(i_0_3098,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_1791]),
[final] ).
cnf(i_0_3099,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_1792]),
[final] ).
cnf(i_0_3100,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_1792]),
[final] ).
cnf(i_0_3101,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_1793,c_0_1427]),
[final] ).
cnf(i_0_3102,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_1794,c_0_1427]),
[final] ).
cnf(i_0_3103,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk9_0)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
inference(split_conjunct,[status(thm)],[i_0_1564]),
[final] ).
cnf(i_0_3104,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_1795,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3105,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_1796,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3106,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(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)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3107,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),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,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3108,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(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_1797]),
[final] ).
cnf(i_0_3109,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(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_1798]),
[final] ).
cnf(i_0_3110,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(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_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3111,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(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_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3112,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(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_1799]),
[final] ).
cnf(i_0_3113,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(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_1800]),
[final] ).
cnf(i_0_3114,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_1801]),
[final] ).
cnf(i_0_3115,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_1802]),
[final] ).
cnf(i_0_3116,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_1803]),
[final] ).
cnf(i_0_3117,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_1804]),
[final] ).
cnf(i_0_3118,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_1805]),
[final] ).
cnf(i_0_3119,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_1806]),
[final] ).
cnf(i_0_3120,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_1807]),
[final] ).
cnf(i_0_3121,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ 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)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1778]),
[final] ).
cnf(i_0_3122,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field(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_1808]),
[final] ).
cnf(i_0_3123,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_1809]),
[final] ).
cnf(i_0_3124,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(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_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_3125,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field(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_1810]),
[final] ).
cnf(i_0_3126,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ 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))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1778]),
[final] ).
cnf(i_0_3127,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field(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_1811]),
[final] ).
cnf(i_0_3128,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(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_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_3129,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field(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_1812]),
[final] ).
cnf(i_0_3130,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3),X1)),esk33_2(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1813]),
[final] ).
cnf(i_0_3131,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_1814]),
[final] ).
cnf(i_0_3132,plain,
( 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_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3133,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3134,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_1816]),
[final] ).
cnf(i_0_3135,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_1817]),
[final] ).
cnf(i_0_3136,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_1818]),
[final] ).
cnf(i_0_3137,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_1819]),
[final] ).
cnf(i_0_3138,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_1820]),
[final] ).
cnf(i_0_3139,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_1821]),
[final] ).
cnf(i_0_3140,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_1822]),
[final] ).
cnf(i_0_3141,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_1823]),
[final] ).
cnf(i_0_3142,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_1824]),
[final] ).
cnf(i_0_3143,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_1823]),
[final] ).
cnf(i_0_3144,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_1825]),
[final] ).
cnf(i_0_3145,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_1783]),
[final] ).
cnf(i_0_3146,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_1783]),
[final] ).
cnf(i_0_3147,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_1826]),
[final] ).
cnf(i_0_3148,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_1827]),
[final] ).
cnf(i_0_3149,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_1828]),
[final] ).
cnf(i_0_3150,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_1829]),
[final] ).
cnf(i_0_3151,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_1830]),
[final] ).
cnf(i_0_3152,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_1784]),
[final] ).
cnf(i_0_3153,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_1831]),
[final] ).
cnf(i_0_3154,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_1829]),
[final] ).
cnf(i_0_3155,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_1832]),
[final] ).
cnf(i_0_3156,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_1784]),
[final] ).
cnf(i_0_3157,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_1833]),
[final] ).
cnf(i_0_3158,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_1665]),
[final] ).
cnf(i_0_3159,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_1834]),
[final] ).
cnf(i_0_3160,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_1667]),
[final] ).
cnf(i_0_3161,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_1835]),
[final] ).
cnf(i_0_3162,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_1669]),
[final] ).
cnf(i_0_3163,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_1836]),
[final] ).
cnf(i_0_3164,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_1671]),
[final] ).
cnf(i_0_3165,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_1837]),
[final] ).
cnf(i_0_3166,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_1838,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3167,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_1839,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3168,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_1840,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3169,plain,
( X1 = esk75_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_1841]),
[final] ).
cnf(i_0_3170,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_1842]),
[final] ).
cnf(i_0_3171,plain,
( c_SEQ_Oincseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk42_2(X2,X1)),hAPP(X2,esk43_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_3172,plain,
( c_SEQ_Odecseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk32_2(X2,X1)),hAPP(X2,esk31_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1844]),
[final] ).
cnf(i_0_3173,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1845]),
[final] ).
cnf(i_0_3174,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_1846]),
[final] ).
cnf(i_0_3175,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_1847]),
[final] ).
cnf(i_0_3176,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_1848]),
[final] ).
cnf(i_0_3177,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_1849]),
[final] ).
cnf(i_0_3178,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_1850]),
[final] ).
cnf(i_0_3179,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk8_1(X1))),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_3180,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)),
inference(split_conjunct,[status(thm)],[i_0_1851]),
[final] ).
cnf(i_0_3181,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r) ),
inference(split_conjunct,[status(thm)],[i_0_1852]),
[final] ).
cnf(i_0_3182,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_1853]),
[final] ).
cnf(i_0_3183,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_1854]),
[final] ).
cnf(i_0_3184,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_1680]),
[final] ).
cnf(i_0_3185,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_1855]),
[final] ).
cnf(i_0_3186,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_1856]),
[final] ).
cnf(i_0_3187,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_1857]),
[final] ).
cnf(i_0_3188,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_1858]),
[final] ).
cnf(i_0_3189,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_1859]),
[final] ).
cnf(i_0_3190,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_1681]),
[final] ).
cnf(i_0_3191,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_1860]),
[final] ).
cnf(i_0_3192,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk26_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_1861,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3193,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_1862,c_0_1427]),
[final] ).
cnf(i_0_3194,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_1863]),
[final] ).
cnf(i_0_3195,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_1864]),
[final] ).
cnf(i_0_3196,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_1865,c_0_1427]),
[final] ).
cnf(i_0_3197,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_1866,c_0_1427]),
[final] ).
cnf(i_0_3198,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk26_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_1867,c_0_1427]),
[final] ).
cnf(i_0_3199,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ouminus__class_Ouminus(X1,X4),X3)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_3200,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_1771]),
[final] ).
cnf(i_0_3201,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_1869]),
[final] ).
cnf(i_0_3202,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_1770]),
[final] ).
cnf(i_0_3203,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_1870]),
[final] ).
cnf(i_0_3204,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_1871]),
[final] ).
cnf(i_0_3205,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
| ~ 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_1872]),
[final] ).
cnf(i_0_3206,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_1769]),
[final] ).
cnf(i_0_3207,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_1873]),
[final] ).
cnf(i_0_3208,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_1874]),
[final] ).
cnf(i_0_3209,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(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_1815]),
[final] ).
cnf(i_0_3210,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(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,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3211,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X1))
| ~ 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_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3212,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_1772]),
[final] ).
cnf(i_0_3213,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X1))
| ~ 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,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3214,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_1875,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3215,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_1876,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3216,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_1877]),
[final] ).
cnf(i_0_3217,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_1878]),
[final] ).
cnf(i_0_3218,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_1879]),
[final] ).
cnf(i_0_3219,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_1880]),
[final] ).
cnf(i_0_3220,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_1775]),
[final] ).
cnf(i_0_3221,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_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_1476]),
[final] ).
cnf(i_0_3222,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),esk79_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_1476]),
[final] ).
cnf(i_0_3223,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_1881]),
[final] ).
cnf(i_0_3224,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_1882]),
[final] ).
cnf(i_0_3225,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_1883]),
[final] ).
cnf(i_0_3226,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_1884]),
[final] ).
cnf(i_0_3227,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_1885]),
[final] ).
cnf(i_0_3228,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_1886]),
[final] ).
cnf(i_0_3229,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_1887,c_0_1427]),
[final] ).
cnf(i_0_3230,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_1888]),
[final] ).
cnf(i_0_3231,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_1889]),
[final] ).
cnf(i_0_3232,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_1890]),
[final] ).
cnf(i_0_3233,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_1891]),
[final] ).
cnf(i_0_3234,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_1892]),
[final] ).
cnf(i_0_3235,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk81_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_1476]),
[final] ).
cnf(i_0_3236,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,esk79_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_1476]),
[final] ).
cnf(i_0_3237,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3238,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_3239,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1895]),
[final] ).
cnf(i_0_3240,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_3241,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_1897]),
[final] ).
cnf(i_0_3242,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_1898]),
[final] ).
cnf(i_0_3243,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_1899]),
[final] ).
cnf(i_0_3244,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = c_Rings_Oinverse__class_Odivide(X1,X3,X4)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1900]),
[final] ).
cnf(i_0_3245,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) = c_Rings_Oinverse__class_Odivide(X1,X3,X4)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1901]),
[final] ).
cnf(i_0_3246,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_1902,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3247,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_1903,c_0_1427]),
[final] ).
cnf(i_0_3248,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))
| ~ epred2_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_3249,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_1724]),
[final] ).
cnf(i_0_3250,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_1904]),
[final] ).
cnf(i_0_3251,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_1905]),
[final] ).
cnf(i_0_3252,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_1906]),
[final] ).
cnf(i_0_3253,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_1907,c_0_1427]),
[final] ).
cnf(i_0_3254,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_1908,c_0_1427]),
[final] ).
cnf(i_0_3255,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_1909,c_0_1427]),
[final] ).
cnf(i_0_3256,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_1910]),
[final] ).
cnf(i_0_3257,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Rings_Oinverse__class_Odivide(X1,X3,X4)) = c_Rings_Oinverse__class_Odivide(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1911]),
[final] ).
cnf(i_0_3258,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_1912,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3259,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_1913,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3260,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_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)
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3261,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),esk83_3(X2,X1,X3))
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3262,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_1914]),
[final] ).
cnf(i_0_3263,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_1914]),
[final] ).
cnf(i_0_3264,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_1915]),
[final] ).
cnf(i_0_3265,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_1915]),
[final] ).
cnf(i_0_3266,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk85_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3267,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,esk83_3(X2,X1,X3),X1)
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3268,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_1643]),
[final] ).
cnf(i_0_3269,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_1916]),
[final] ).
cnf(i_0_3270,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_1645]),
[final] ).
cnf(i_0_3271,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_1917]),
[final] ).
cnf(i_0_3272,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_1281]),
[final] ).
cnf(i_0_3273,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_3274,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_1919]),
[final] ).
cnf(i_0_3275,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_3276,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1750]),
[final] ).
cnf(i_0_3277,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_1920]),
[final] ).
cnf(i_0_3278,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_1921]),
[final] ).
cnf(i_0_3279,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_1922]),
[final] ).
cnf(i_0_3280,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_1923]),
[final] ).
cnf(i_0_3281,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_1924]),
[final] ).
cnf(i_0_3282,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_1925]),
[final] ).
cnf(i_0_3283,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_1926]),
[final] ).
cnf(i_0_3284,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_1927]),
[final] ).
cnf(i_0_3285,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_1928,c_0_1427]),
[final] ).
cnf(i_0_3286,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_1929,c_0_1427]),
[final] ).
cnf(i_0_3287,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_1930,c_0_1427]),
[final] ).
cnf(i_0_3288,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_1931,c_0_1427]),
[final] ).
cnf(i_0_3289,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,esk10_0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1932]),
[final] ).
cnf(i_0_3290,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_1933]),
[final] ).
cnf(i_0_3291,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_1934,c_0_1427]),
[final] ).
cnf(i_0_3292,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_1935,c_0_1427]),
[final] ).
cnf(i_0_3293,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_1936,c_0_1427]),
[final] ).
cnf(i_0_3294,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_1937,c_0_1427]),
[final] ).
cnf(i_0_3295,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_1938,c_0_1427]),
[final] ).
cnf(i_0_3296,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_1939]),
[final] ).
cnf(i_0_3297,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_1940,c_0_1427]),
[final] ).
cnf(i_0_3298,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_1941,c_0_1427]),
[final] ).
cnf(i_0_3299,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_1942]),
[final] ).
cnf(i_0_3300,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_1943,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3301,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_1944]),
[final] ).
cnf(i_0_3302,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_1507]),
[final] ).
cnf(i_0_3303,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_1280]),
[final] ).
cnf(i_0_3304,plain,
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1945]),
[final] ).
cnf(i_0_3305,plain,
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3306,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_1947]),
[final] ).
cnf(i_0_3307,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_1948]),
[final] ).
cnf(i_0_3308,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_1948]),
[final] ).
cnf(i_0_3309,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_1949]),
[final] ).
cnf(i_0_3310,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_1950]),
[final] ).
cnf(i_0_3311,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_1951]),
[final] ).
cnf(i_0_3312,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_1952,c_0_1427]),
[final] ).
cnf(i_0_3313,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rw,[status(thm)],[i_0_1953,c_0_1427]),
[final] ).
cnf(i_0_3314,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_1954,c_0_1427]),c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3315,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_1955,c_0_1427]),c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3316,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk20_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_1956,c_0_1427]),
[final] ).
cnf(i_0_3317,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_1957]),
[final] ).
cnf(i_0_3318,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_1957]),
[final] ).
cnf(i_0_3319,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_1958]),
[final] ).
cnf(i_0_3320,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_1959,c_0_1427]),c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3321,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| X5 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X3) != c_Rings_Oinverse__class_Odivide(X1,X4,X5)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1960]),
[final] ).
cnf(i_0_3322,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,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_1961]),
[final] ).
cnf(i_0_3323,plain,
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_3324,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,X5) = c_Rings_Oinverse__class_Odivide(X1,X4,X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X5 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1960]),
[final] ).
cnf(i_0_3325,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_1962]),
[final] ).
cnf(i_0_3326,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_1963]),
[final] ).
cnf(i_0_3327,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_1645]),
[final] ).
cnf(i_0_3328,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_1643]),
[final] ).
cnf(i_0_3329,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_1964]),
[final] ).
cnf(i_0_3330,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_1732]),
[final] ).
cnf(i_0_3331,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_1904]),
[final] ).
cnf(i_0_3332,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_1904]),
[final] ).
cnf(i_0_3333,plain,
c_Rings_Oinverse__class_Odivide(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),X1)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3334,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1895]),
[final] ).
cnf(i_0_3335,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_3336,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3337,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_3338,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_1897]),
[final] ).
cnf(i_0_3339,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk85_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)
| epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3340,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk81_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_1476]),
[final] ).
cnf(i_0_3341,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),esk83_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3342,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),esk79_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_1476]),
[final] ).
cnf(i_0_3343,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk75_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_1841]),
[final] ).
cnf(i_0_3344,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk74_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_1966]),
[final] ).
cnf(i_0_3345,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk85_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)
| epred2_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3346,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk81_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_1476]),
[final] ).
cnf(i_0_3347,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,esk83_3(X2,X1,X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3348,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,esk79_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_1476]),
[final] ).
cnf(i_0_3349,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_1957]),
[final] ).
cnf(i_0_3350,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_1883]),
[final] ).
cnf(i_0_3351,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_1884]),
[final] ).
cnf(i_0_3352,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_1885]),
[final] ).
cnf(i_0_3353,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_1881]),
[final] ).
cnf(i_0_3354,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_1882]),
[final] ).
cnf(i_0_3355,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_1967,c_0_1427]),
[final] ).
cnf(i_0_3356,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_1968]),
[final] ).
cnf(i_0_3357,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1969]),
[final] ).
cnf(i_0_3358,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1970]),
[final] ).
cnf(i_0_3359,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1971]),
[final] ).
cnf(i_0_3360,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_1972,c_0_1427]),
[final] ).
cnf(i_0_3361,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_1973]),
[final] ).
cnf(i_0_3362,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_1974]),
[final] ).
cnf(i_0_3363,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_1975]),
[final] ).
cnf(i_0_3364,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_1976]),
[final] ).
cnf(i_0_3365,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_1977]),
[final] ).
cnf(i_0_3366,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_1978]),
[final] ).
cnf(i_0_3367,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1979]),
[final] ).
cnf(i_0_3368,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1980]),
[final] ).
cnf(i_0_3369,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_1958]),
[final] ).
cnf(i_0_3370,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_1981]),
[final] ).
cnf(i_0_3371,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk75_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_1841]),
[final] ).
cnf(i_0_3372,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk74_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_1966]),
[final] ).
cnf(i_0_3373,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1971]),
[final] ).
cnf(i_0_3374,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1970]),
[final] ).
cnf(i_0_3375,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_1982]),
[final] ).
cnf(i_0_3376,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk34_2(X2,X3))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_3377,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_1983,c_0_1427]),
[final] ).
cnf(i_0_3378,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_1984]),
[final] ).
cnf(i_0_3379,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_1985,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3380,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_1986,c_0_1427]),
[final] ).
cnf(i_0_3381,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1987]),
[final] ).
cnf(i_0_3382,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_3383,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_1814]),
[final] ).
cnf(i_0_3384,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_1814]),
[final] ).
cnf(i_0_3385,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1989]),
[final] ).
cnf(i_0_3386,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1990]),
[final] ).
cnf(i_0_3387,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_1792]),
[final] ).
cnf(i_0_3388,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_1991]),
[final] ).
cnf(i_0_3389,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_1992]),
[final] ).
cnf(i_0_3390,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_1933]),
[final] ).
cnf(i_0_3391,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_1993,c_0_1427]),
[final] ).
cnf(i_0_3392,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_1994,c_0_1427]),
[final] ).
cnf(i_0_3393,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_1995,c_0_1427]),
[final] ).
cnf(i_0_3394,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_1927]),
[final] ).
cnf(i_0_3395,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_1939]),
[final] ).
cnf(i_0_3396,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_1996,c_0_1427]),
[final] ).
cnf(i_0_3397,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_1997,c_0_1427]),
[final] ).
cnf(i_0_3398,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_1998,c_0_1427]),
[final] ).
cnf(i_0_3399,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_1999,c_0_1427]),
[final] ).
cnf(i_0_3400,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_2000,c_0_1427]),
[final] ).
cnf(i_0_3401,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_2001,c_0_1427]),
[final] ).
cnf(i_0_3402,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_2002]),
[final] ).
cnf(i_0_3403,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_2003]),
[final] ).
cnf(i_0_3404,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),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_1989]),
[final] ).
cnf(i_0_3405,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),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_2004]),
[final] ).
cnf(i_0_3406,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(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_2005]),
[final] ).
cnf(i_0_3407,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),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_2006]),
[final] ).
cnf(i_0_3408,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(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_2007]),
[final] ).
cnf(i_0_3409,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,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_1987]),
[final] ).
cnf(i_0_3410,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,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_2008]),
[final] ).
cnf(i_0_3411,plain,
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2),X3) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2009]),
[final] ).
cnf(i_0_3412,plain,
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2),X3) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2010]),
[final] ).
cnf(i_0_3413,plain,
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2011]),
[final] ).
cnf(i_0_3414,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_1942]),
[final] ).
cnf(i_0_3415,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_2012]),
[final] ).
cnf(i_0_3416,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_2013]),
[final] ).
cnf(i_0_3417,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_2014]),
[final] ).
cnf(i_0_3418,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_1964]),
[final] ).
cnf(i_0_3419,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_2015]),
[final] ).
cnf(i_0_3420,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_2016]),
[final] ).
cnf(i_0_3421,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_1423]),
[final] ).
cnf(i_0_3422,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_2017]),
[final] ).
cnf(i_0_3423,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_2018]),
[final] ).
cnf(i_0_3424,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_2019]),
[final] ).
cnf(i_0_3425,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_2020]),
[final] ).
cnf(i_0_3426,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_2021]),
[final] ).
cnf(i_0_3427,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_2022]),
[final] ).
cnf(i_0_3428,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_2023]),
[final] ).
cnf(i_0_3429,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_2024]),
[final] ).
cnf(i_0_3430,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_2025]),
[final] ).
cnf(i_0_3431,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_2026,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3432,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_2027,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3433,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_2028,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3434,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_2029,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3435,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2030]),
[final] ).
cnf(i_0_3436,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3437,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2032]),
[final] ).
cnf(i_0_3438,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_2033]),
[final] ).
cnf(i_0_3439,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_2034]),
[final] ).
cnf(i_0_3440,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_1962]),
[final] ).
cnf(i_0_3441,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_1963]),
[final] ).
cnf(i_0_3442,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_2035]),
[final] ).
cnf(i_0_3443,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_2036]),
[final] ).
cnf(i_0_3444,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_2037]),
[final] ).
cnf(i_0_3445,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_2038]),
[final] ).
cnf(i_0_3446,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_2039]),
[final] ).
cnf(i_0_3447,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_2040]),
[final] ).
cnf(i_0_3448,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_2041]),
[final] ).
cnf(i_0_3449,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_2042]),
[final] ).
cnf(i_0_3450,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_2043]),
[final] ).
cnf(i_0_3451,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2044]),
[final] ).
cnf(i_0_3452,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2045]),
[final] ).
cnf(i_0_3453,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(split_conjunct,[status(thm)],[i_0_2046]),
[final] ).
cnf(i_0_3454,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_2047]),
[final] ).
cnf(i_0_3455,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_2048]),
[final] ).
cnf(i_0_3456,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_SMT_Oz3div(X2,X1) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2049]),
[final] ).
cnf(i_0_3457,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2050]),
[final] ).
cnf(i_0_3458,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2051]),
[final] ).
cnf(i_0_3459,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2052]),
[final] ).
cnf(i_0_3460,plain,
( c_Orderings_Oord__class_Oless(X1,esk67_3(X2,X3,X1),c_Groups_Oone__class_Oone(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1488]),
[final] ).
cnf(i_0_3461,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),esk67_3(X2,X3,X1))
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1488]),
[final] ).
cnf(i_0_3462,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_2053,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3463,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_2054]),
[final] ).
cnf(i_0_3464,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_2055]),
[final] ).
cnf(i_0_3465,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_2056]),
[final] ).
cnf(i_0_3466,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_2055]),
[final] ).
cnf(i_0_3467,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2057]),
[final] ).
cnf(i_0_3468,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2058]),
[final] ).
cnf(i_0_3469,plain,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2059]),
[final] ).
cnf(i_0_3470,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
| ~ 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_2060]),
[final] ).
cnf(i_0_3471,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
| ~ 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_2061]),
[final] ).
cnf(i_0_3472,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_2062,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3473,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_2063,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3474,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_1476]),
[final] ).
cnf(i_0_3475,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_2064]),
[final] ).
cnf(i_0_3476,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_2064]),
[final] ).
cnf(i_0_3477,plain,
( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2065]),
[final] ).
cnf(i_0_3478,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X2) = c_Divides_Odiv__class_Omod(X1,X3,X2)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2066]),
[final] ).
cnf(i_0_3479,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2067]),
[final] ).
cnf(i_0_3480,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_2068]),
[final] ).
cnf(i_0_3481,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2069]),
[final] ).
cnf(i_0_3482,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_2070]),
[final] ).
cnf(i_0_3483,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_2071]),
[final] ).
cnf(i_0_3484,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_2072]),
[final] ).
cnf(i_0_3485,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_1843]),
[final] ).
cnf(i_0_3486,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_1844]),
[final] ).
cnf(i_0_3487,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_2073,c_0_1427]),
[final] ).
cnf(i_0_3488,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk9_0),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
inference(split_conjunct,[status(thm)],[i_0_1564]),
[final] ).
cnf(i_0_3489,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)),
inference(split_conjunct,[status(thm)],[i_0_2074]),
[final] ).
cnf(i_0_3490,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_2075,c_0_1427]),
[final] ).
cnf(i_0_3491,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_2076,c_0_1427]),
[final] ).
cnf(i_0_3492,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)
| epred2_3(X2,X1,X3)
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3493,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2077]),
[final] ).
cnf(i_0_3494,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_1958]),
[final] ).
cnf(i_0_3495,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2078]),
[final] ).
cnf(i_0_3496,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2078]),
[final] ).
cnf(i_0_3497,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2079]),
[final] ).
cnf(i_0_3498,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2079]),
[final] ).
cnf(i_0_3499,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2080]),
[final] ).
cnf(i_0_3500,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2080]),
[final] ).
cnf(i_0_3501,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2081]),
[final] ).
cnf(i_0_3502,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2081]),
[final] ).
cnf(i_0_3503,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2082]),
[final] ).
cnf(i_0_3504,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)),
inference(split_conjunct,[status(thm)],[i_0_2083]),
[final] ).
cnf(i_0_3505,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)),
inference(split_conjunct,[status(thm)],[i_0_2084]),
[final] ).
cnf(i_0_3506,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2)) = c_Rings_Oinverse__class_Odivide(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2085]),
[final] ).
cnf(i_0_3507,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2086]),
[final] ).
cnf(i_0_3508,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_2087,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3509,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_2088,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3510,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_2089,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3511,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_2090,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3512,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_2091]),
[final] ).
cnf(i_0_3513,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2092]),
[final] ).
cnf(i_0_3514,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2093]),
[final] ).
cnf(i_0_3515,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2094]),
[final] ).
cnf(i_0_3516,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2095]),
[final] ).
cnf(i_0_3517,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)) = c_Rings_Oinverse__class_Odivide(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2096]),
[final] ).
cnf(i_0_3518,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2097]),
[final] ).
cnf(i_0_3519,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_3520,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2099]),
[final] ).
cnf(i_0_3521,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2100]),
[final] ).
cnf(i_0_3522,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_2055]),
[final] ).
cnf(i_0_3523,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_2101]),
[final] ).
cnf(i_0_3524,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk8_1(X1)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_3525,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk7_1(X1)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1449]),
[final] ).
cnf(i_0_3526,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2102]),
[final] ).
cnf(i_0_3527,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2103]),
[final] ).
cnf(i_0_3528,plain,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3529,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[i_0_2105,c_0_1427]),
[final] ).
cnf(i_0_3530,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_2055]),
[final] ).
cnf(i_0_3531,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_2055]),
[final] ).
cnf(i_0_3532,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2050]),
[final] ).
cnf(i_0_3533,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Lattices_Oboolean__algebra(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_3534,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2051]),
[final] ).
cnf(i_0_3535,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2107]),
[final] ).
cnf(i_0_3536,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2052]),
[final] ).
cnf(i_0_3537,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_2108,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3538,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_2109]),
[final] ).
cnf(i_0_3539,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_2055]),
[final] ).
cnf(i_0_3540,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Oplus__class_Oplus(X1,X2,X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2110]),
[final] ).
cnf(i_0_3541,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2111]),
[final] ).
cnf(i_0_3542,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2112]),
[final] ).
cnf(i_0_3543,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2113]),
[final] ).
cnf(i_0_3544,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2114]),
[final] ).
cnf(i_0_3545,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2115]),
[final] ).
cnf(i_0_3546,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X2) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2116]),
[final] ).
cnf(i_0_3547,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_2117]),
[final] ).
cnf(i_0_3548,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_2118,c_0_1427]),
[final] ).
cnf(i_0_3549,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_2119]),
[final] ).
cnf(i_0_3550,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk23_1(X1))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,esk22_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,esk21_0) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_3551,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk4_1(X1))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,esk3_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_s____) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_3552,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2097]),
[final] ).
cnf(i_0_3553,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_3554,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2099]),
[final] ).
cnf(i_0_3555,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2100]),
[final] ).
cnf(i_0_3556,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2120]),
[final] ).
cnf(i_0_3557,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2121]),
[final] ).
cnf(i_0_3558,plain,
( X2 = X3
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_3559,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_2123]),
[final] ).
cnf(i_0_3560,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk40_2(X2,X1))
| ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1486]),
[final] ).
cnf(i_0_3561,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2111]),
[final] ).
cnf(i_0_3562,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2112]),
[final] ).
cnf(i_0_3563,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2113]),
[final] ).
cnf(i_0_3564,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2114]),
[final] ).
cnf(i_0_3565,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_2124,c_0_1427]),
[final] ).
cnf(i_0_3566,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_2125,c_0_1427]),
[final] ).
cnf(i_0_3567,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2)
| X1 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2126]),
[final] ).
cnf(i_0_3568,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_2127]),
[final] ).
cnf(i_0_3569,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2092]),
[final] ).
cnf(i_0_3570,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2093]),
[final] ).
cnf(i_0_3571,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,X3,X2)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_3572,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_2129]),
[final] ).
cnf(i_0_3573,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_2130]),
[final] ).
cnf(i_0_3574,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_2131]),
[final] ).
cnf(i_0_3575,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_2132]),
[final] ).
cnf(i_0_3576,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2133]),
[final] ).
cnf(i_0_3577,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_2134]),
[final] ).
cnf(i_0_3578,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_2135]),
[final] ).
cnf(i_0_3579,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_2136]),
[final] ).
cnf(i_0_3580,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_2137]),
[final] ).
cnf(i_0_3581,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_2138]),
[final] ).
cnf(i_0_3582,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_2139]),
[final] ).
cnf(i_0_3583,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_2140]),
[final] ).
cnf(i_0_3584,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_2141]),
[final] ).
cnf(i_0_3585,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_2142]),
[final] ).
cnf(i_0_3586,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_2143]),
[final] ).
cnf(i_0_3587,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_2144]),
[final] ).
cnf(i_0_3588,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_2145]),
[final] ).
cnf(i_0_3589,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_2146]),
[final] ).
cnf(i_0_3590,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_2147]),
[final] ).
cnf(i_0_3591,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_2148]),
[final] ).
cnf(i_0_3592,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_2101]),
[final] ).
cnf(i_0_3593,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3594,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_3595,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_2151,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3596,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_2152,c_0_1427]),c_0_1427]),
[final] ).
cnf(i_0_3597,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| hAPP(c_Polynomial_Opoly(X1,X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| c_Polynomial_Oorder(X1,X3,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2153]),
[final] ).
cnf(i_0_3598,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_2154]),
[final] ).
cnf(i_0_3599,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,esk35_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_1315]),
[final] ).
cnf(i_0_3600,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2155]),
[final] ).
cnf(i_0_3601,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_2156,c_0_1427]),
[final] ).
cnf(i_0_3602,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Rings_Oinverse__class_Odivide(X1,X3,X2)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2157]),
[final] ).
cnf(i_0_3603,plain,
( c_Divides_Odiv__class_Odiv(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2158]),
[final] ).
cnf(i_0_3604,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)
| epred2_3(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3605,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_1476]),
[final] ).
cnf(i_0_3606,plain,
c_Divides_Odiv__class_Omod(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_Ozero__class_Ozero(tc_Nat_Onat),
inference(rw,[status(thm)],[i_0_2159,c_0_1427]),
[final] ).
cnf(i_0_3607,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_2160]),
[final] ).
cnf(i_0_3608,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_2161]),
[final] ).
cnf(i_0_3609,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_2162]),
[final] ).
cnf(i_0_3610,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_2163]),
[final] ).
cnf(i_0_3611,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_2164]),
[final] ).
cnf(i_0_3612,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_2165]),
[final] ).
cnf(i_0_3613,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_2166,c_0_1427]),
[final] ).
cnf(i_0_3614,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_2167]),
[final] ).
cnf(i_0_3615,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_2168]),
[final] ).
cnf(i_0_3616,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_2169]),
[final] ).
cnf(i_0_3617,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_2169]),
[final] ).
cnf(i_0_3618,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_2170,c_0_1427]),
[final] ).
cnf(i_0_3619,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_2171]),
[final] ).
cnf(i_0_3620,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_2172]),
[final] ).
cnf(i_0_3621,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk23_1(X1)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,esk21_0) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_3622,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk4_1(X1)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_s____) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_3623,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2173]),
[final] ).
cnf(i_0_3624,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2174]),
[final] ).
cnf(i_0_3625,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Rings_Oinverse__class_Odivide(X1,X2,X3)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2175]),
[final] ).
cnf(i_0_3626,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2133]),
[final] ).
cnf(i_0_3627,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_2176,c_0_1427]),
[final] ).
cnf(i_0_3628,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_1927]),
[final] ).
cnf(i_0_3629,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_2177,c_0_1427]),
[final] ).
cnf(i_0_3630,plain,
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2178]),
[final] ).
cnf(i_0_3631,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_2179,c_0_1427]),
[final] ).
cnf(i_0_3632,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2180]),
[final] ).
cnf(i_0_3633,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2181]),
[final] ).
cnf(i_0_3634,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk30_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2182]),
[final] ).
cnf(i_0_3635,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk24_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2183]),
[final] ).
cnf(i_0_3636,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk34_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_1716]),
[final] ).
cnf(i_0_3637,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_2184,c_0_1427]),
[final] ).
cnf(i_0_3638,plain,
( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk69_2(X2,X1))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2185]),
[final] ).
cnf(i_0_3639,plain,
( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk54_2(X2,X1))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_3640,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2187]),
[final] ).
cnf(i_0_3641,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_2188]),
[final] ).
cnf(i_0_3642,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_2189]),
[final] ).
cnf(i_0_3643,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_2190]),
[final] ).
cnf(i_0_3644,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_2191]),
[final] ).
cnf(i_0_3645,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2192]),
[final] ).
cnf(i_0_3646,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_2193]),
[final] ).
cnf(i_0_3647,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_2194]),
[final] ).
cnf(i_0_3648,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_2195]),
[final] ).
cnf(i_0_3649,plain,
( c_SMT_Oz3div(X2,X1) = 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),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2049]),
[final] ).
cnf(i_0_3650,plain,
( c_SMT_Oz3mod(X2,X1) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,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_2196]),
[final] ).
cnf(i_0_3651,plain,
( c_Rings_Oinverse__class_Odivide(X2,X3,X4) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2197]),
[final] ).
cnf(i_0_3652,plain,
( X1 = c_Rings_Oinverse__class_Odivide(X2,X4,X3)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3) != X4
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_3653,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_2199]),
[final] ).
cnf(i_0_3654,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_2200]),
[final] ).
cnf(i_0_3655,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) = X4
| X3 != c_Rings_Oinverse__class_Odivide(X2,X4,X1)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_3656,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4) = X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Rings_Oinverse__class_Odivide(X2,X3,X4)
| ~ class_Rings_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2201]),
[final] ).
cnf(i_0_3657,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1)
| c_Rings_Oinverse__class_Odivide(X2,X3,X1) != X4
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2197]),
[final] ).
cnf(i_0_3658,plain,
( X2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X3) != X4
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2202]),
[final] ).
cnf(i_0_3659,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_1962]),
[final] ).
cnf(i_0_3660,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_1963]),
[final] ).
cnf(i_0_3661,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Oinverse__class_Odivide(X2,X3,X1) = X4
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2197]),
[final] ).
cnf(i_0_3662,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X3,X2) = X4
| ~ class_Rings_Odivision__ring(X1)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2203]),
[final] ).
cnf(i_0_3663,plain,
( c_Rings_Oinverse__class_Odivide(X2,X1,X4) = X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)
| ~ class_Rings_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2202]),
[final] ).
cnf(i_0_3664,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Rings_Oinverse__class_Odivide(X2,X4,X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) != X4
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_3665,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Rings_Oinverse__class_Odivide(X1,X4,X2)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_2204]),
[final] ).
cnf(i_0_3666,plain,
( X2 = c_Rings_Oinverse__class_Odivide(X1,X4,X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != X4
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2201]),
[final] ).
cnf(i_0_3667,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk25_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_2205,c_0_1427]),
[final] ).
cnf(i_0_3668,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_2206]),
[final] ).
cnf(i_0_3669,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_2207]),
[final] ).
cnf(i_0_3670,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_2199]),
[final] ).
cnf(i_0_3671,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_2200]),
[final] ).
cnf(i_0_3672,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_2208]),
[final] ).
cnf(i_0_3673,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_2209]),
[final] ).
cnf(i_0_3674,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_2210]),
[final] ).
cnf(i_0_3675,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_2211]),
[final] ).
cnf(i_0_3676,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_2212]),
[final] ).
cnf(i_0_3677,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_2213]),
[final] ).
cnf(i_0_3678,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_2214]),
[final] ).
cnf(i_0_3679,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_2215]),
[final] ).
cnf(i_0_3680,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_2216]),
[final] ).
cnf(i_0_3681,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_2217]),
[final] ).
cnf(i_0_3682,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_2218]),
[final] ).
cnf(i_0_3683,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_2127]),
[final] ).
cnf(i_0_3684,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_2219]),
[final] ).
cnf(i_0_3685,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_2220]),
[final] ).
cnf(i_0_3686,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_2033]),
[final] ).
cnf(i_0_3687,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2221]),
[final] ).
cnf(i_0_3688,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_2169]),
[final] ).
cnf(i_0_3689,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_2222]),
[final] ).
cnf(i_0_3690,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_2223]),
[final] ).
cnf(i_0_3691,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_2217]),
[final] ).
cnf(i_0_3692,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_2218]),
[final] ).
cnf(i_0_3693,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_2224]),
[final] ).
cnf(i_0_3694,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_2101]),
[final] ).
cnf(i_0_3695,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_SMT_Oz3mod(X2,X1) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2196]),
[final] ).
cnf(i_0_3696,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_2225,c_0_1427]),
[final] ).
cnf(i_0_3697,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_2226]),
[final] ).
cnf(i_0_3698,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_2226]),
[final] ).
cnf(i_0_3699,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_2227]),
[final] ).
cnf(i_0_3700,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(split_conjunct,[status(thm)],[i_0_2228]),
[final] ).
cnf(i_0_3701,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_2229]),
[final] ).
cnf(i_0_3702,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,X2,X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2230]),
[final] ).
cnf(i_0_3703,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_2231]),
[final] ).
cnf(i_0_3704,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,esk22_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,esk21_0) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_3705,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,esk3_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_s____) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_3706,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_2232]),
[final] ).
cnf(i_0_3707,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_2233]),
[final] ).
cnf(i_0_3708,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_2234]),
[final] ).
cnf(i_0_3709,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_2235]),
[final] ).
cnf(i_0_3710,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_2236]),
[final] ).
cnf(i_0_3711,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_2237]),
[final] ).
cnf(i_0_3712,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_2238]),
[final] ).
cnf(i_0_3713,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_2239]),
[final] ).
cnf(i_0_3714,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_2232]),
[final] ).
cnf(i_0_3715,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_2240]),
[final] ).
cnf(i_0_3716,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X1),X3),X4) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(X3,X4))
| ~ class_Groups_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2241]),
[final] ).
cnf(i_0_3717,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_2182]),
[final] ).
cnf(i_0_3718,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_2183]),
[final] ).
cnf(i_0_3719,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1979]),
[final] ).
cnf(i_0_3720,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3721,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_2233]),
[final] ).
cnf(i_0_3722,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_2243]),
[final] ).
cnf(i_0_3723,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_2234]),
[final] ).
cnf(i_0_3724,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_2235]),
[final] ).
cnf(i_0_3725,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_2244]),
[final] ).
cnf(i_0_3726,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_2245]),
[final] ).
cnf(i_0_3727,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_2237]),
[final] ).
cnf(i_0_3728,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_2238]),
[final] ).
cnf(i_0_3729,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_2246]),
[final] ).
cnf(i_0_3730,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_3731,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[i_0_2247,c_0_1427]),
[final] ).
cnf(i_0_3732,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2248]),
[final] ).
cnf(i_0_3733,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2185]),
[final] ).
cnf(i_0_3734,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_3735,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_1476]),
[final] ).
cnf(i_0_3736,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_3737,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_3738,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk42_2(X1,X2),esk43_2(X1,X2))
| c_SEQ_Oincseq(X2,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_3739,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk31_2(X1,X2),esk32_2(X1,X2))
| c_SEQ_Odecseq(X2,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1844]),
[final] ).
cnf(i_0_3740,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2251]),
[final] ).
cnf(i_0_3741,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[i_0_2252]),
[final] ).
cnf(i_0_3742,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_2253]),
[final] ).
cnf(i_0_3743,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_2253]),
[final] ).
cnf(i_0_3744,plain,
( hBOOL(hAPP(X2,X3))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ epred2_3(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_3745,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2254]),
[final] ).
cnf(i_0_3746,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_2219]),
[final] ).
cnf(i_0_3747,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(esk2_0,X1)),v_r),
inference(split_conjunct,[status(thm)],[i_0_1271]),
[final] ).
cnf(i_0_3748,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_2255]),
[final] ).
cnf(i_0_3749,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_2256]),
[final] ).
cnf(i_0_3750,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_2257]),
[final] ).
cnf(i_0_3751,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_2258]),
[final] ).
cnf(i_0_3752,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_2259]),
[final] ).
cnf(i_0_3753,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_2141]),
[final] ).
cnf(i_0_3754,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_2260]),
[final] ).
cnf(i_0_3755,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_2261]),
[final] ).
cnf(i_0_3756,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_2262]),
[final] ).
cnf(i_0_3757,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_2144]),
[final] ).
cnf(i_0_3758,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_2263]),
[final] ).
cnf(i_0_3759,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_2143]),
[final] ).
cnf(i_0_3760,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_2264]),
[final] ).
cnf(i_0_3761,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_2265]),
[final] ).
cnf(i_0_3762,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_2266]),
[final] ).
cnf(i_0_3763,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2267]),
[final] ).
cnf(i_0_3764,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2268]),
[final] ).
cnf(i_0_3765,plain,
( X3 = c_Groups_Ouminus__class_Ouminus(X1,X2)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2269]),
[final] ).
cnf(i_0_3766,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_2270]),
[final] ).
cnf(i_0_3767,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_2271]),
[final] ).
cnf(i_0_3768,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2272]),
[final] ).
cnf(i_0_3769,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_2123]),
[final] ).
cnf(i_0_3770,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk47_2(X1,X2))
| ~ c_SEQ_OBseq(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1422]),
[final] ).
cnf(i_0_3771,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk44_2(X1,X2))
| ~ c_SEQ_OBseq(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1421]),
[final] ).
cnf(i_0_3772,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk40_2(X1,X2))
| ~ c_SEQ_OBseq(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1486]),
[final] ).
cnf(i_0_3773,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_2273,c_0_1427]),
[final] ).
cnf(i_0_3774,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_2274]),
[final] ).
cnf(i_0_3775,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_2275,c_0_1427]),
[final] ).
cnf(i_0_3776,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_2276]),
[final] ).
cnf(i_0_3777,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_2277]),
[final] ).
cnf(i_0_3778,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_2278]),
[final] ).
cnf(i_0_3779,plain,
( c_Polynomial_Oorder(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(X1,X3),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2153]),
[final] ).
cnf(i_0_3780,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Oinverse__class_Odivide(X2,X4,X1) != X3
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2197]),
[final] ).
cnf(i_0_3781,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Rings_Oinverse__class_Odivide(X2,X4,X1)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_3782,plain,
( X2 = X3
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X3) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2279]),
[final] ).
cnf(i_0_3783,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_2280]),
[final] ).
cnf(i_0_3784,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_2281]),
[final] ).
cnf(i_0_3785,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_2282]),
[final] ).
cnf(i_0_3786,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_2283]),
[final] ).
cnf(i_0_3787,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_2284]),
[final] ).
cnf(i_0_3788,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_2285]),
[final] ).
cnf(i_0_3789,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_2286]),
[final] ).
cnf(i_0_3790,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_2287]),
[final] ).
cnf(i_0_3791,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_2288]),
[final] ).
cnf(i_0_3792,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_2289]),
[final] ).
cnf(i_0_3793,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_2290]),
[final] ).
cnf(i_0_3794,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_2291]),
[final] ).
cnf(i_0_3795,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_2292]),
[final] ).
cnf(i_0_3796,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_3797,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_2294]),
[final] ).
cnf(i_0_3798,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2295]),
[final] ).
cnf(i_0_3799,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_2210]),
[final] ).
cnf(i_0_3800,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_2211]),
[final] ).
cnf(i_0_3801,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_2208]),
[final] ).
cnf(i_0_3802,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_2231]),
[final] ).
cnf(i_0_3803,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_2253]),
[final] ).
cnf(i_0_3804,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2254]),
[final] ).
cnf(i_0_3805,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2218]),
[final] ).
cnf(i_0_3806,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2141]),
[final] ).
cnf(i_0_3807,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_3808,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_3809,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2298]),
[final] ).
cnf(i_0_3810,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2255]),
[final] ).
cnf(i_0_3811,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2255]),
[final] ).
cnf(i_0_3812,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_2299]),
[final] ).
cnf(i_0_3813,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_2300]),
[final] ).
cnf(i_0_3814,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_2227]),
[final] ).
cnf(i_0_3815,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_2301]),
[final] ).
cnf(i_0_3816,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_3817,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_2303]),
[final] ).
cnf(i_0_3818,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_2304,c_0_1427]),
[final] ).
cnf(i_0_3819,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_2305,c_0_1427]),
[final] ).
cnf(i_0_3820,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_2306,c_0_1427]),
[final] ).
cnf(i_0_3821,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_2307,c_0_1427]),
[final] ).
cnf(i_0_3822,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_2308,c_0_1427]),
[final] ).
cnf(i_0_3823,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_2309,c_0_1427]),
[final] ).
cnf(i_0_3824,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_2310]),
[final] ).
cnf(i_0_3825,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_2311]),
[final] ).
cnf(i_0_3826,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_2312]),
[final] ).
cnf(i_0_3827,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_3828,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_3829,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2315]),
[final] ).
cnf(i_0_3830,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_2316]),
[final] ).
cnf(i_0_3831,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_2316]),
[final] ).
cnf(i_0_3832,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_2317]),
[final] ).
cnf(i_0_3833,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_2318,c_0_1427]),
[final] ).
cnf(i_0_3834,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_2319,c_0_1427]),
[final] ).
cnf(i_0_3835,plain,
( c_Groups_Oplus__class_Oplus(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2268]),
[final] ).
cnf(i_0_3836,plain,
( c_Groups_Oplus__class_Oplus(X2,X3,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2269]),
[final] ).
cnf(i_0_3837,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk62_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1609]),
[final] ).
cnf(i_0_3838,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_1606]),
[final] ).
cnf(i_0_3839,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk59_2(X1,X2))
| ~ class_RealVector_Oreal__normed__field(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1583]),
[final] ).
cnf(i_0_3840,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk66_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1608]),
[final] ).
cnf(i_0_3841,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk65_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1605]),
[final] ).
cnf(i_0_3842,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk63_2(X1,X2))
| ~ class_RealVector_Oreal__normed__field(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_3843,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_2320]),
[final] ).
cnf(i_0_3844,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_2321]),
[final] ).
cnf(i_0_3845,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_2322]),
[final] ).
cnf(i_0_3846,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_2323]),
[final] ).
cnf(i_0_3847,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_2324]),
[final] ).
cnf(i_0_3848,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_2325]),
[final] ).
cnf(i_0_3849,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1))),
inference(split_conjunct,[status(thm)],[i_0_2326]),
[final] ).
cnf(i_0_3850,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2327]),
[final] ).
cnf(i_0_3851,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2328]),
[final] ).
cnf(i_0_3852,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2233]),
[final] ).
cnf(i_0_3853,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2277]),
[final] ).
cnf(i_0_3854,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2277]),
[final] ).
cnf(i_0_3855,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2234]),
[final] ).
cnf(i_0_3856,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2329]),
[final] ).
cnf(i_0_3857,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_3858,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2237]),
[final] ).
cnf(i_0_3859,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2331]),
[final] ).
cnf(i_0_3860,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2332]),
[final] ).
cnf(i_0_3861,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk6_1(X1)),v_r),
inference(split_conjunct,[status(thm)],[i_0_1272]),
[final] ).
cnf(i_0_3862,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk5_1(X1)),v_r),
inference(split_conjunct,[status(thm)],[i_0_1273]),
[final] ).
cnf(i_0_3863,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_2321]),
[final] ).
cnf(i_0_3864,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk28_0)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,esk27_0),
inference(split_conjunct,[status(thm)],[i_0_2333]),
[final] ).
cnf(i_0_3865,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_3866,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_2334]),
[final] ).
cnf(i_0_3867,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2335]),
[final] ).
cnf(i_0_3868,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2336]),
[final] ).
cnf(i_0_3869,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1813]),
[final] ).
cnf(i_0_3870,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2251]),
[final] ).
cnf(i_0_3871,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_2337]),
[final] ).
cnf(i_0_3872,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r),
inference(split_conjunct,[status(thm)],[fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096]),
[final] ).
cnf(i_0_3873,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_2338]),
[final] ).
cnf(i_0_3874,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_2338]),
[final] ).
cnf(i_0_3875,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_2339]),
[final] ).
cnf(i_0_3876,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_2339]),
[final] ).
cnf(i_0_3877,plain,
( c_Rings_Oinverse__class_Odivide(X2,X4,X3) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2197]),
[final] ).
cnf(i_0_3878,plain,
( X1 = c_Rings_Oinverse__class_Odivide(X2,X4,X3)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_3879,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),
inference(split_conjunct,[status(thm)],[i_0_2340]),
[final] ).
cnf(i_0_3880,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2341]),
[final] ).
cnf(i_0_3881,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_2342]),
[final] ).
cnf(i_0_3882,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_3883,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_2343]),
[final] ).
cnf(i_0_3884,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_2344]),
[final] ).
cnf(i_0_3885,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_2345]),
[final] ).
cnf(i_0_3886,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_2346]),
[final] ).
cnf(i_0_3887,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_2347]),
[final] ).
cnf(i_0_3888,plain,
( c_Rings_Oinverse__class_Odivide(X3,X1,X2) = c_Groups_Oone__class_Oone(X3)
| X2 = c_Groups_Ozero__class_Ozero(X3)
| X1 != X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2279]),
[final] ).
cnf(i_0_3889,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_2288]),
[final] ).
cnf(i_0_3890,plain,
( c_Rings_Oinverse__class_Odivide(X2,X1,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2348]),
[final] ).
cnf(i_0_3891,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_2289]),
[final] ).
cnf(i_0_3892,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_2349]),
[final] ).
cnf(i_0_3893,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_2350]),
[final] ).
cnf(i_0_3894,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_2351]),
[final] ).
cnf(i_0_3895,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_2352]),
[final] ).
cnf(i_0_3896,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_2353]),
[final] ).
cnf(i_0_3897,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2254]),
[final] ).
cnf(i_0_3898,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_2283]),
[final] ).
cnf(i_0_3899,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_2283]),
[final] ).
cnf(i_0_3900,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2354]),
[final] ).
cnf(i_0_3901,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_2355]),
[final] ).
cnf(i_0_3902,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2356]),
[final] ).
cnf(i_0_3903,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2357]),
[final] ).
cnf(i_0_3904,plain,
( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2358]),
[final] ).
cnf(i_0_3905,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_2359]),
[final] ).
cnf(i_0_3906,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2360]),
[final] ).
cnf(i_0_3907,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk28_0),v_r),
inference(split_conjunct,[status(thm)],[i_0_2333]),
[final] ).
cnf(i_0_3908,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_2294]),
[final] ).
cnf(i_0_3909,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Oinverse__class_Odivide(X2,X1,X1) = c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2348]),
[final] ).
cnf(i_0_3910,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_2361]),
[final] ).
cnf(i_0_3911,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2362]),
[final] ).
cnf(i_0_3912,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_2363]),
[final] ).
cnf(i_0_3913,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_2364]),
[final] ).
cnf(i_0_3914,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_2365]),
[final] ).
cnf(i_0_3915,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_2366]),
[final] ).
cnf(i_0_3916,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk60_1(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3917,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk64_1(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1447]),
[final] ).
cnf(i_0_3918,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_2290]),
[final] ).
cnf(i_0_3919,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_2291]),
[final] ).
cnf(i_0_3920,plain,
( hAPP(c_Polynomial_Opoly(X2,X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2153]),
[final] ).
cnf(i_0_3921,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_2367]),
[final] ).
cnf(i_0_3922,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_2368]),
[final] ).
cnf(i_0_3923,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_2369]),
[final] ).
cnf(i_0_3924,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_2370]),
[final] ).
cnf(i_0_3925,plain,
( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2371]),
[final] ).
cnf(i_0_3926,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_2372]),
[final] ).
cnf(i_0_3927,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_2373]),
[final] ).
cnf(i_0_3928,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_2374]),
[final] ).
cnf(i_0_3929,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_2375]),
[final] ).
cnf(i_0_3930,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2376]),
[final] ).
cnf(i_0_3931,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_2316]),
[final] ).
cnf(i_0_3932,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_2377]),
[final] ).
cnf(i_0_3933,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_2378]),
[final] ).
cnf(i_0_3934,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_2379]),
[final] ).
cnf(i_0_3935,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_2380]),
[final] ).
cnf(i_0_3936,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_2381]),
[final] ).
cnf(i_0_3937,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_2382]),
[final] ).
cnf(i_0_3938,plain,
( c_Divides_Odiv__class_Omod(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2383]),
[final] ).
cnf(i_0_3939,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2132]),
[final] ).
cnf(i_0_3940,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2132]),
[final] ).
cnf(i_0_3941,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2384]),
[final] ).
cnf(i_0_3942,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_3943,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_2385]),
[final] ).
cnf(i_0_3944,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_2386]),
[final] ).
cnf(i_0_3945,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_2387]),
[final] ).
cnf(i_0_3946,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_2388]),
[final] ).
cnf(i_0_3947,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_2303]),
[final] ).
cnf(i_0_3948,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2389]),
[final] ).
cnf(i_0_3949,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_2390,c_0_1427]),
[final] ).
cnf(i_0_3950,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_2055]),
[final] ).
cnf(i_0_3951,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2391]),
[final] ).
cnf(i_0_3952,plain,
( X2 = X3
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3)
| ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2392]),
[final] ).
cnf(i_0_3953,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_2338]),
[final] ).
cnf(i_0_3954,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_2339]),
[final] ).
cnf(i_0_3955,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2393]),
[final] ).
cnf(i_0_3956,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2394]),
[final] ).
cnf(i_0_3957,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_2301]),
[final] ).
cnf(i_0_3958,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_2395]),
[final] ).
cnf(i_0_3959,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_2396]),
[final] ).
cnf(i_0_3960,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_3961,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_3962,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_3963,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_2397]),
[final] ).
cnf(i_0_3964,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2398]),
[final] ).
cnf(i_0_3965,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_2399]),
[final] ).
cnf(i_0_3966,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(split_conjunct,[status(thm)],[i_0_2400]),
[final] ).
cnf(i_0_3967,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_2401]),
[final] ).
cnf(i_0_3968,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_2402]),
[final] ).
cnf(i_0_3969,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_2403]),
[final] ).
cnf(i_0_3970,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2400]),
[final] ).
cnf(i_0_3971,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_2404]),
[final] ).
cnf(i_0_3972,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_2405]),
[final] ).
cnf(i_0_3973,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2235]),
[final] ).
cnf(i_0_3974,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2245]),
[final] ).
cnf(i_0_3975,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2406]),
[final] ).
cnf(i_0_3976,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2238]),
[final] ).
cnf(i_0_3977,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_2407]),
[final] ).
cnf(i_0_3978,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_2408]),
[final] ).
cnf(i_0_3979,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2409]),
[final] ).
cnf(i_0_3980,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_2410]),
[final] ).
cnf(i_0_3981,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2411]),
[final] ).
cnf(i_0_3982,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_2412]),
[final] ).
cnf(i_0_3983,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_3984,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_2334]),
[final] ).
cnf(i_0_3985,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_2334]),
[final] ).
cnf(i_0_3986,plain,
( X2 = X3
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2413]),
[final] ).
cnf(i_0_3987,plain,
( X2 = X3
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2414]),
[final] ).
cnf(i_0_3988,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_2415]),
[final] ).
cnf(i_0_3989,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_2416]),
[final] ).
cnf(i_0_3990,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_2417]),
[final] ).
cnf(i_0_3991,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2418]),
[final] ).
cnf(i_0_3992,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2419]),
[final] ).
cnf(i_0_3993,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2420]),
[final] ).
cnf(i_0_3994,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_2421]),
[final] ).
cnf(i_0_3995,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_2422]),
[final] ).
cnf(i_0_3996,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_2423]),
[final] ).
cnf(i_0_3997,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2424]),
[final] ).
cnf(i_0_3998,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2425]),
[final] ).
cnf(i_0_3999,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X3) = X2
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2426]),
[final] ).
cnf(i_0_4000,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X3) = X2
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2426]),
[final] ).
cnf(i_0_4001,plain,
( X3 = c_Groups_Ouminus__class_Ouminus(X2,X1)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2427]),
[final] ).
cnf(i_0_4002,plain,
( X3 = c_Groups_Ouminus__class_Ouminus(X2,X1)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2427]),
[final] ).
cnf(i_0_4003,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_2428]),
[final] ).
cnf(i_0_4004,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_2428]),
[final] ).
cnf(i_0_4005,plain,
( X1 = X2
| c_RealDef_Oreal(tc_Nat_Onat,X1) != c_RealDef_Oreal(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2429]),
[final] ).
cnf(i_0_4006,plain,
( c_Groups_Ozero__class_Ozero(X1) = X2
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2430]),
[final] ).
cnf(i_0_4007,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2431]),
[final] ).
cnf(i_0_4008,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_2432]),
[final] ).
cnf(i_0_4009,plain,
( class_Groups_Ouminus(tc_fun(X2,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2433]),
[final] ).
cnf(i_0_4010,plain,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2434]),
[final] ).
cnf(i_0_4011,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2435]),
[final] ).
cnf(i_0_4012,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2436]),
[final] ).
cnf(i_0_4013,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2437]),
[final] ).
cnf(i_0_4014,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2438]),
[final] ).
cnf(i_0_4015,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X2
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2439]),
[final] ).
cnf(i_0_4016,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X1)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2440]),
[final] ).
cnf(i_0_4017,plain,
( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2431]),
[final] ).
cnf(i_0_4018,plain,
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| c_Groups_Ozero__class_Ozero(X1) != X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2430]),
[final] ).
cnf(i_0_4019,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_2432]),
[final] ).
cnf(i_0_4020,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2441]),
[final] ).
cnf(i_0_4021,plain,
( c_Groups_Ouminus__class_Ouminus(X2,X1) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2439]),
[final] ).
cnf(i_0_4022,plain,
( X1 = c_Groups_Ouminus__class_Ouminus(X2,X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2440]),
[final] ).
cnf(i_0_4023,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_2442]),
[final] ).
cnf(i_0_4024,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_2443]),
[final] ).
cnf(i_0_4025,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2444]),
[final] ).
cnf(i_0_4026,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2445]),
[final] ).
cnf(i_0_4027,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2446]),
[final] ).
cnf(i_0_4028,plain,
( c_RealDef_Oreal(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2446]),
[final] ).
cnf(i_0_4029,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_2447]),
[final] ).
cnf(i_0_4030,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_2448]),
[final] ).
cnf(i_0_4031,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_2449]),
[final] ).
cnf(i_0_4032,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__1]),
[final] ).
cnf(i_0_4033,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__zero]),
[final] ).
cnf(i_0_4034,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_zminus__0]),
[final] ).
cnf(i_0_4035,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_2450]),
[final] ).
cnf(i_0_4036,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2451]),
[final] ).
cnf(i_0_4037,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2452]),
[final] ).
cnf(i_0_4038,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2453]),
[final] ).
cnf(i_0_4039,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2454]),
[final] ).
cnf(i_0_4040,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2455]),
[final] ).
cnf(i_0_4041,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2456]),
[final] ).
cnf(i_0_4042,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2457]),
[final] ).
cnf(i_0_4043,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2458]),
[final] ).
cnf(i_0_4044,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2459]),
[final] ).
cnf(i_0_4045,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2460]),
[final] ).
cnf(i_0_4046,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2461]),
[final] ).
cnf(i_0_4047,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2462]),
[final] ).
cnf(i_0_4048,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2463]),
[final] ).
cnf(i_0_4049,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2464]),
[final] ).
cnf(i_0_4050,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2465]),
[final] ).
cnf(i_0_4051,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2466]),
[final] ).
cnf(i_0_4052,plain,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2467]),
[final] ).
cnf(i_0_4053,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2468]),
[final] ).
cnf(i_0_4054,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2469]),
[final] ).
cnf(i_0_4055,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2470]),
[final] ).
cnf(i_0_4056,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2471]),
[final] ).
cnf(i_0_4057,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2472]),
[final] ).
cnf(i_0_4058,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2473]),
[final] ).
cnf(i_0_4059,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2474]),
[final] ).
cnf(i_0_4060,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2475]),
[final] ).
cnf(i_0_4061,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2476]),
[final] ).
cnf(i_0_4062,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2477]),
[final] ).
cnf(i_0_4063,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2478]),
[final] ).
cnf(i_0_4064,plain,
( class_Groups_Ouminus(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2479]),
[final] ).
cnf(i_0_4065,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2480]),
[final] ).
cnf(i_0_4066,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2481]),
[final] ).
cnf(i_0_4067,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2482]),
[final] ).
cnf(i_0_4068,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2483]),
[final] ).
cnf(i_0_4069,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2484]),
[final] ).
cnf(i_0_4070,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2485]),
[final] ).
cnf(i_0_4071,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2486]),
[final] ).
cnf(i_0_4072,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2487]),
[final] ).
cnf(i_0_4073,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2488]),
[final] ).
cnf(i_0_4074,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2489]),
[final] ).
cnf(i_0_4075,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2490]),
[final] ).
cnf(i_0_4076,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2491]),
[final] ).
cnf(i_0_4077,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2492]),
[final] ).
cnf(i_0_4078,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2493]),
[final] ).
cnf(i_0_4079,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_2494]),
[final] ).
cnf(i_0_4080,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2495]),
[final] ).
cnf(i_0_4081,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2496]),
[final] ).
cnf(i_0_4082,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2497]),
[final] ).
cnf(i_0_4083,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2498]),
[final] ).
cnf(i_0_4084,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_2499]),
[final] ).
cnf(i_0_4085,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2500]),
[final] ).
cnf(i_0_4086,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2501]),
[final] ).
cnf(i_0_4087,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2502]),
[final] ).
cnf(i_0_4088,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2503]),
[final] ).
cnf(i_0_4089,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2504]),
[final] ).
cnf(i_0_4090,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2505]),
[final] ).
cnf(i_0_4091,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2506]),
[final] ).
cnf(i_0_4092,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_4093,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_4094,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_4095,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_4096,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_4097,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_4098,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_4099,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_4100,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_4101,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_4102,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
[final] ).
cnf(i_0_4103,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]),
[final] ).
cnf(i_0_4104,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]),
[final] ).
cnf(i_0_4105,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4106,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4107,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4108,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4109,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
[final] ).
cnf(i_0_4110,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
[final] ).
cnf(i_0_4111,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]),
[final] ).
cnf(i_0_4112,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Power_Opower]),
[final] ).
cnf(i_0_4113,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_4114,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_4115,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_4116,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_4117,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_4118,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_4119,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_4120,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_4121,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_4122,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_4123,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_4124,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_4125,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_4126,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_4127,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_4128,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_4129,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_4130,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_4131,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_4132,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_4133,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_4134,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_4135,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_4136,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_4137,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_4138,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
[final] ).
cnf(i_0_4139,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]),
[final] ).
cnf(i_0_4140,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_4141,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_4142,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_4143,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_4144,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_4145,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_4146,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_4147,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]),
[final] ).
cnf(i_0_4148,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
[final] ).
cnf(i_0_4149,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
[final] ).
cnf(i_0_4150,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]),
[final] ).
cnf(i_0_4151,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]),
[final] ).
cnf(i_0_4152,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_4153,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_4154,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_4155,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_4156,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_4157,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_4158,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_4159,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
[final] ).
cnf(i_0_4160,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
[final] ).
cnf(i_0_4161,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]),
[final] ).
cnf(i_0_4162,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]),
[final] ).
cnf(i_0_4163,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4164,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4165,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4166,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4167,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_4168,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_4169,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_4170,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_4171,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4172,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4173,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4174,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4175,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_4176,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_4177,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_4178,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_4179,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_4180,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_4181,plain,
class_Rings_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
[final] ).
cnf(i_0_4182,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]),
[final] ).
cnf(i_0_4183,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]),
[final] ).
cnf(i_0_4184,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_4185,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_4186,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]),
[final] ).
cnf(i_0_4187,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]),
[final] ).
cnf(i_0_4188,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
[final] ).
cnf(i_0_4189,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
[final] ).
cnf(i_0_4190,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_4191,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_4192,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_4193,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_4194,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
[final] ).
cnf(i_0_4195,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
[final] ).
cnf(i_0_4196,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ouminus]),
[final] ).
cnf(i_0_4197,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ouminus]),
[final] ).
cnf(i_0_4198,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
[final] ).
cnf(i_0_4199,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
[final] ).
cnf(i_0_4200,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]),
[final] ).
cnf(i_0_4201,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]),
[final] ).
cnf(i_0_4202,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_4203,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_4204,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_4205,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_4206,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
[final] ).
cnf(i_0_4207,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_4208,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]),
[final] ).
cnf(i_0_4209,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
[final] ).
cnf(i_0_4210,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_4211,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]),
[final] ).
cnf(i_0_4212,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_4213,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
[final] ).
cnf(i_0_4214,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_4215,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]),
[final] ).
cnf(i_0_4216,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_4217,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_4218,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_4219,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_4220,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_4221,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_4222,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_4223,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_4224,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_4225,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_4226,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_4227,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_4228,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
[final] ).
cnf(i_0_4229,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_4230,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]),
[final] ).
cnf(i_0_4231,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_4232,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_4233,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_4234,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero]),
[final] ).
cnf(i_0_4235,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero]),
[final] ).
cnf(i_0_4236,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_4237,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_4238,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_4239,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_4240,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_4241,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_4242,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_4243,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_4244,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_4245,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_4246,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_4247,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_4248,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_4249,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_4250,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_4251,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_4252,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_4253,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_4254,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_4255,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_4256,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_4257,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4258,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4259,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4260,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4261,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
[final] ).
cnf(i_0_4262,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_4263,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]),
[final] ).
cnf(i_0_4264,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]),
[final] ).
cnf(i_0_4265,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_4266,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_4267,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_4268,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_4269,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_4270,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_4271,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_4272,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_4273,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_4274,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_4275,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_4276,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_4277,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_4278,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_4279,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
[final] ).
cnf(i_0_4280,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_4281,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]),
[final] ).
cnf(i_0_4282,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]),
[final] ).
cnf(i_0_4283,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]),
[final] ).
cnf(i_0_4284,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]),
[final] ).
cnf(i_0_4285,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_4286,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_4287,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_4288,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4289,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4290,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4291,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_4292,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_4293,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield__inverse__zero]),
[final] ).
cnf(i_0_4294,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield__inverse__zero]),
[final] ).
cnf(i_0_4295,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
[final] ).
cnf(i_0_4296,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]),
[final] ).
cnf(i_0_4297,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]),
[final] ).
cnf(i_0_4298,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]),
[final] ).
cnf(i_0_4299,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__field]),
[final] ).
cnf(i_0_4300,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__field]),
[final] ).
cnf(i_0_4301,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]),
[final] ).
cnf(i_0_4302,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_4303,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_4304,negated_conjecture,
~ v_thesis____,
inference(split_conjunct,[status(thm)],[i_0_2507]),
[final] ).
cnf(i_0_4305,axiom,
X1 = X1 ).
cnf(i_0_4306,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_4307,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_4308,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_4309,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_4310,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_4311,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_4312,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_4313,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_4314,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_4315,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_4316,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_4317,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_4318,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_4319,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_4320,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_4321,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).
cnf(i_0_4322,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).
cnf(i_0_4323,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X1,X3,X4) = c_Rings_Oinverse__class_Odivide(X2,X3,X4) ) ).
cnf(i_0_4324,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X3,X1,X4) = c_Rings_Oinverse__class_Odivide(X3,X2,X4) ) ).
cnf(i_0_4325,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X3,X4,X1) = c_Rings_Oinverse__class_Odivide(X3,X4,X2) ) ).
cnf(i_0_4326,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_4327,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_4328,axiom,
( X1 != X2
| c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).
cnf(i_0_4329,axiom,
( X1 != X2
| c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).
cnf(i_0_4330,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_4331,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_4332,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_4333,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_4334,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_4335,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_4336,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_4337,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_4338,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_4339,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_4340,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_4341,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_4342,axiom,
( X1 != X2
| c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).
cnf(i_0_4343,axiom,
( X1 != X2
| c_Complex_Orcis(X1,X3) = c_Complex_Orcis(X2,X3) ) ).
cnf(i_0_4344,axiom,
( X1 != X2
| c_Complex_Orcis(X3,X1) = c_Complex_Orcis(X3,X2) ) ).
cnf(i_0_4345,axiom,
( X1 != X2
| esk75_2(X1,X3) = esk75_2(X2,X3) ) ).
cnf(i_0_4346,axiom,
( X1 != X2
| esk75_2(X3,X1) = esk75_2(X3,X2) ) ).
cnf(i_0_4347,axiom,
( X1 != X2
| c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).
cnf(i_0_4348,axiom,
( X1 != X2
| c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).
cnf(i_0_4349,axiom,
( X1 != X2
| c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).
cnf(i_0_4350,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).
cnf(i_0_4351,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).
cnf(i_0_4352,axiom,
( X1 != X2
| c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).
cnf(i_0_4353,axiom,
( X1 != X2
| c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).
cnf(i_0_4354,axiom,
( X1 != X2
| ~ c_SEQ_OBseq(X1,X3)
| c_SEQ_OBseq(X2,X3) ) ).
cnf(i_0_4355,axiom,
( X1 != X2
| ~ c_SEQ_OBseq(X3,X1)
| c_SEQ_OBseq(X3,X2) ) ).
cnf(i_0_4356,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4357,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4358,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4359,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4360,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4361,axiom,
( X1 != X2
| ~ epred1_3(X1,X3,X4)
| epred1_3(X2,X3,X4) ) ).
cnf(i_0_4362,axiom,
( X1 != X2
| ~ epred1_3(X3,X1,X4)
| epred1_3(X3,X2,X4) ) ).
cnf(i_0_4363,axiom,
( X1 != X2
| ~ epred1_3(X3,X4,X1)
| epred1_3(X3,X4,X2) ) ).
cnf(i_0_4364,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4365,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4366,axiom,
( X1 != X2
| ~ epred2_3(X1,X3,X4)
| epred2_3(X2,X3,X4) ) ).
cnf(i_0_4367,axiom,
( X1 != X2
| ~ epred2_3(X3,X1,X4)
| epred2_3(X3,X2,X4) ) ).
cnf(i_0_4368,axiom,
( X1 != X2
| ~ epred2_3(X3,X4,X1)
| epred2_3(X3,X4,X2) ) ).
cnf(i_0_4369,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_4370,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4371,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4372,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4373,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4374,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4375,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4376,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4377,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4378,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_4379,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_4380,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_4381,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_4382,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4383,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4384,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4385,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4386,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4387,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4388,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4389,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_4390,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4391,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4392,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4393,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4394,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4395,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4396,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4397,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4398,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4399,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4400,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4401,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_4402,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4403,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4404,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4405,axiom,
( X1 != X2
| ~ c_SEQ_Oincseq(X1,X3)
| c_SEQ_Oincseq(X2,X3) ) ).
cnf(i_0_4406,axiom,
( X1 != X2
| ~ c_SEQ_Oincseq(X3,X1)
| c_SEQ_Oincseq(X3,X2) ) ).
cnf(i_0_4407,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4408,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4409,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X1,X3)
| c_SEQ_Odecseq(X2,X3) ) ).
cnf(i_0_4410,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X3,X1)
| c_SEQ_Odecseq(X3,X2) ) ).
cnf(i_0_4411,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4412,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4413,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4414,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4415,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4416,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4417,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4418,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4419,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_4420,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4421,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4422,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_4423,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4424,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4425,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4426,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4427,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4428,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_4429,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4430,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4431,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4432,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4433,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4434,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4435,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4436,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_4437,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4438,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4439,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_4440,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4441,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4442,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_4305_001,axiom,
X1 = X1 ).
cnf(i_0_4306_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_4307_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_4308_004,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_4309_005,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_4310_006,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_4311_007,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_4312_008,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_4313_009,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_4314_010,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_4315_011,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_4316_012,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_4317_013,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_4318_014,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_4319_015,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_4320_016,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_4321_017,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).
cnf(i_0_4322_018,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).
cnf(i_0_4323_019,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X1,X3,X4) = c_Rings_Oinverse__class_Odivide(X2,X3,X4) ) ).
cnf(i_0_4324_020,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X3,X1,X4) = c_Rings_Oinverse__class_Odivide(X3,X2,X4) ) ).
cnf(i_0_4325_021,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X3,X4,X1) = c_Rings_Oinverse__class_Odivide(X3,X4,X2) ) ).
cnf(i_0_4326_022,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_4327_023,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_4328_024,axiom,
( X1 != X2
| c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).
cnf(i_0_4329_025,axiom,
( X1 != X2
| c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).
cnf(i_0_4330_026,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_4331_027,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_4332_028,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_4333_029,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_4334_030,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_4335_031,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_4336_032,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_4337_033,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_4338_034,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_4339_035,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_4340_036,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_4341_037,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_4342_038,axiom,
( X1 != X2
| c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).
cnf(i_0_4343_039,axiom,
( X1 != X2
| c_Complex_Orcis(X1,X3) = c_Complex_Orcis(X2,X3) ) ).
cnf(i_0_4344_040,axiom,
( X1 != X2
| c_Complex_Orcis(X3,X1) = c_Complex_Orcis(X3,X2) ) ).
cnf(i_0_4345_041,axiom,
( X1 != X2
| esk75_2(X1,X3) = esk75_2(X2,X3) ) ).
cnf(i_0_4346_042,axiom,
( X1 != X2
| esk75_2(X3,X1) = esk75_2(X3,X2) ) ).
cnf(i_0_4347_043,axiom,
( X1 != X2
| c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).
cnf(i_0_4348_044,axiom,
( X1 != X2
| c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).
cnf(i_0_4349_045,axiom,
( X1 != X2
| c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).
cnf(i_0_4350_046,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).
cnf(i_0_4351_047,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).
cnf(i_0_4352_048,axiom,
( X1 != X2
| c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).
cnf(i_0_4353_049,axiom,
( X1 != X2
| c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).
cnf(i_0_4354_050,axiom,
( X1 != X2
| ~ c_SEQ_OBseq(X1,X3)
| c_SEQ_OBseq(X2,X3) ) ).
cnf(i_0_4355_051,axiom,
( X1 != X2
| ~ c_SEQ_OBseq(X3,X1)
| c_SEQ_OBseq(X3,X2) ) ).
cnf(i_0_4356_052,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4357_053,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4358_054,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4359_055,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4360_056,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4361_057,axiom,
( X1 != X2
| ~ epred1_3(X1,X3,X4)
| epred1_3(X2,X3,X4) ) ).
cnf(i_0_4362_058,axiom,
( X1 != X2
| ~ epred1_3(X3,X1,X4)
| epred1_3(X3,X2,X4) ) ).
cnf(i_0_4363_059,axiom,
( X1 != X2
| ~ epred1_3(X3,X4,X1)
| epred1_3(X3,X4,X2) ) ).
cnf(i_0_4364_060,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4365_061,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4366_062,axiom,
( X1 != X2
| ~ epred2_3(X1,X3,X4)
| epred2_3(X2,X3,X4) ) ).
cnf(i_0_4367_063,axiom,
( X1 != X2
| ~ epred2_3(X3,X1,X4)
| epred2_3(X3,X2,X4) ) ).
cnf(i_0_4368_064,axiom,
( X1 != X2
| ~ epred2_3(X3,X4,X1)
| epred2_3(X3,X4,X2) ) ).
cnf(i_0_4369_065,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_4370_066,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4371_067,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4372_068,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4373_069,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4374_070,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4375_071,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4376_072,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4377_073,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4378_074,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_4379_075,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_4380_076,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_4381_077,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_4382_078,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4383_079,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4384_080,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4385_081,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4386_082,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4387_083,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4388_084,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4389_085,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_4390_086,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4391_087,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4392_088,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4393_089,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4394_090,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4395_091,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4396_092,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4397_093,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4398_094,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4399_095,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4400_096,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4401_097,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_4402_098,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4403_099,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4404_100,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4405_101,axiom,
( X1 != X2
| ~ c_SEQ_Oincseq(X1,X3)
| c_SEQ_Oincseq(X2,X3) ) ).
cnf(i_0_4406_102,axiom,
( X1 != X2
| ~ c_SEQ_Oincseq(X3,X1)
| c_SEQ_Oincseq(X3,X2) ) ).
cnf(i_0_4407_103,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4408_104,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4409_105,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X1,X3)
| c_SEQ_Odecseq(X2,X3) ) ).
cnf(i_0_4410_106,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X3,X1)
| c_SEQ_Odecseq(X3,X2) ) ).
cnf(i_0_4411_107,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4412_108,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4413_109,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4414_110,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4415_111,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4416_112,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4417_113,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4418_114,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4419_115,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_4420_116,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4421_117,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4422_118,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_4423_119,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4424_120,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4425_121,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4426_122,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4427_123,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4428_124,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_4429_125,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4430_126,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4431_127,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4432_128,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4433_129,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4434_130,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4435_131,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4436_132,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_4437_133,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4438_134,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4439_135,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_4440_136,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4441_137,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4442_138,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_4443,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),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| hBOOL(hAPP(hAPP(X3,X4),X1))
| ~ hBOOL(hAPP(hAPP(X3,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),X4),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4),X1),X2))) ),
inference(equality_inference,[],[2522]) ).
cnf(i_0_4444,plain,
( ~ 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(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(X3,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),X4),X2),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X2),X1))) ),
inference(equality_inference,[],[2523]) ).
cnf(i_0_4445,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,[],[2533]) ).
cnf(i_0_4446,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,[],[2534]) ).
cnf(i_0_4447,plain,
( ~ class_Rings_Oidom(X1)
| X2 = X2
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(equality_inference,[],[2545]) ).
cnf(i_0_4448,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,[],[2549]) ).
cnf(i_0_4449,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,[],[2550]) ).
cnf(i_0_4450,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,[],[2563]) ).
cnf(i_0_4451,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,[],[2564]) ).
cnf(i_0_4452,plain,
X1 = X1,
inference(equality_inference,[],[2609]) ).
cnf(i_0_4453,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X3
| X4 = X4 ),
inference(equality_inference,[],[2613]) ).
cnf(i_0_4454,plain,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(equality_inference,[],[2614]) ).
cnf(i_0_4455,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(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,[],[2649]) ).
cnf(i_0_4456,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,[],[2650]) ).
cnf(i_0_4457,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,[],[2655]) ).
cnf(i_0_4458,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_Omod(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) = X2
| 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__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(equality_inference,[],[2708]) ).
cnf(i_0_4459,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,[],[2709]) ).
cnf(i_0_4460,plain,
( ~ epred2_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__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| hBOOL(hAPP(X1,X4)) ),
inference(equality_inference,[],[2721]) ).
cnf(i_0_4461,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,[],[2722]) ).
cnf(i_0_4462,plain,
( ~ epred2_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,X4)) ),
inference(equality_inference,[],[2723]) ).
cnf(i_0_4463,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,[],[2724]) ).
cnf(i_0_4464,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Divides_Odiv__class_Omod(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) = 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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(equality_inference,[],[2778]) ).
cnf(i_0_4465,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,[],[2779]) ).
cnf(i_0_4466,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,[],[2802]) ).
cnf(i_0_4467,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,[],[2824]) ).
cnf(i_0_4468,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Divides_Odiv__class_Omod(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) = X2
| 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,[],[2847]) ).
cnf(i_0_4469,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,[],[2848]) ).
cnf(i_0_4470,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,[],[2925]) ).
cnf(i_0_4471,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,[],[3013]) ).
cnf(i_0_4472,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(equality_inference,[],[3014]) ).
cnf(i_0_4473,plain,
( X1 = esk75_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,[],[3169]) ).
cnf(i_0_4474,plain,
( ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
inference(equality_inference,[],[3199]) ).
cnf(i_0_4475,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,[],[3215]) ).
cnf(i_0_4476,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,[],[3216]) ).
cnf(i_0_4477,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,[],[3272]) ).
cnf(i_0_4478,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,[],[3298]) ).
cnf(i_0_4479,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,[],[3303]) ).
cnf(i_0_4480,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,[],[3314]) ).
cnf(i_0_4481,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,[],[3315]) ).
cnf(i_0_4482,plain,
( ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) ),
inference(equality_inference,[],[3321]) ).
cnf(i_0_4483,plain,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(equality_inference,[],[3323]) ).
cnf(i_0_4484,plain,
( ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X3,X2) = c_Rings_Oinverse__class_Odivide(X1,X3,X2) ),
inference(equality_inference,[],[3324]) ).
cnf(i_0_4485,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,[],[3338]) ).
cnf(i_0_4486,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
inference(equality_inference,[],[3356]) ).
cnf(i_0_4487,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,[],[3418]) ).
cnf(i_0_4488,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,[],[3431]) ).
cnf(i_0_4489,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,[],[3432]) ).
cnf(i_0_4490,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,[],[3433]) ).
cnf(i_0_4491,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,[],[3434]) ).
cnf(i_0_4492,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,[],[3438]) ).
cnf(i_0_4493,plain,
( X1 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(equality_inference,[],[3439]) ).
cnf(i_0_4494,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,[],[3475]) ).
cnf(i_0_4495,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,[],[3476]) ).
cnf(i_0_4496,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,[],[3537]) ).
cnf(i_0_4497,plain,
( ~ class_Rings_Oidom(X1)
| X2 = X2
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(equality_inference,[],[3558]) ).
cnf(i_0_4498,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,[],[3565]) ).
cnf(i_0_4499,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,[],[3566]) ).
cnf(i_0_4500,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[3579]) ).
cnf(i_0_4501,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[3580]) ).
cnf(i_0_4502,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[3582]) ).
cnf(i_0_4503,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,[],[3618]) ).
cnf(i_0_4504,plain,
X1 = X1,
inference(equality_inference,[],[3619]) ).
cnf(i_0_4505,plain,
X1 = X1,
inference(equality_inference,[],[3620]) ).
cnf(i_0_4506,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,[],[3628]) ).
cnf(i_0_4507,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,[],[3629]) ).
cnf(i_0_4508,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Odivide(X1,X3,X2)),X2) = X3 ),
inference(equality_inference,[],[3655]) ).
cnf(i_0_4509,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Odivide(X1,X3,X2)),X2) = X3 ),
inference(equality_inference,[],[3656]) ).
cnf(i_0_4510,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Odivide(X1,X3,X2)),X2) ),
inference(equality_inference,[],[3657]) ).
cnf(i_0_4511,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Odivide(X1,X3,X2)),X2) ),
inference(equality_inference,[],[3658]) ).
cnf(i_0_4512,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,[],[3660]) ).
cnf(i_0_4513,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2) = X3 ),
inference(equality_inference,[],[3661]) ).
cnf(i_0_4514,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2) = X3 ),
inference(equality_inference,[],[3663]) ).
cnf(i_0_4515,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Rings_Oinverse__class_Odivide(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2) ),
inference(equality_inference,[],[3664]) ).
cnf(i_0_4516,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Rings_Oinverse__class_Odivide(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2) ),
inference(equality_inference,[],[3666]) ).
cnf(i_0_4517,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3672]) ).
cnf(i_0_4518,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3673]) ).
cnf(i_0_4519,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3675]) ).
cnf(i_0_4520,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3676]) ).
cnf(i_0_4521,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,[],[3696]) ).
cnf(i_0_4522,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,[],[3699]) ).
cnf(i_0_4523,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(equality_inference,[],[3718]) ).
cnf(i_0_4524,plain,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) ),
inference(equality_inference,[],[3730]) ).
cnf(i_0_4525,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(equality_inference,[],[3733]) ).
cnf(i_0_4526,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[3734]) ).
cnf(i_0_4527,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,[],[3735]) ).
cnf(i_0_4528,plain,
X1 = X1,
inference(equality_inference,[],[3737]) ).
cnf(i_0_4529,plain,
( ~ epred2_3(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| hBOOL(hAPP(X1,X2)) ),
inference(equality_inference,[],[3744]) ).
cnf(i_0_4530,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,[],[3746]) ).
cnf(i_0_4531,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,[],[3775]) ).
cnf(i_0_4532,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,[],[3800]) ).
cnf(i_0_4533,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,[],[3801]) ).
cnf(i_0_4534,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,[],[3802]) ).
cnf(i_0_4535,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,[],[3803]) ).
cnf(i_0_4536,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3804]) ).
cnf(i_0_4537,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3807]) ).
cnf(i_0_4538,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3809]) ).
cnf(i_0_4539,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3810]) ).
cnf(i_0_4540,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3811]) ).
cnf(i_0_4541,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[3832]) ).
cnf(i_0_4542,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3835]) ).
cnf(i_0_4543,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3836]) ).
cnf(i_0_4544,plain,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3844]) ).
cnf(i_0_4545,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(equality_inference,[],[3852]) ).
cnf(i_0_4546,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3856]) ).
cnf(i_0_4547,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3857]) ).
cnf(i_0_4548,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3858]) ).
cnf(i_0_4549,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(equality_inference,[],[3865]) ).
cnf(i_0_4550,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(equality_inference,[],[3870]) ).
cnf(i_0_4551,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(equality_inference,[],[3882]) ).
cnf(i_0_4552,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X2) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3888]) ).
cnf(i_0_4553,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,[],[3889]) ).
cnf(i_0_4554,plain,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3890]) ).
cnf(i_0_4555,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,[],[3891]) ).
cnf(i_0_4556,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3897]) ).
cnf(i_0_4557,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,[],[3898]) ).
cnf(i_0_4558,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,[],[3899]) ).
cnf(i_0_4559,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,[],[3908]) ).
cnf(i_0_4560,plain,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3918]) ).
cnf(i_0_4561,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3919]) ).
cnf(i_0_4562,plain,
( ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3920]) ).
cnf(i_0_4563,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3940]) ).
cnf(i_0_4564,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3941]) ).
cnf(i_0_4565,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3942]) ).
cnf(i_0_4566,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,[],[3950]) ).
cnf(i_0_4567,plain,
( ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1)
| X2 = X2 ),
inference(equality_inference,[],[3952]) ).
cnf(i_0_4568,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3975]) ).
cnf(i_0_4569,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3976]) ).
cnf(i_0_4570,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,[],[3984]) ).
cnf(i_0_4571,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,[],[3985]) ).
cnf(i_0_4572,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| X2 = X2 ),
inference(equality_inference,[],[3986]) ).
cnf(i_0_4573,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[3987]) ).
cnf(i_0_4574,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2 ),
inference(equality_inference,[],[4000]) ).
cnf(i_0_4575,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(equality_inference,[],[4002]) ).
cnf(i_0_4576,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,[],[4004]) ).
cnf(i_0_4577,plain,
X1 = X1,
inference(equality_inference,[],[4005]) ).
cnf(i_0_4578,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[4017]) ).
cnf(i_0_4579,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[4018]) ).
cnf(i_0_4580,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,[],[4019]) ).
cnf(i_0_4581,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[4021]) ).
cnf(i_0_4582,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[4022]) ).
cnf(i_0_4583,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(equality_inference,[],[4028]) ).
cnf(i_0_4584,plain,
$false,
inference(scs_inference,[],[i_0_4304,i_0_3747,i_0_2524,i_0_2514]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW219+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 06:26:44 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 6.18/5.86 % Version : CSE_E---1.7
% 6.18/5.86 % Problem : theBenchmark.p
% 6.18/5.86 % SZS status Theorem for theBenchmark.p
% 6.18/5.86 % SZS output start CNFRefutation
% See solution above
% 6.35/6.01 % Total time : 5.504s
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