%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW287+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:29:23 PM UTC 2026
% Result : Theorem 53.21s 11.68s
% Output : CNFRefutation 80.26s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f4724ERROR: Could not build tree for root c_109647ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ! [X2] : hAPP(X1,X2) = hAPP(X0,X2)
=> X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(f2,axiom,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pe) ).
fof(f3,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dp) ).
fof(f4,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(v_n____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n) ).
fof(f6,axiom,
! [X0] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
=> ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bx_O_A_091_124_Ap_Advd_Aq_A_094_ASuc_An_059_Apoly_Ap_Ax_A_061_A0_059_Apoly_Aq_Ax_A_126_061_A0_A_124_093_A_061_061_062_AFalse_096) ).
fof(f7,axiom,
( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_091_124_AALL_Ax_O_Apoly_Ap_Ax_A_061_A0_A_N_N_062_Apoly_Aq_Ax_A_061_A0_059_Adegree_Ap_A_061_Adegree_Ap_059_Adegree_Ap_A_126_061_A0_A_124_093_061_061_062_Ap_Advd_Aq_A_094_Adegree_Ap_096) ).
fof(f9,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__power) ).
fof(f11,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
fof(f13,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__same) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( class_Rings_Ozero__neq__one(X2)
& class_Rings_Ono__zero__divisors(X2)
& class_Rings_Omult__zero(X2)
& class_Power_Opower(X2) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
fof(f15,axiom,
! [X0,X1,X2] :
( class_Rings_Oring__1__no__zero__divisors(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(X2)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(f16,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
=> X0 = c_Groups_Ozero__class_Ozero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).
fof(f17,axiom,
! [X0,X1,X2] :
( ! [X3] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) = X0
=> ( X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nullstellensatz__lemma) ).
fof(f18,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( hAPP(c_Polynomial_Opoly(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( c_Polynomial_Oorder(X2,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).
fof(f19,axiom,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).
fof(f20,axiom,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(f21,axiom,
! [X0,X1] :
( ( class_Rings_Osemiring__0(X1)
& class_Power_Opower(X1) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0)) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).
fof(f22,axiom,
! [X0] :
( class_Groups_Ozero(X0)
=> c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__0) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).
fof(f24,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( class_Rings_Oidom(X2)
& class_Int_Oring__char__0(X2) )
=> ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
<=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(f26,axiom,
~ ! [X0] : c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Nat_OSuc(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bn_O_Adegree_Ap_A_061_ASuc_An_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(f28,axiom,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> ( ( X0 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Nat_OSuc(c_Polynomial_Odegree(X1,X0)) )
& ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__def) ).
fof(f35,axiom,
! [X0] : c_Nat_OSuc(X0) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(f36,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> ( c_Polynomial_Osynthetic__div(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> c_Polynomial_Odegree(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__eq__0__iff) ).
fof(f42,axiom,
! [X0,X1] :
( X1 = X0
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
fof(f49,axiom,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
fof(f50,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
fof(f64,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
fof(f68,axiom,
! [X0] : X0 != c_Nat_OSuc(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(f69,axiom,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
fof(f71,axiom,
! [X0,X1,X2] :
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).
fof(f72,axiom,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
fof(f73,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ozero(X3)
=> ( hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) = X1
=> c_Polynomial_Opoly__rec(X0,X3,X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__0) ).
fof(f75,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(X2,X0,X1),c_Polynomial_Odegree(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__degree) ).
fof(f76,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
=> ( X0 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__degree__le) ).
fof(f77,axiom,
! [X0,X1] :
( 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_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
fof(f79,axiom,
! [X0,X1,X2] :
( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).
fof(f80,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
<=> ( ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) )
& ( X2 = c_Groups_Ozero__class_Ozero(X3)
=> X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).
fof(f83,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
fof(f87,axiom,
! [X0,X1,X2,X3,X4] :
( class_Groups_Ozero(X4)
=> ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
<=> ( X2 = X0
& X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
fof(f88,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> ( c_Polynomial_Osmult(X3,X2,X1) = c_Polynomial_OpCons(X3,X0,X1)
=> X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
fof(f89,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__smult__le) ).
fof(f90,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_Groups_Ozero(X5)
=> c_Polynomial_Opoly__rec(X4,X5,X3,X2,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X2,X1),X0),c_If(X4,c_fequal(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3,c_Polynomial_Opoly__rec(X4,X5,X3,X2,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec_Osimps) ).
fof(f91,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Nat_OSuc(c_Polynomial_Odegree(X2,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__le) ).
fof(f92,axiom,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(f93,axiom,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(f94,axiom,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(f95,axiom,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(f96,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> ( X1 = c_Nat_OSuc(X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(f97,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(f101,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(f102,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_Groups_Ozero(X5)
=> ( hAPP(hAPP(hAPP(X4,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3) = X3
=> c_Polynomial_Opoly__rec(X2,X5,X3,X4,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X4,X1),X0),c_Polynomial_Opoly__rec(X2,X5,X3,X4,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__pCons) ).
fof(f103,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).
fof(f104,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X0,X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult) ).
fof(f105,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(f106,axiom,
! [X0] :
( class_Groups_Ozero(X0)
=> c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).
fof(f107,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
fof(f108,axiom,
! [X0,X1,X2] :
( 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),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
fof(f109,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( c_Polynomial_Osmult(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).
fof(f110,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(f111,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X2)),X1))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X0)),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__dvd) ).
fof(f112,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__le) ).
fof(f113,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).
fof(f114,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X1,X0)))
=> ( X1 != c_Groups_Ozero__class_Ozero(X3)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__cancel) ).
fof(f116,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__iff) ).
fof(f117,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osynthetic__div(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Polynomial_OpCons(X3,hAPP(c_Polynomial_Opoly(X3,X1),X0),c_Polynomial_Osynthetic__div(X3,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).
fof(f118,axiom,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__0) ).
fof(f119,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
=> c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Nat_OSuc(c_Polynomial_Odegree(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__eq) ).
fof(f120,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> X2 = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).
fof(f121,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1)))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
fof(f122,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( ( X1 != c_Groups_Ozero__class_Ozero(X2)
=> c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Odegree(X2,X0) )
& ( X1 = c_Groups_Ozero__class_Ozero(X2)
=> c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__smult__eq) ).
fof(f125,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__0(X4)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X3,c_Polynomial_Osmult(X4,X2,X1)) = c_Polynomial_OpCons(X4,X0,X1)
=> ( X1 = c_Polynomial_Osynthetic__div(X4,X3,X2)
& X0 = hAPP(c_Polynomial_Opoly(X4,X3),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
fof(f126,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,c_Polynomial_Osmult(X2,X0,c_Polynomial_Osynthetic__div(X2,X1,X0))) = c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0),c_Polynomial_Osynthetic__div(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct) ).
fof(f127,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__linear__power) ).
fof(f128,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) = c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__single) ).
fof(f129,axiom,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__0) ).
fof(f130,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> X2 = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(f131,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
fof(f132,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> c_Polynomial_Omonom(X2,X1,c_Nat_OSuc(X0)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__Suc) ).
fof(f138,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(f139,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X0)
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(f140,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(f141,axiom,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(f142,axiom,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(f143,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)
<=> X1 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(f144,axiom,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(f145,axiom,
! [X0,X1] :
( class_Rings_Olinordered__semidom(X1)
=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(f146,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ozero(X3)
=> ( c_Polynomial_Omonom(X3,X2,X1) = c_Polynomial_Omonom(X3,X0,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__iff) ).
fof(f147,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__monom) ).
fof(f148,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( X1 != X0
=> ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
=> c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(f151,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(f152,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(f157,axiom,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(f162,axiom,
! [X0,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(f167,axiom,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( X1 = X0
| c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(f168,axiom,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( X1 != X0
<=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(f169,axiom,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> ~ c_Orderings_Oord__class_Oless(X1,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(f172,axiom,
! [X0,X1] :
( X1 != X0
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(f177,axiom,
! [X0,X1,X2,X3,X4] :
( class_Groups_Ocomm__monoid__add(X4)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pCons) ).
fof(f178,axiom,
! [X0,X1,X2] :
( class_Groups_Ocomm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
=> c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X0,X1)) = c_Polynomial_Odegree(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__eq__left) ).
fof(f179,axiom,
! [X0,X1,X2] :
( class_Groups_Ocomm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
=> c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) = c_Polynomial_Odegree(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__eq__right) ).
fof(f180,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__less) ).
fof(f181,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).
fof(f182,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__left) ).
fof(f183,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(f184,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(f185,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(f186,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(f195,axiom,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> X1 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(f199,axiom,
! [X0,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(f200,axiom,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(f203,axiom,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(f204,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).
fof(f205,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> ( c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Oone__class_Oone(X3))
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(f206,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(f207,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__offset__poly) ).
fof(f208,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).
fof(f209,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).
fof(f211,axiom,
! [X0] :
( class_Rings_Ozero__neq__one(X0)
=> c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(f212,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).
fof(f213,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(f214,axiom,
! [X0,X1] :
( class_Groups_Omonoid__mult(X1)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0) = c_Groups_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
fof(f218,axiom,
! [X0] :
( X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(f219,axiom,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
fof(f221,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(f223,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(f224,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> ( c_Nat_OSuc(X1) != X0
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(f229,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> ( X1 = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(f230,axiom,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(f231,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(f235,axiom,
! [X0,X1] :
( ( X1 = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(f236,axiom,
! [X0,X1] :
( class_Groups_Omonoid__mult(X1)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(f237,axiom,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(f238,axiom,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(f239,axiom,
! [X0] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
fof(f240,axiom,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).
fof(f241,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__right) ).
fof(f242,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__1__left) ).
fof(f243,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
fof(f244,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),c_Groups_Oone__class_Oone(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
fof(f246,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
fof(f247,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> ( ( X0 = c_Groups_Oone__class_Oone(X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power) ).
fof(f248,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0)))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).
fof(f249,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
fof(f250,axiom,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(f251,axiom,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(f252,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(f253,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
fof(f255,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> ( ? [X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& X1 = c_Nat_OSuc(X2) )
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(f256,axiom,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(f257,axiom,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
<=> ? [X1] : X0 = c_Nat_OSuc(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(f258,axiom,
! [X0,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,X1,X0)
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
fof(f259,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__pos__nat) ).
fof(f261,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(f263,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(f264,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(f266,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(f267,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__le) ).
fof(f269,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__1) ).
fof(f270,axiom,
! [X0,X1,X2] :
( 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(f271,axiom,
! [X0,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),X0))
<=> ( X0 = 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) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(f273,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
fof(f274,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)) = c_Polynomial_Odegree(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__offset__poly) ).
fof(f276,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Polynomial_Omonom(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> X1 = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).
fof(f277,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(X2)
=> c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__monom__eq) ).
fof(f278,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__monom__le) ).
fof(f279,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
fof(f280,axiom,
! [X0,X1] :
( ( class_Rings_Osemiring__0(X1)
& class_Power_Opower(X1) )
=> ( ( X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = c_Groups_Ozero__class_Ozero(X1) )
& ( X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = c_Groups_Oone__class_Oone(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
fof(f281,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X0)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
fof(f285,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(f287,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(f295,axiom,
! [X0,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( X1 = X0
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(f296,axiom,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( X1 = X0
<=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(f297,axiom,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(f298,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Oord(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
<=> ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(f299,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
=> X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
fof(f300,axiom,
! [X0,X1,X2] :
( 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,X1,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
fof(f303,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(f304,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(f305,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(f306,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(f307,axiom,
! [X0,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),X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(f308,axiom,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( X0 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
fof(f309,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Oord(X3)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(f311,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(f312,axiom,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(f313,axiom,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X1
=> X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(f317,axiom,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f319,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(f320,axiom,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(f321,axiom,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> 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,X2,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(f322,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(f325,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(f326,axiom,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(f327,axiom,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(f328,axiom,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__reduce) ).
fof(f330,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(f331,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(f332,axiom,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> 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,X2,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(f333,axiom,
! [X0,X1,X2] :
( 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,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(f336,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(f337,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
<=> ? [X2] : X0 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(f339,axiom,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
fof(f340,axiom,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
<=> ( ( X0 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(f342,axiom,
! [X0,X1] :
( 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,X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(f344,axiom,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(f345,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> ? [X2] : X0 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(f347,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oab__semigroup__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(f350,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ocancel__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X2,X0)
=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(f351,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ocancel__ab__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X2,X0)
=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(f352,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ocancel__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X0,X1)
=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(f354,axiom,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(f355,axiom,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(f357,axiom,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
fof(f358,axiom,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(f359,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
<=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(f360,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(f361,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(f362,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(f363,axiom,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oordered__ab__semigroup__add(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
fof(f364,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(f365,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(f366,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
<=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(f367,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
<=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(f368,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(f369,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(f370,axiom,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless(X4,X1,X0)
=> c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(f371,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(f372,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(f373,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(f374,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(f375,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(f376,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(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),X0)
=> ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(f378,axiom,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(f379,axiom,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(f380,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(f381,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(f382,axiom,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(f383,axiom,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(f384,axiom,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless(X4,X1,X0)
=> c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(f385,axiom,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
=> c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(f386,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(f387,axiom,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(f389,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Nat_OSuc(c_Polynomial_Oorder(X2,X0,X1)))),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__2) ).
fof(f390,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(f392,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(f393,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(f394,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(f395,axiom,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)
<=> X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(f396,axiom,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
<=> X2 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(f399,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
<=> c_Groups_Ouminus__class_Ouminus(X2,X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
fof(f400,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0)
<=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(f401,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring(X2)
=> c_Polynomial_Osmult(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__left) ).
fof(f402,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring(X2)
=> hAPP(c_Polynomial_Opoly(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).
fof(f404,axiom,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_OpCons(X2,X1,X0)) = c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__pCons) ).
fof(f405,axiom,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__monom) ).
fof(f408,axiom,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( X0 = c_Groups_Ouminus__class_Ouminus(X1,X0)
<=> X0 = c_Groups_Ozero__class_Ozero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
fof(f409,axiom,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(f410,axiom,
! [X0] :
( class_Groups_Ogroup__add(X0)
=> c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(f411,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).
fof(f412,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).
fof(f413,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
fof(f414,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
fof(f415,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).
fof(f416,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).
fof(f417,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
fof(f418,axiom,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
fof(f419,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).
fof(f420,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(f421,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(f422,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
fof(f423,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
fof(f424,axiom,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(f425,axiom,
! [X0,X1] :
( class_Groups_Oab__group__add(X1)
=> c_Polynomial_Odegree(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0)) = c_Polynomial_Odegree(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__minus) ).
fof(f426,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring(X2)
=> c_Polynomial_Osmult(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__right) ).
fof(f427,axiom,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(f428,axiom,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
fof(f429,axiom,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(f430,axiom,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(f431,axiom,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
fof(f432,axiom,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(f433,axiom,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(f434,axiom,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
fof(f436,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( X1 = c_Groups_Ouminus__class_Ouminus(X2,X0)
<=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(f437,axiom,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).
fof(f438,axiom,
! [X0,X1] :
( class_Groups_Oab__group__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).
fof(f439,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
<=> X0 = c_Groups_Ouminus__class_Ouminus(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
fof(f440,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).
fof(f441,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( 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),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( X1 = c_Groups_Ouminus__class_Ouminus(X2,X0)
| X1 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
fof(f442,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X2),c_Groups_Oplus__class_Oplus(X4,X1,X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(f443,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(f445,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(f446,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(f447,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f448,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(f449,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(f450,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(f451,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(f452,axiom,
! [X0,X1] :
( 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),X0)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
=> X1 = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).
fof(f453,axiom,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).
fof(f454,axiom,
! [X0,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,X1,X0)
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
fof(f455,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( hAPP(c_Polynomial_Opoly(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__0__iff__dvd) ).
fof(f456,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0))
<=> hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__iff__poly__eq__0) ).
fof(f457,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(f458,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(f459,axiom,
! [X0,X1,X2] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
=> ( X1 = c_Groups_Oplus__class_Oplus(X2,X1,X0)
<=> X0 = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(f460,axiom,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Ozero__class_Ozero(X1)
<=> X0 = c_Groups_Ozero__class_Ozero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(f461,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Oorder(X2,X1,X0))),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__1) ).
fof(f462,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Osynthetic__div(X2,X0,X1)),c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X0),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).
fof(f463,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
<=> ? [X2] : X0 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(f464,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
& X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) )
| c_Polynomial_Opos__poly(X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).
fof(f466,axiom,
! [X0,X1,X2] :
( class_Lattices_Oboolean__algebra(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
fof(f467,axiom,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(f468,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(f469,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
<=> ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
fof(f470,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(f471,axiom,
! [X0,X1] :
( 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)),X0)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(f472,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
=> 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)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(f473,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(f474,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(f475,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(f476,axiom,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
fof(f477,axiom,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> 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),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
fof(f478,axiom,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(f479,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(f480,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(f481,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(f482,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(f483,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(f484,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(f485,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__0(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Polynomial_Omonom(X4,X3,X2)),c_Polynomial_Omonom(X4,X1,X0)) = c_Polynomial_Omonom(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__monom) ).
fof(f486,axiom,
! [X0] :
( 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),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
fof(f487,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(f490,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(f491,axiom,
! [X0,X1,X2,X3,X4] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
=> ( ( X1 != X0
& X3 != X2 )
<=> c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) != c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
fof(f492,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(f493,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( X1 = X0
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(f494,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| X1 = X0
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(f495,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(f496,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(f497,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).
fof(f498,axiom,
! [X0,X1,X2] :
( class_Rings_Oring(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
fof(f499,axiom,
! [X0,X1,X2] :
( class_Rings_Oring(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
fof(f500,axiom,
! [X0,X1,X2] :
( class_Rings_Oring(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
fof(f501,axiom,
! [X0,X1,X2] :
( class_Rings_Oring(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),c_Groups_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
fof(f502,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
<=> ( X1 = c_Groups_Ouminus__class_Ouminus(X2,X0)
| X1 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
fof(f503,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(f506,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(f508,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(f509,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(f510,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f511,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(f512,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f513,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(f514,axiom,
! [X0,X1] :
( class_Rings_Omult__zero(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(f515,axiom,
! [X0,X1] :
( class_Rings_Omult__zero(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(f516,axiom,
! [X0,X1,X2] :
( class_Rings_Oring__no__zero__divisors(X2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X0 = c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(f518,axiom,
! [X0,X1,X2] :
( class_Rings_Ono__zero__divisors(X2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
=> ( X0 = c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
fof(f519,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(f520,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Osemiring(X4)
=> c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oplus__class_Oplus(X4,X3,X1)),X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(f521,axiom,
! [X0,X1] :
( class_Groups_Omonoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(f522,axiom,
! [X0,X1] :
( class_Groups_Ocomm__monoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
fof(f523,axiom,
! [X0,X1] :
( class_Groups_Omonoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(f524,axiom,
! [X0,X1] :
( class_Groups_Ocomm__monoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(f525,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
fof(f526,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
fof(f527,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).
fof(f528,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).
fof(f529,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X1),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
fof(f530,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Odvd(X3)
=> ( X2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).
fof(f531,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
fof(f532,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
fof(f533,axiom,
! [X0,X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(f534,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ocomm__monoid__mult(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(f535,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).
fof(f539,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Polynomial_Opos__poly(X2,X1)
=> ( c_Polynomial_Opos__poly(X2,X0)
=> c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__mult) ).
fof(f540,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oab__semigroup__mult(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(f541,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
fof(f542,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
fof(f543,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__smult) ).
fof(f544,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0) = c_Polynomial_Osmult(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__left) ).
fof(f545,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__right) ).
fof(f546,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
fof(f547,axiom,
! [X0,X1] :
( class_Rings_Olinordered__ring(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(f548,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(f549,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(f550,axiom,
! [X0,X1,X2] :
( class_Rings_Oordered__cancel__semiring(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),X0)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(f555,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Oordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
fof(f556,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Oordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
fof(f557,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Oordered__comm__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
fof(f558,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Oordered__ring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
fof(f559,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Oordered__ring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
fof(f560,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Oordered__semiring(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
=> c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
fof(f561,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Oordered__semiring(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
=> c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
fof(f562,axiom,
! [X0,X1,X2] :
( class_Rings_Oordered__ring(X2)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
fof(f563,axiom,
! [X0,X1,X2] :
( class_Rings_Oordered__cancel__semiring(X2)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
fof(f566,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__comm__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(f567,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(f568,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(f569,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(f571,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(f572,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(f573,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(f574,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
fof(f575,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(f576,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(f577,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(f578,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X1,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(f579,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
<=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X2,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(f580,axiom,
! [X0,X1] :
( class_Rings_Olinordered__ring(X1)
=> ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Ozero__class_Ozero(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(f581,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(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),X0),X0)) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(f582,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> ( ( X1 != X0
& X3 = X2 )
=> c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X1)) != c_Groups_Oplus__class_Oplus(X5,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(f583,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(f584,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Oidom(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| X2 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(f585,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Oidom(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| X1 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(f586,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,X0) = 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))),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(f587,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X0,c_Groups_Oone__class_Oone(X2))),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(f588,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2))),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(f589,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).
fof(f590,axiom,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> ( c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
| c_Polynomial_Opos__poly(X1,X0)
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__total) ).
fof(f591,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__ring__1(X3)
=> hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Omonom(X3,c_Groups_Oone__class_Oone(X3),X2)),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__replicate__append) ).
fof(f592,axiom,
! [X0,X1] :
( class_Rings_Ocomm__ring__1(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(f593,axiom,
! [X0,X1] :
( class_Rings_Oring__1__no__zero__divisors(X1)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
<=> ( X0 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| X0 = c_Groups_Oone__class_Oone(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
fof(f594,axiom,
! [X0,X1,X2] :
( class_Power_Opower(X2)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).
fof(f595,axiom,
! [X0,X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).
fof(f597,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(f598,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(f599,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
fof(f600,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(f601,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Polynomial_Opos__poly(X2,X1)
=> ( c_Polynomial_Opos__poly(X2,X0)
=> c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__add) ).
fof(f602,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,X2,c_Polynomial_OpCons(X3,X1,X0)) = c_Polynomial_OpCons(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),c_Polynomial_Osmult(X3,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__pCons) ).
fof(f603,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(f604,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__monom) ).
fof(f605,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(f606,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(f607,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(f608,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(f609,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(f610,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(f611,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Olinordered__semiring__strict(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X3)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
=> c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(f612,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Olinordered__semiring__strict(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
=> ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X1)
=> c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(f613,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Olinordered__semiring__strict(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
=> c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
fof(f614,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Olinordered__semiring__strict(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
=> c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
fof(f615,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(f616,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(f617,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring(X2)
=> c_Orderings_Oord__class_Oless__eq(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),X0),X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(f618,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(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),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
<=> ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(f619,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring(X2)
=> ~ c_Orderings_Oord__class_Oless(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),X0),X0)),c_Groups_Ozero__class_Ozero(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(f620,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(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),X0),X0)))
<=> ( X0 != c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(f621,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(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),X0)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
fof(f622,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(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),X0)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(f623,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(f624,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
fof(f625,axiom,
! [X0,X1,X2] :
( class_Rings_Oring__1(X2)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).
fof(f626,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__mult__le) ).
fof(f627,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
=> ( X0 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
=> c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__mult__eq) ).
fof(f628,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(f629,axiom,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).
fof(f630,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ouminus(X3)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).
fof(f631,axiom,
! [X0,X1,X2] :
( class_Lattices_Oboolean__algebra(X2)
=> ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0)
<=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(f632,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).
fof(f633,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Olinordered__semiring__1(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X3)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X2,X3)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
=> ( c_Groups_Oplus__class_Oplus(X5,X1,X0) = c_Groups_Oone__class_Oone(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
fof(f634,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(f635,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__left) ).
fof(f636,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
fof(f637,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Olinordered__semiring__1__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X3)
=> ( c_Orderings_Oord__class_Oless(X5,X2,X3)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
=> ( c_Groups_Oplus__class_Oplus(X5,X1,X0) = c_Groups_Oone__class_Oone(X5)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
fof(f638,axiom,
! [X0,X1,X2] :
( ( class_Rings_Osemiring__0(X2)
& class_Rings_Odvd(X2) )
=> ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
<=> ? [X3] :
( hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X3,c_Groups_Ozero__class_Ozero(X2)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
fof(f639,axiom,
! [X0,X1] :
( 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(f640,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Opcompose(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X0),c_Polynomial_Opcompose(X3,X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__pCons) ).
fof(f641,axiom,
! [X0] :
( class_Power_Opower(X0)
=> c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(f642,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(f643,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(f644,axiom,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(f645,axiom,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(f646,axiom,
! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = 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,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(f647,axiom,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
fof(f648,axiom,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(f649,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(f650,axiom,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
<=> ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
fof(f652,axiom,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
fof(f653,axiom,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(f655,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
fof(f656,axiom,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0)
<=> X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(f657,axiom,
! [X0,X1] :
( 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),X0)
=> 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),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(f658,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(f659,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(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),X2),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
fof(f660,axiom,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> 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),X2),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
fof(f663,axiom,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
fof(f664,axiom,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
fof(f665,axiom,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(f667,axiom,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(f668,axiom,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(f669,axiom,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__period) ).
fof(f670,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
fof(f671,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(f672,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(f673,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(f674,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f675,axiom,
! [X0,X1,X2] :
( X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mono) ).
fof(f676,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Opcompose(X2,X1,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),c_Polynomial_Odegree(X2,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pcompose__le) ).
fof(f680,axiom,
! [X0,X1,X2] :
( 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),X0),X1))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(f681,axiom,
! [X0,X1,X2] :
( 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),X2),X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(f682,axiom,
! [X0,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),X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(f683,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(f684,axiom,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
fof(f685,axiom,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
fof(f686,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(f687,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X0 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X1 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(f688,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(f689,axiom,
! [X0,X1] :
( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
=> ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(f690,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
=> ( X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
fof(f691,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(f692,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__0) ).
fof(f693,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Opcompose(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pcompose) ).
fof(f694,axiom,
! [X0,X1,X2,X3] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(f695,axiom,
! [X0,X1,X2,X3,X4] : hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(X2,X1),hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
fof(f696,axiom,
! [X0,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)),X0)
=> 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),X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).
fof(f697,axiom,
! [X0,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)),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
fof(f698,axiom,
! [X0,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)),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
fof(f699,axiom,
! [X0,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),X0))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
fof(f701,axiom,
! [X0,X1,X2] :
( 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),X0),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,X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
fof(f702,axiom,
! [X0,X1,X2] :
( 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),X2),X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
fof(f703,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__power__le) ).
fof(f704,axiom,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
fof(f705,axiom,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
fof(f706,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),X1))
<=> X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
fof(f707,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X1))
<=> X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
fof(f709,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(f711,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))
=> ( 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,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
fof(f712,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
fof(f713,axiom,
! [X0,X1,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),X1),X0))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,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),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
fof(f714,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(f715,axiom,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(f716,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(f717,axiom,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(f718,axiom,
! [X0,X1,X2,X3,X4,X5] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0)
=> ( 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),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> ( 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,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(f719,axiom,
! [X0,X1,X2,X3,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),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X0)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(f720,axiom,
! [X0,X1,X2,X3,X4,X5] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0)
=> ( 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),X1),X0))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
=> ( 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),X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(f721,axiom,
! [X0,X1,X2,X3,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),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0))
=> ( 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,X4)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
fof(f722,axiom,
! [X0,X1,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),X1),X0),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),X0)
=> ( 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,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
fof(f723,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
=> ( 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),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(f724,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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),X2),X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
fof(f725,axiom,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
<=> ( X1 = X0
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(f726,axiom,
! [X0,X1,X2,X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X0)) = 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,X3,X1)),X2),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(f727,axiom,
! [X0,X1,X2] :
( 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(f728,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
<=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(f729,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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),X2),X0)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(f730,axiom,
! [X0,X1,X2,X3,X4] :
( class_Fields_Ofield(X4)
=> ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
<=> ( ( X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ) )
& ( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
=> X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) )
& X3 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__def) ).
fof(f732,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
<=> ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
& X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__0__iff) ).
fof(f733,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
<=> ( X0 = X2
& X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0__iff) ).
fof(f734,axiom,
! [X0,X1] :
( class_Fields_Ofield(X1)
=> c_Polynomial_Opdivmod__rel(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__0) ).
fof(f735,axiom,
! [X0,X1] :
( class_Fields_Ofield(X1)
=> c_Polynomial_Opdivmod__rel(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0) ).
fof(f736,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,X4,X3,X2,X1)
=> c_Polynomial_Opdivmod__rel(X5,c_Polynomial_Osmult(X5,X0,X4),X3,c_Polynomial_Osmult(X5,X0,X2),c_Polynomial_Osmult(X5,X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__smult__left) ).
fof(f737,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( class_Fields_Ofield(X6)
=> ( c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
=> ( c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
=> ( X2 = X0
& X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__unique) ).
fof(f740,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( class_Fields_Ofield(X7)
=> ( c_Polynomial_Opdivmod__rel(X7,X6,X5,X4,X3)
=> ( c_Polynomial_Opdivmod__rel(X7,X4,X2,X1,X0)
=> c_Polynomial_Opdivmod__rel(X7,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X2),X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X0),X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__mult) ).
fof(f742,axiom,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(f744,axiom,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
fof(f748,axiom,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
fof(f750,axiom,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
fof(f751,axiom,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
fof(f752,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( ! [X3] :
( hBOOL(hAPP(X1,X3))
=> hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> ! [X3] :
( hBOOL(hAPP(X1,X3))
=> hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).
fof(f753,axiom,
! [X0,X1] :
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X1,X0))
=> ? [X2] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
=> ~ hBOOL(hAPP(X1,X3)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
fof(f754,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
=> ( hAPP(c_Polynomial_Ocoeff(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__zero__or__degree__less) ).
fof(f755,axiom,
! [X0,X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
fof(f756,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1)) = hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X0),X1))
=> X1 = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__dvd__antisym) ).
fof(f757,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ozero(X3)
=> ( ( X2 != X1
=> hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) = c_Groups_Ozero__class_Ozero(X3) )
& ( X2 = X1
=> hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__monom) ).
fof(f758,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__add) ).
fof(f759,axiom,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
fof(f760,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(f761,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(f762,axiom,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(f763,axiom,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(f764,axiom,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(f765,axiom,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(f766,axiom,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(f767,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(f768,axiom,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(f769,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__ring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).
fof(f772,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
fof(f773,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oab__group__add(X3)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Ominus__class_Ominus(X3,X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__monom) ).
fof(f774,axiom,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oab__group__add(X4)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Ominus__class_Ominus(X4,X3,X1),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__pCons) ).
fof(f775,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__ring(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).
fof(f776,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__ring(X3)
=> c_Polynomial_Osmult(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__left) ).
fof(f777,axiom,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(f778,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oab__group__add(X3)
=> hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__diff) ).
fof(f779,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Polynomial_Ocoeff(X2,X1) = c_Polynomial_Ocoeff(X2,X0)
<=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__inject) ).
fof(f780,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( X1 = X0
<=> ! [X3] : hAPP(c_Polynomial_Ocoeff(X2,X1),X3) = hAPP(c_Polynomial_Ocoeff(X2,X0),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expand__poly__eq) ).
fof(f781,axiom,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oab__group__add(X4)
=> ( c_Groups_Ominus__class_Ominus(X4,X3,X2) = c_Groups_Ominus__class_Ominus(X4,X1,X0)
=> ( X3 = X2
<=> X1 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(f782,axiom,
! [X0,X1,X2,X3,X4] :
( class_Groups_Ominus(X4)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).
fof(f783,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> ( 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,X0,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).
fof(f784,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(f785,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)
<=> X1 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
fof(f786,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(f787,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(f788,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(f789,axiom,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(f790,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(f791,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(f792,axiom,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(f793,axiom,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(f794,axiom,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(f796,axiom,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oordered__ab__group__add(X4)
=> ( c_Groups_Ominus__class_Ominus(X4,X3,X2) = c_Groups_Ominus__class_Ominus(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X2)
<=> c_Orderings_Oord__class_Oless(X4,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
fof(f797,axiom,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oordered__ab__group__add(X4)
=> ( c_Groups_Ominus__class_Ominus(X4,X3,X2) = c_Groups_Ominus__class_Ominus(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
<=> c_Orderings_Oord__class_Oless__eq(X4,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(f798,axiom,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(f800,axiom,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> ( X1 = X0
<=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(f801,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
<=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(f802,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Ozero(X3)
=> hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X2,X1)),c_Nat_OSuc(X0)) = hAPP(c_Polynomial_Ocoeff(X3,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons__Suc) ).
fof(f803,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Ocoeff(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__smult) ).
fof(f804,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons__0) ).
fof(f807,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).
fof(f808,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(f809,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(f812,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
fof(f815,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
fof(f817,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
fof(f818,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD1) ).
fof(f819,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD) ).
fof(f820,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> ( 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,X0,X2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(f821,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(f822,axiom,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(f823,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(f824,axiom,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__0) ).
fof(f826,axiom,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(f827,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(f828,axiom,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(f829,axiom,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Nat_OSuc(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
fof(f830,axiom,
! [X0,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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
fof(f831,axiom,
! [X0,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,X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(f832,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
fof(f833,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(f834,axiom,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
fof(f835,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).
fof(f836,axiom,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ouminus__class_Ouminus(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).
fof(f837,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Oring(X4)
=> c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
fof(f838,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Oring(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
<=> c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
fof(f839,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Oring(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
<=> X2 = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
fof(f840,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(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),X2),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
fof(f841,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
fof(f842,axiom,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Ocoeff(X2,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__minus) ).
fof(f843,axiom,
! [X0,X1,X2,X3,X4] :
( class_RealVector_Oreal__normed__algebra(X4)
=> c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),c_Groups_Ominus__class_Ominus(X4,X2,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(f845,axiom,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
fof(f847,axiom,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
fof(f848,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).
fof(f849,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).
fof(f850,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).
fof(f851,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).
fof(f852,axiom,
! [X0,X1] :
( class_Rings_Oring__1(X1)
=> c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Oone__class_Oone(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Oone__class_Oone(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
fof(f854,axiom,
! [X0,X1,X2,X3] :
( ( class_Rings_Odvd(X3)
& class_Rings_Ocomm__ring(X3) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> ! [X4,X5] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).
fof(f856,axiom,
! [X0,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,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
fof(f857,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> ~ ( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(f858,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> ( ! [X3] :
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3)
=> hBOOL(hAPP(X2,X3)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(f859,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Nat_OSuc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
fof(f860,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(f861,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
=> hAPP(c_Polynomial_Ocoeff(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__eq__0) ).
fof(f862,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( hAPP(c_Polynomial_Ocoeff(X2,X1),X0) != c_Groups_Ozero__class_Ozero(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Polynomial_Odegree(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__degree) ).
fof(f863,axiom,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
fof(f864,axiom,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(f865,axiom,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(f866,axiom,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
fof(f867,axiom,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(f868,axiom,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)
<=> X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(f870,axiom,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> ( hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0)) = c_Groups_Ozero__class_Ozero(X1)
<=> X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leading__coeff__0__iff) ).
fof(f871,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Polynomial_Odegree(X2,c_Polynomial_Osynthetic__div(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__synthetic__div) ).
fof(f873,axiom,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
fof(f874,axiom,
! [X0,X1] :
( ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) )
& ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).
fof(f875,axiom,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> ( 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),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
fof(f876,axiom,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> ( 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),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
fof(f877,axiom,
! [X0,X1] :
( ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)) )
& ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(f878,axiom,
! [X0,X1] :
( ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(f879,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1))),hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__mult__degree__sum) ).
fof(f880,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> ( ( X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1) )
& ( X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Oone__class_Oone(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__1) ).
fof(f881,axiom,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> ( c_Polynomial_Opos__poly(X1,X0)
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__def) ).
fof(f882,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)),X0) = c_Groups_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__linear__power) ).
fof(f883,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> c_Groups_Ominus__class_Ominus(X2,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),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
fof(f884,axiom,
! [X0,X1,X2] :
( class_Power_Opower(X2)
=> ( ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = c_Groups_Oone__class_Oone(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
fof(f885,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__realpow__diff) ).
fof(f886,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
<=> ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| X1 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__poly__def) ).
fof(f887,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
<=> c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__poly__def) ).
fof(f888,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__ring(X3)
=> c_Polynomial_Osmult(X3,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__right) ).
fof(f889,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).
fof(f890,axiom,
! [X0,X1] :
( class_Groups_Oab__group__add(X1)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
fof(f891,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(f892,axiom,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).
fof(f893,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__diff__le) ).
fof(f894,axiom,
! [X0,X1,X2,X3] :
( class_Groups_Oab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__diff__less) ).
fof(f895,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
fof(f896,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(f897,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(f898,axiom,
! [X0,X1] :
( class_Groups_Oab__group__add(X1)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
fof(f899,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
fof(f900,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( class_Fields_Ofield(X6)
=> ( c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
=> ( X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> ( X1 = c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4)))
=> c_Polynomial_Opdivmod__rel(X6,c_Polynomial_OpCons(X6,X0,X5),X4,c_Polynomial_OpCons(X6,X1,X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X0,X2),c_Polynomial_Osmult(X6,X1,X4))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__pCons) ).
fof(f901,axiom,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
fof(f903,axiom,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__field(X3)
=> c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Odiff) ).
fof(f905,axiom,
! [X0,X1] :
( class_Rings_Odivision__ring(X1)
=> c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).
fof(f907,axiom,
! [X0,X1] :
( class_Rings_Odivision__ring__inverse__zero(X1)
=> ( ( X0 != c_Groups_Ozero__class_Ozero(X1)
=> c_Rings_Oinverse__class_Odivide(X1,X0,X0) = c_Groups_Oone__class_Oone(X1) )
& ( X0 = c_Groups_Ozero__class_Ozero(X1)
=> c_Rings_Oinverse__class_Odivide(X1,X0,X0) = c_Groups_Ozero__class_Ozero(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).
fof(f909,axiom,
! [X0,X1,X2] :
( class_Rings_Odivision__ring(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(X2)
=> ( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = c_Groups_Oone__class_Oone(X2)
<=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
fof(f910,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X2,X1)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).
fof(f911,axiom,
! [X0,X1] :
( class_Rings_Odivision__ring__inverse__zero(X1)
=> c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).
fof(f913,axiom,
! [X0,X1,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),X1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).
fof(f917,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Odivision__ring(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) = X0
=> X1 = c_Rings_Oinverse__class_Odivide(X3,X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
fof(f919,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Odivision__ring(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> ( c_Rings_Oinverse__class_Odivide(X3,X1,X2) = X0
<=> X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
fof(f921,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Odivision__ring(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
fof(f922,axiom,
! [X0,X1] :
( class_RealVector_Oreal__normed__field(X1)
=> c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ozero) ).
fof(f923,axiom,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__field(X3)
=> c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Oadd) ).
fof(f924,axiom,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__field(X2)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ominus) ).
fof(f925,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__diff) ).
fof(f928,axiom,
! [X0,X1,X2,X3,X4] :
( class_Fields_Ofield__inverse__zero(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Rings_Oinverse__class_Odivide(X4,X3,X2)),c_Rings_Oinverse__class_Odivide(X4,X1,X0)) = c_Rings_Oinverse__class_Odivide(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
fof(f929,axiom,
! [X0,X1,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) = c_Rings_Oinverse__class_Odivide(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__right) ).
fof(f943,axiom,
! [X0,X1,X2,X3,X4] :
( class_Fields_Ofield(X4)
=> ( X3 != c_Groups_Ozero__class_Ozero(X4)
=> ( X2 != c_Groups_Ozero__class_Ozero(X4)
=> ( c_Rings_Oinverse__class_Odivide(X4,X1,X3) = c_Rings_Oinverse__class_Odivide(X4,X0,X2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
fof(f944,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) = c_Rings_Oinverse__class_Odivide(X3,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
fof(f965,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2)),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).
fof(f966,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
fof(f967,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).
fof(f968,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
fof(f969,axiom,
! [X0,X1,X2,X3,X4] :
( class_Fields_Ofield(X4)
=> ( X3 != c_Groups_Ozero__class_Ozero(X4)
=> ( X2 != c_Groups_Ozero__class_Ozero(X4)
=> c_Groups_Oplus__class_Oplus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).
fof(f970,axiom,
! [X0,X1,X2,X3,X4] :
( class_Fields_Ofield(X4)
=> ( X3 != c_Groups_Ozero__class_Ozero(X4)
=> ( X2 != c_Groups_Ozero__class_Ozero(X4)
=> c_Groups_Ominus__class_Ominus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__frac__eq) ).
fof(f971,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).
fof(f972,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> c_Groups_Ominus__class_Ominus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).
fof(f983,axiom,
! [X0,X1,X2,X3,X4,X5] :
( class_RealVector_Oreal__field(X5)
=> c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X1)),X0) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X3,X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X4,X2),X0)),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__mult__lemma) ).
fof(f984,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,X0),X2) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2)),c_Polynomial_Osmult(X3,c_Rings_Oinverse__class_Odivide(X3,hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2))),c_Polynomial_Odegree(X3,X2)),hAPP(c_Polynomial_Ocoeff(X3,X2),c_Polynomial_Odegree(X3,X2))),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pCons) ).
fof(f985,axiom,
! [X0,X1,X2] :
( class_Fields_Ofield(X2)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mod__minus__right) ).
fof(f986,axiom,
! [X0,X1,X2] :
( class_Fields_Ofield(X2)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mod__minus__left) ).
fof(f987,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0) = c_Polynomial_Osmult(X3,X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__smult__left) ).
fof(f988,axiom,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__smult__right) ).
fof(f989,axiom,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__0) ).
fof(f990,axiom,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__0) ).
fof(f991,axiom,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Omod(X1,X0,X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__self) ).
fof(f992,axiom,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
=> c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__mod__0) ).
fof(f993,axiom,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
<=> c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
fof(f994,axiom,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0) = c_Divides_Odiv__class_Omod(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).
fof(f995,axiom,
! [X0,X1,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod__imp__dvd) ).
fof(f996,axiom,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(f997,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
fof(f998,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(f999,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(f1000,axiom,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(f1001,axiom,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> class_Orderings_Opreorder(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(f1002,axiom,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(f1003,axiom,
! [X0,X1] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(f1004,axiom,
! [X0,X1] :
( class_Groups_Ouminus(X1)
=> class_Groups_Ouminus(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(f1005,axiom,
! [X0,X1] :
( class_Groups_Ominus(X1)
=> class_Groups_Ominus(tc_fun(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(f1006,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f1007,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f1008,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f1010,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(f1011,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(f1012,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(f1013,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(f1014,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(f1015,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(f1016,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(f1017,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(f1018,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(f1019,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(f1020,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(f1021,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(f1022,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(f1023,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(f1024,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(f1025,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(f1026,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(f1027,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(f1028,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(f1029,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(f1030,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(f1031,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(f1032,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(f1033,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(f1034,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(f1035,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(f1036,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(f1038,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(f1039,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(f1040,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(f1041,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(f1042,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(f1043,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(f1044,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(f1046,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(f1047,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(f1048,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(f1049,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(f1050,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(f1051,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(f1052,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(f1053,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(f1054,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(f1055,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(f1056,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(f1057,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(f1058,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(f1059,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(f1060,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(f1062,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(f1063,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f1064,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f1065,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f1067,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(f1068,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(f1069,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(f1070,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(f1071,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(f1072,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(f1073,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(f1074,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(f1075,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f1076,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(f1077,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(f1078,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(f1079,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(f1080,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(f1081,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(f1082,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(f1083,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(f1084,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(f1086,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(f1087,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(f1088,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(f1089,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(f1091,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(f1092,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(f1093,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(f1094,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(f1095,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(f1096,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(f1097,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(f1098,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(f1100,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(f1101,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(f1102,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(f1103,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(f1104,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(f1105,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(f1106,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(f1107,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f1108,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(f1109,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1110,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(f1111,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(f1112,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f1113,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(f1114,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(f1115,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
fof(f1116,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(f1117,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(f1118,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(f1119,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(f1120,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(f1121,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1122,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(f1123,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(f1124,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
fof(f1125,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(f1126,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(f1127,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(f1128,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(f1129,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(f1130,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(f1131,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(f1132,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(f1133,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(f1134,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(f1135,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(f1136,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(f1137,axiom,
class_Groups_Ouminus(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
fof(f1138,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(f1139,axiom,
class_Groups_Ominus(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).
fof(f1140,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(f1141,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(f1142,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(f1143,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(f1144,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(f1146,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
fof(f1147,axiom,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f1148,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f1149,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f1150,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(f1151,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(f1152,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(f1153,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(f1154,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(f1155,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(f1156,axiom,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(f1157,axiom,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(f1158,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(f1159,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(f1160,axiom,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(f1161,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(f1162,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(f1163,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(f1164,axiom,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(f1165,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(f1166,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(f1167,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(f1168,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(f1169,axiom,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(f1170,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(f1171,axiom,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(f1172,axiom,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(f1173,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(f1174,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(f1175,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(f1176,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(f1177,axiom,
! [X0] :
( class_Fields_Ofield(X0)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(f1179,axiom,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(f1180,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(f1181,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(f1182,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(f1183,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(f1184,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(f1185,axiom,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(f1187,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(f1188,axiom,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(f1189,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(f1190,axiom,
! [X0] :
( class_Rings_Ocomm__ring(X0)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(f1191,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(f1192,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(f1193,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(f1194,axiom,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(f1195,axiom,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
fof(f1196,axiom,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(f1197,axiom,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Ominus(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
fof(f1198,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Power_Opower(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(f1199,axiom,
! [X0] :
( class_Groups_Ozero(X0)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(f1200,axiom,
! [X0] :
( class_Rings_Ocomm__ring(X0)
=> class_Rings_Oring(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(f1201,axiom,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(f1203,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
fof(f1204,axiom,
! [X0,X1] :
( X1 = X0
| ~ hBOOL(c_fequal(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(f1205,axiom,
! [X0,X1] :
( hBOOL(c_fequal(X1,X0))
| X1 != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(f1206,conjecture,
( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1207,negated_conjecture,
~ ( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
inference(negated_conjecture,[status(cth)],[f1206]) ).
fof(f1208,plain,
! [X0,X1,X2] :
( ( class_Rings_Osemiring__0(X2)
& class_Rings_Odvd(X2) )
=> ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
<=> ? [X4] :
( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) ) ) ),
inference(rectify,[],[f638]) ).
fof(f1209,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( ! [X3] :
( hBOOL(hAPP(X1,X3))
=> hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> ! [X4] :
( hBOOL(hAPP(X1,X4))
=> hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)))) ) ) ) ),
inference(rectify,[],[f752]) ).
fof(f1255,plain,
! [X0,X1] :
( ? [X2] : hAPP(X1,X2) != hAPP(X0,X2)
| X1 = X0 ),
inference(ennf_transformation,[],[f1]) ).
fof(f1257,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(ennf_transformation,[],[f6]) ).
fof(f1258,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(flattening,[],[f1257]) ).
fof(f1259,plain,
( ? [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) )
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(ennf_transformation,[],[f7]) ).
fof(f1260,plain,
( ? [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) )
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(flattening,[],[f1259]) ).
fof(f1262,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1))) ),
inference(ennf_transformation,[],[f9]) ).
fof(f1263,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f1264,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f1267,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))) ),
inference(ennf_transformation,[],[f13]) ).
fof(f1268,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))) ),
inference(flattening,[],[f1267]) ).
fof(f1269,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f1270,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(flattening,[],[f1269]) ).
fof(f1271,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oring__1__no__zero__divisors(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f1272,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oring__1__no__zero__divisors(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ),
inference(flattening,[],[f1271]) ).
fof(f1273,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| X0 = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f1274,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| X0 = c_Groups_Ozero__class_Ozero(X1) ),
inference(flattening,[],[f1273]) ).
fof(f1275,plain,
! [X0,X1,X2] :
( ? [X3] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X3) )
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0))) ),
inference(ennf_transformation,[],[f17]) ).
fof(f1276,plain,
! [X0,X1,X2] :
( ? [X3] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X3) )
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0))) ),
inference(flattening,[],[f1275]) ).
fof(f1277,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( hAPP(c_Polynomial_Opoly(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( c_Polynomial_Oorder(X2,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f1278,plain,
! [X0,X1] :
( ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f1279,plain,
! [X0,X1] :
( ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(flattening,[],[f1278]) ).
fof(f1280,plain,
! [X0] :
( ~ class_Groups_Ozero(X0)
| c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(ennf_transformation,[],[f22]) ).
fof(f1281,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f1282,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0)) ),
inference(flattening,[],[f1281]) ).
fof(f1283,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f1284,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ~ class_Int_Oring__char__0(X2)
| ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
<=> X1 = X0 ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f1285,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ~ class_Int_Oring__char__0(X2)
| ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
<=> X1 = X0 ) ),
inference(flattening,[],[f1284]) ).
fof(f1286,plain,
? [X0] : c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(X0),
inference(ennf_transformation,[],[f26]) ).
fof(f1287,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Nat_OSuc(c_Polynomial_Odegree(X1,X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f1288,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| ( c_Polynomial_Osynthetic__div(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> c_Polynomial_Odegree(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f1291,plain,
! [X0,X1] :
( X0 != X1
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f1303,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| X1 = X0 ),
inference(ennf_transformation,[],[f49]) ).
fof(f1304,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| X1 = X0 ),
inference(flattening,[],[f1303]) ).
fof(f1305,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0)) ),
inference(ennf_transformation,[],[f50]) ).
fof(f1306,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0)) ),
inference(flattening,[],[f1305]) ).
fof(f1333,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(ennf_transformation,[],[f64]) ).
fof(f1335,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f1338,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f1339,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ozero(X3)
| hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) != X1
| c_Polynomial_Opoly__rec(X0,X3,X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X1 ),
inference(ennf_transformation,[],[f73]) ).
fof(f1340,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ozero(X3)
| hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) != X1
| c_Polynomial_Opoly__rec(X0,X3,X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X1 ),
inference(flattening,[],[f1339]) ).
fof(f1342,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(X2,X0,X1),c_Polynomial_Odegree(X2,X1)) ),
inference(ennf_transformation,[],[f75]) ).
fof(f1343,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(X2,X0,X1),c_Polynomial_Odegree(X2,X1)) ),
inference(flattening,[],[f1342]) ).
fof(f1344,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)) ),
inference(ennf_transformation,[],[f76]) ).
fof(f1345,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)) ),
inference(flattening,[],[f1344]) ).
fof(f1346,plain,
! [X0,X1] :
( ~ 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_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ),
inference(ennf_transformation,[],[f77]) ).
fof(f1349,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ),
inference(ennf_transformation,[],[f79]) ).
fof(f1350,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) )
& ( c_Groups_Ozero__class_Ozero(X3) != X2
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ) ) ),
inference(ennf_transformation,[],[f80]) ).
fof(f1353,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f1354,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(flattening,[],[f1353]) ).
fof(f1356,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Ozero(X4)
| ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
<=> ( X2 = X0
& X3 = X1 ) ) ),
inference(ennf_transformation,[],[f87]) ).
fof(f1357,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,X1) != c_Polynomial_OpCons(X3,X0,X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(ennf_transformation,[],[f88]) ).
fof(f1358,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,X1) != c_Polynomial_OpCons(X3,X0,X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(flattening,[],[f1357]) ).
fof(f1359,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0)) ),
inference(ennf_transformation,[],[f89]) ).
fof(f1360,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Groups_Ozero(X5)
| c_Polynomial_Opoly__rec(X4,X5,X3,X2,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X2,X1),X0),c_If(X4,c_fequal(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3,c_Polynomial_Opoly__rec(X4,X5,X3,X2,X0))) ),
inference(ennf_transformation,[],[f90]) ).
fof(f1361,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Nat_OSuc(c_Polynomial_Odegree(X2,X0))) ),
inference(ennf_transformation,[],[f91]) ).
fof(f1366,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(ennf_transformation,[],[f101]) ).
fof(f1367,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Groups_Ozero(X5)
| hAPP(hAPP(hAPP(X4,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3) != X3
| c_Polynomial_Opoly__rec(X2,X5,X3,X4,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X4,X1),X0),c_Polynomial_Opoly__rec(X2,X5,X3,X4,X0)) ),
inference(ennf_transformation,[],[f102]) ).
fof(f1368,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Groups_Ozero(X5)
| hAPP(hAPP(hAPP(X4,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3) != X3
| c_Polynomial_Opoly__rec(X2,X5,X3,X4,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X4,X1),X0),c_Polynomial_Opoly__rec(X2,X5,X3,X4,X0)) ),
inference(flattening,[],[f1367]) ).
fof(f1369,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) ),
inference(ennf_transformation,[],[f103]) ).
fof(f1370,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) ),
inference(flattening,[],[f1369]) ).
fof(f1371,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X0,X1))) ),
inference(ennf_transformation,[],[f104]) ).
fof(f1372,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X0,X1))) ),
inference(flattening,[],[f1371]) ).
fof(f1373,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(ennf_transformation,[],[f105]) ).
fof(f1374,plain,
! [X0] :
( ~ class_Groups_Ozero(X0)
| c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f106]) ).
fof(f1375,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(ennf_transformation,[],[f107]) ).
fof(f1376,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(flattening,[],[f1375]) ).
fof(f1377,plain,
! [X0,X1,X2] :
( ~ 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),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(ennf_transformation,[],[f108]) ).
fof(f1378,plain,
! [X0,X1,X2] :
( ~ 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),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(flattening,[],[f1377]) ).
fof(f1379,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( c_Polynomial_Osmult(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(ennf_transformation,[],[f109]) ).
fof(f1380,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(ennf_transformation,[],[f110]) ).
fof(f1381,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X2)),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X0)),X1)) ),
inference(ennf_transformation,[],[f111]) ).
fof(f1382,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X2)),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X0)),X1)) ),
inference(flattening,[],[f1381]) ).
fof(f1383,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X0))) ),
inference(ennf_transformation,[],[f112]) ).
fof(f1384,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X0))) ),
inference(flattening,[],[f1383]) ).
fof(f1385,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))) ),
inference(ennf_transformation,[],[f113]) ).
fof(f1386,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))) ),
inference(flattening,[],[f1385]) ).
fof(f1387,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X1,X0)))
| c_Groups_Ozero__class_Ozero(X3) = X1
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X0)) ),
inference(ennf_transformation,[],[f114]) ).
fof(f1388,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X1,X0)))
| c_Groups_Ozero__class_Ozero(X3) = X1
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X0)) ),
inference(flattening,[],[f1387]) ).
fof(f1391,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) ) ),
inference(ennf_transformation,[],[f116]) ).
fof(f1392,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) ) ),
inference(flattening,[],[f1391]) ).
fof(f1393,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osynthetic__div(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Polynomial_OpCons(X3,hAPP(c_Polynomial_Opoly(X3,X1),X0),c_Polynomial_Osynthetic__div(X3,X1,X0)) ),
inference(ennf_transformation,[],[f117]) ).
fof(f1394,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(ennf_transformation,[],[f118]) ).
fof(f1395,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Nat_OSuc(c_Polynomial_Odegree(X2,X1)) ),
inference(ennf_transformation,[],[f119]) ).
fof(f1396,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Nat_OSuc(c_Polynomial_Odegree(X2,X1)) ),
inference(flattening,[],[f1395]) ).
fof(f1397,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| X2 = X0 ),
inference(ennf_transformation,[],[f120]) ).
fof(f1398,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| X2 = X0 ),
inference(flattening,[],[f1397]) ).
fof(f1399,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1)))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(ennf_transformation,[],[f121]) ).
fof(f1400,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1)))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(flattening,[],[f1399]) ).
fof(f1401,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( ( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Odegree(X2,X0) )
& ( c_Groups_Ozero__class_Ozero(X2) != X1
| c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(ennf_transformation,[],[f122]) ).
fof(f1403,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Ocomm__semiring__0(X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X3,c_Polynomial_Osmult(X4,X2,X1)) != c_Polynomial_OpCons(X4,X0,X1)
| ( X1 = c_Polynomial_Osynthetic__div(X4,X3,X2)
& X0 = hAPP(c_Polynomial_Opoly(X4,X3),X2) ) ),
inference(ennf_transformation,[],[f125]) ).
fof(f1404,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Ocomm__semiring__0(X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X3,c_Polynomial_Osmult(X4,X2,X1)) != c_Polynomial_OpCons(X4,X0,X1)
| ( X1 = c_Polynomial_Osynthetic__div(X4,X3,X2)
& X0 = hAPP(c_Polynomial_Opoly(X4,X3),X2) ) ),
inference(flattening,[],[f1403]) ).
fof(f1405,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,c_Polynomial_Osmult(X2,X0,c_Polynomial_Osynthetic__div(X2,X1,X0))) = c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0),c_Polynomial_Osynthetic__div(X2,X1,X0)) ),
inference(ennf_transformation,[],[f126]) ).
fof(f1406,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) = X0 ),
inference(ennf_transformation,[],[f127]) ).
fof(f1407,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) = c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) ),
inference(ennf_transformation,[],[f128]) ).
fof(f1408,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(ennf_transformation,[],[f129]) ).
fof(f1409,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 = X0 ),
inference(ennf_transformation,[],[f130]) ).
fof(f1410,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 = X0 ),
inference(flattening,[],[f1409]) ).
fof(f1411,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)) ),
inference(ennf_transformation,[],[f131]) ).
fof(f1412,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)) ),
inference(flattening,[],[f1411]) ).
fof(f1413,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| c_Polynomial_Omonom(X2,X1,c_Nat_OSuc(X0)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0)) ),
inference(ennf_transformation,[],[f132]) ).
fof(f1417,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f138]) ).
fof(f1418,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f1417]) ).
fof(f1419,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
inference(ennf_transformation,[],[f139]) ).
fof(f1420,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
inference(flattening,[],[f1419]) ).
fof(f1421,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(ennf_transformation,[],[f140]) ).
fof(f1422,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(flattening,[],[f1421]) ).
fof(f1423,plain,
! [X0] :
( ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(ennf_transformation,[],[f141]) ).
fof(f1424,plain,
! [X0] :
( ~ class_Rings_Olinordered__semidom(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(ennf_transformation,[],[f142]) ).
fof(f1425,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)
<=> X1 = X0 ) ),
inference(ennf_transformation,[],[f143]) ).
fof(f1426,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)
<=> X1 = X0 ) ),
inference(flattening,[],[f1425]) ).
fof(f1427,plain,
! [X0] :
( ~ class_Rings_Olinordered__semidom(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))) ),
inference(ennf_transformation,[],[f144]) ).
fof(f1428,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))) ),
inference(ennf_transformation,[],[f145]) ).
fof(f1429,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ozero(X3)
| ( c_Polynomial_Omonom(X3,X2,X1) = c_Polynomial_Omonom(X3,X0,X1)
<=> X2 = X0 ) ),
inference(ennf_transformation,[],[f146]) ).
fof(f1430,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocomm__monoid__add(X3)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1) ),
inference(ennf_transformation,[],[f147]) ).
fof(f1431,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1) ),
inference(ennf_transformation,[],[f148]) ).
fof(f1432,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1) ),
inference(flattening,[],[f1431]) ).
fof(f1437,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,X0,X1) ),
inference(ennf_transformation,[],[f151]) ).
fof(f1438,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,X0,X1) ),
inference(flattening,[],[f1437]) ).
fof(f1439,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(ennf_transformation,[],[f152]) ).
fof(f1440,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(flattening,[],[f1439]) ).
fof(f1449,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ),
inference(ennf_transformation,[],[f157]) ).
fof(f1450,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ),
inference(flattening,[],[f1449]) ).
fof(f1459,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ),
inference(ennf_transformation,[],[f162]) ).
fof(f1460,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ),
inference(flattening,[],[f1459]) ).
fof(f1469,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( X1 = X0
| c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
inference(ennf_transformation,[],[f167]) ).
fof(f1470,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| ( X1 != X0
<=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(ennf_transformation,[],[f168]) ).
fof(f1471,plain,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X0,X0) ),
inference(ennf_transformation,[],[f169]) ).
fof(f1472,plain,
! [X0,X1] :
( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(ennf_transformation,[],[f172]) ).
fof(f1473,plain,
! [X0,X1] :
( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(flattening,[],[f1472]) ).
fof(f1478,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Ocomm__monoid__add(X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X2,X0)) ),
inference(ennf_transformation,[],[f177]) ).
fof(f1479,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ocomm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X0,X1)) = c_Polynomial_Odegree(X2,X0) ),
inference(ennf_transformation,[],[f178]) ).
fof(f1480,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ocomm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X0,X1)) = c_Polynomial_Odegree(X2,X0) ),
inference(flattening,[],[f1479]) ).
fof(f1481,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ocomm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) = c_Polynomial_Odegree(X2,X0) ),
inference(ennf_transformation,[],[f179]) ).
fof(f1482,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ocomm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) = c_Polynomial_Odegree(X2,X0) ),
inference(flattening,[],[f1481]) ).
fof(f1483,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocomm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ),
inference(ennf_transformation,[],[f180]) ).
fof(f1484,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocomm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ),
inference(flattening,[],[f1483]) ).
fof(f1485,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(ennf_transformation,[],[f181]) ).
fof(f1486,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0)) ),
inference(ennf_transformation,[],[f182]) ).
fof(f1487,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,X0,X1) ),
inference(ennf_transformation,[],[f183]) ).
fof(f1488,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,X0,X1) ),
inference(flattening,[],[f1487]) ).
fof(f1489,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(ennf_transformation,[],[f184]) ).
fof(f1490,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(flattening,[],[f1489]) ).
fof(f1491,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,X0,X1) ),
inference(ennf_transformation,[],[f185]) ).
fof(f1492,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,X0,X1) ),
inference(flattening,[],[f1491]) ).
fof(f1493,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(ennf_transformation,[],[f186]) ).
fof(f1494,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(flattening,[],[f1493]) ).
fof(f1511,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> X1 = X0 ) ),
inference(ennf_transformation,[],[f195]) ).
fof(f1512,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> X1 = X0 ) ),
inference(flattening,[],[f1511]) ).
fof(f1518,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Opreorder(X2)
| ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
inference(ennf_transformation,[],[f199]) ).
fof(f1519,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X2)
| ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
inference(ennf_transformation,[],[f200]) ).
fof(f1523,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ),
inference(ennf_transformation,[],[f203]) ).
fof(f1524,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Oone__class_Oone(X1) ),
inference(ennf_transformation,[],[f204]) ).
fof(f1525,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Oone__class_Oone(X3))
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)) ),
inference(ennf_transformation,[],[f205]) ).
fof(f1526,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Oone__class_Oone(X3))
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)) ),
inference(flattening,[],[f1525]) ).
fof(f1527,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(ennf_transformation,[],[f206]) ).
fof(f1528,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(flattening,[],[f1527]) ).
fof(f1529,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(ennf_transformation,[],[f207]) ).
fof(f1530,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0))) ),
inference(ennf_transformation,[],[f208]) ).
fof(f1531,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0))) ),
inference(flattening,[],[f1530]) ).
fof(f1532,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(ennf_transformation,[],[f209]) ).
fof(f1534,plain,
! [X0] :
( ~ class_Rings_Ozero__neq__one(X0)
| c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ),
inference(ennf_transformation,[],[f211]) ).
fof(f1535,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0))) ),
inference(ennf_transformation,[],[f212]) ).
fof(f1536,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0))) ),
inference(flattening,[],[f1535]) ).
fof(f1537,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0)) ),
inference(ennf_transformation,[],[f213]) ).
fof(f1538,plain,
! [X0,X1] :
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0) = c_Groups_Oone__class_Oone(X1) ),
inference(ennf_transformation,[],[f214]) ).
fof(f1542,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f221]) ).
fof(f1545,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0) ),
inference(ennf_transformation,[],[f223]) ).
fof(f1546,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0) ),
inference(flattening,[],[f1545]) ).
fof(f1547,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Nat_OSuc(X1) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(ennf_transformation,[],[f224]) ).
fof(f1548,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Nat_OSuc(X1) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(flattening,[],[f1547]) ).
fof(f1556,plain,
! [X0,X1] :
( ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f235]) ).
fof(f1557,plain,
! [X0,X1] :
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
inference(ennf_transformation,[],[f236]) ).
fof(f1558,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0 ),
inference(ennf_transformation,[],[f237]) ).
fof(f1559,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 ),
inference(ennf_transformation,[],[f238]) ).
fof(f1560,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0)) ),
inference(ennf_transformation,[],[f241]) ).
fof(f1561,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0 ),
inference(ennf_transformation,[],[f242]) ).
fof(f1562,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0))) ),
inference(ennf_transformation,[],[f243]) ).
fof(f1563,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),c_Groups_Oone__class_Oone(X2)) ),
inference(ennf_transformation,[],[f244]) ).
fof(f1564,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),c_Groups_Oone__class_Oone(X2)) ),
inference(flattening,[],[f1563]) ).
fof(f1567,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(ennf_transformation,[],[f246]) ).
fof(f1568,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(flattening,[],[f1567]) ).
fof(f1569,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| ( c_Groups_Oone__class_Oone(X2) != X0
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))) ),
inference(ennf_transformation,[],[f247]) ).
fof(f1570,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| ( c_Groups_Oone__class_Oone(X2) != X0
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))) ),
inference(flattening,[],[f1569]) ).
fof(f1571,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f248]) ).
fof(f1572,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f1571]) ).
fof(f1573,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(ennf_transformation,[],[f249]) ).
fof(f1574,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(flattening,[],[f1573]) ).
fof(f1575,plain,
! [X0] :
( ~ class_Rings_Olinordered__semidom(X0)
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(ennf_transformation,[],[f250]) ).
fof(f1576,plain,
! [X0] :
( ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(ennf_transformation,[],[f251]) ).
fof(f1577,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(ennf_transformation,[],[f252]) ).
fof(f1578,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(flattening,[],[f1577]) ).
fof(f1579,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(ennf_transformation,[],[f253]) ).
fof(f1580,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(flattening,[],[f1579]) ).
fof(f1582,plain,
! [X0,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,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(ennf_transformation,[],[f258]) ).
fof(f1583,plain,
! [X0,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,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(flattening,[],[f1582]) ).
fof(f1584,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(ennf_transformation,[],[f259]) ).
fof(f1585,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(flattening,[],[f1584]) ).
fof(f1586,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(ennf_transformation,[],[f263]) ).
fof(f1587,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(ennf_transformation,[],[f264]) ).
fof(f1589,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f266]) ).
fof(f1590,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocomm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ),
inference(ennf_transformation,[],[f267]) ).
fof(f1591,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocomm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ),
inference(flattening,[],[f1590]) ).
fof(f1592,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(ennf_transformation,[],[f269]) ).
fof(f1593,plain,
! [X0,X1,X2] :
( ~ 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f270]) ).
fof(f1594,plain,
! [X0,X1,X2] :
( ~ 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f1593]) ).
fof(f1596,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ),
inference(ennf_transformation,[],[f273]) ).
fof(f1597,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)) = c_Polynomial_Odegree(X2,X1) ),
inference(ennf_transformation,[],[f274]) ).
fof(f1599,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( c_Polynomial_Omonom(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> X1 = c_Groups_Ozero__class_Ozero(X2) ) ),
inference(ennf_transformation,[],[f276]) ).
fof(f1600,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0 ),
inference(ennf_transformation,[],[f277]) ).
fof(f1601,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0 ),
inference(flattening,[],[f1600]) ).
fof(f1602,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)),X0) ),
inference(ennf_transformation,[],[f278]) ).
fof(f1603,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(ennf_transformation,[],[f279]) ).
fof(f1604,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(flattening,[],[f1603]) ).
fof(f1605,plain,
! [X0,X1] :
( ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = c_Groups_Ozero__class_Ozero(X1) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = c_Groups_Oone__class_Oone(X1) ) ) ),
inference(ennf_transformation,[],[f280]) ).
fof(f1606,plain,
! [X0,X1] :
( ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = c_Groups_Ozero__class_Ozero(X1) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = c_Groups_Oone__class_Oone(X1) ) ) ),
inference(flattening,[],[f1605]) ).
fof(f1607,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
inference(ennf_transformation,[],[f281]) ).
fof(f1608,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
inference(flattening,[],[f1607]) ).
fof(f1615,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ),
inference(ennf_transformation,[],[f285]) ).
fof(f1616,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ),
inference(flattening,[],[f1615]) ).
fof(f1619,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(ennf_transformation,[],[f287]) ).
fof(f1620,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(flattening,[],[f1619]) ).
fof(f1635,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Opreorder(X2)
| X0 != X1
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ),
inference(ennf_transformation,[],[f295]) ).
fof(f1636,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Opreorder(X2)
| X0 != X1
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ),
inference(flattening,[],[f1635]) ).
fof(f1637,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X2)
| ( X1 = X0
<=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
inference(ennf_transformation,[],[f296]) ).
fof(f1638,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ),
inference(ennf_transformation,[],[f297]) ).
fof(f1639,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ),
inference(flattening,[],[f1638]) ).
fof(f1640,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oord(X3)
| ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
<=> ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) ) ),
inference(ennf_transformation,[],[f298]) ).
fof(f1641,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(ennf_transformation,[],[f299]) ).
fof(f1642,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(flattening,[],[f1641]) ).
fof(f1643,plain,
! [X0,X1,X2] :
( ~ 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,X1,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),X1) ),
inference(ennf_transformation,[],[f300]) ).
fof(f1644,plain,
! [X0,X1,X2] :
( ~ 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,X1,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),X1) ),
inference(flattening,[],[f1643]) ).
fof(f1649,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(ennf_transformation,[],[f303]) ).
fof(f1650,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(flattening,[],[f1649]) ).
fof(f1651,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(ennf_transformation,[],[f304]) ).
fof(f1652,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(flattening,[],[f1651]) ).
fof(f1653,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(ennf_transformation,[],[f305]) ).
fof(f1654,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(flattening,[],[f1653]) ).
fof(f1655,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(ennf_transformation,[],[f306]) ).
fof(f1656,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(flattening,[],[f1655]) ).
fof(f1657,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X0 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(ennf_transformation,[],[f308]) ).
fof(f1658,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X0 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(flattening,[],[f1657]) ).
fof(f1659,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oord(X3)
| ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) ) ),
inference(ennf_transformation,[],[f309]) ).
fof(f1660,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != X1
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(ennf_transformation,[],[f313]) ).
fof(f1661,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
inference(ennf_transformation,[],[f319]) ).
fof(f1662,plain,
! [X0,X1,X2,X3] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f320]) ).
fof(f1663,plain,
! [X0,X1,X2,X3] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f1662]) ).
fof(f1664,plain,
! [X0,X1,X2,X3] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| 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,X2,X0)) ),
inference(ennf_transformation,[],[f321]) ).
fof(f1665,plain,
! [X0,X1,X2,X3] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| 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,X2,X0)) ),
inference(flattening,[],[f1664]) ).
fof(f1666,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(ennf_transformation,[],[f322]) ).
fof(f1670,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(ennf_transformation,[],[f330]) ).
fof(f1671,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f331]) ).
fof(f1672,plain,
! [X0,X1,X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| 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,X2,X0)) ),
inference(ennf_transformation,[],[f332]) ).
fof(f1673,plain,
! [X0,X1,X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| 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,X2,X0)) ),
inference(flattening,[],[f1672]) ).
fof(f1674,plain,
! [X0,X1,X2] :
( ~ 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,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(ennf_transformation,[],[f333]) ).
fof(f1678,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oab__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(ennf_transformation,[],[f347]) ).
fof(f1681,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocancel__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,X0) != c_Groups_Oplus__class_Oplus(X3,X2,X1)
| X1 = X0 ),
inference(ennf_transformation,[],[f350]) ).
fof(f1682,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocancel__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,X0) != c_Groups_Oplus__class_Oplus(X3,X2,X1)
| X1 = X0 ),
inference(flattening,[],[f1681]) ).
fof(f1683,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,X0) != c_Groups_Oplus__class_Oplus(X3,X2,X1)
| X1 = X0 ),
inference(ennf_transformation,[],[f351]) ).
fof(f1684,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,X0) != c_Groups_Oplus__class_Oplus(X3,X2,X1)
| X1 = X0 ),
inference(flattening,[],[f1683]) ).
fof(f1685,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocancel__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X1)
| X2 = X0 ),
inference(ennf_transformation,[],[f352]) ).
fof(f1686,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocancel__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X1)
| X2 = X0 ),
inference(flattening,[],[f1685]) ).
fof(f1688,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(ennf_transformation,[],[f354]) ).
fof(f1689,plain,
! [X0,X1] :
( ~ class_Groups_Omonoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(ennf_transformation,[],[f355]) ).
fof(f1691,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(ennf_transformation,[],[f357]) ).
fof(f1692,plain,
! [X0,X1] :
( ~ class_Groups_Omonoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(ennf_transformation,[],[f358]) ).
fof(f1693,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
<=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ),
inference(ennf_transformation,[],[f359]) ).
fof(f1694,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ),
inference(ennf_transformation,[],[f360]) ).
fof(f1695,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(ennf_transformation,[],[f361]) ).
fof(f1696,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(flattening,[],[f1695]) ).
fof(f1697,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ),
inference(ennf_transformation,[],[f362]) ).
fof(f1698,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ),
inference(flattening,[],[f1697]) ).
fof(f1699,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__ab__semigroup__add(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(ennf_transformation,[],[f363]) ).
fof(f1700,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__ab__semigroup__add(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(flattening,[],[f1699]) ).
fof(f1701,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(ennf_transformation,[],[f364]) ).
fof(f1702,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(flattening,[],[f1701]) ).
fof(f1703,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ),
inference(ennf_transformation,[],[f365]) ).
fof(f1704,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ),
inference(flattening,[],[f1703]) ).
fof(f1705,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
<=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ),
inference(ennf_transformation,[],[f366]) ).
fof(f1706,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
<=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ),
inference(ennf_transformation,[],[f367]) ).
fof(f1707,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(ennf_transformation,[],[f368]) ).
fof(f1708,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(flattening,[],[f1707]) ).
fof(f1709,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ),
inference(ennf_transformation,[],[f369]) ).
fof(f1710,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ),
inference(flattening,[],[f1709]) ).
fof(f1711,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(ennf_transformation,[],[f370]) ).
fof(f1712,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(flattening,[],[f1711]) ).
fof(f1713,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(ennf_transformation,[],[f371]) ).
fof(f1714,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(flattening,[],[f1713]) ).
fof(f1715,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| c_Orderings_Oord__class_Oless(X3,X1,X0) ),
inference(ennf_transformation,[],[f372]) ).
fof(f1716,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| c_Orderings_Oord__class_Oless(X3,X1,X0) ),
inference(flattening,[],[f1715]) ).
fof(f1717,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(ennf_transformation,[],[f373]) ).
fof(f1718,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(flattening,[],[f1717]) ).
fof(f1719,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2)) ),
inference(ennf_transformation,[],[f374]) ).
fof(f1720,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2)) ),
inference(flattening,[],[f1719]) ).
fof(f1721,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(ennf_transformation,[],[f375]) ).
fof(f1722,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(flattening,[],[f1721]) ).
fof(f1723,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(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),X0)
| ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(ennf_transformation,[],[f376]) ).
fof(f1724,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(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),X0)
| ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(flattening,[],[f1723]) ).
fof(f1727,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(ennf_transformation,[],[f378]) ).
fof(f1728,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(ennf_transformation,[],[f379]) ).
fof(f1729,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(ennf_transformation,[],[f380]) ).
fof(f1730,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(flattening,[],[f1729]) ).
fof(f1731,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0)) ),
inference(ennf_transformation,[],[f381]) ).
fof(f1732,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0)) ),
inference(flattening,[],[f1731]) ).
fof(f1733,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(ennf_transformation,[],[f382]) ).
fof(f1734,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(ennf_transformation,[],[f383]) ).
fof(f1735,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(ennf_transformation,[],[f384]) ).
fof(f1736,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(flattening,[],[f1735]) ).
fof(f1737,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(ennf_transformation,[],[f385]) ).
fof(f1738,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(flattening,[],[f1737]) ).
fof(f1739,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
inference(ennf_transformation,[],[f386]) ).
fof(f1740,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(ennf_transformation,[],[f387]) ).
fof(f1743,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Nat_OSuc(c_Polynomial_Oorder(X2,X0,X1)))),X1)) ),
inference(ennf_transformation,[],[f389]) ).
fof(f1744,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Nat_OSuc(c_Polynomial_Oorder(X2,X0,X1)))),X1)) ),
inference(flattening,[],[f1743]) ).
fof(f1745,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
inference(ennf_transformation,[],[f390]) ).
fof(f1749,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| ( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
<=> c_Groups_Ouminus__class_Ouminus(X2,X0) = X1 ) ),
inference(ennf_transformation,[],[f399]) ).
fof(f1750,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0)
<=> X1 = X0 ) ),
inference(ennf_transformation,[],[f400]) ).
fof(f1751,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__ring(X2)
| c_Polynomial_Osmult(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) ),
inference(ennf_transformation,[],[f401]) ).
fof(f1752,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__ring(X2)
| hAPP(c_Polynomial_Opoly(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0)) ),
inference(ennf_transformation,[],[f402]) ).
fof(f1754,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_OpCons(X2,X1,X0)) = c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) ),
inference(ennf_transformation,[],[f404]) ).
fof(f1755,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ),
inference(ennf_transformation,[],[f405]) ).
fof(f1758,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( X0 = c_Groups_Ouminus__class_Ouminus(X1,X0)
<=> X0 = c_Groups_Ozero__class_Ozero(X1) ) ),
inference(ennf_transformation,[],[f408]) ).
fof(f1759,plain,
! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(ennf_transformation,[],[f409]) ).
fof(f1760,plain,
! [X0] :
( ~ class_Groups_Ogroup__add(X0)
| c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) ),
inference(ennf_transformation,[],[f410]) ).
fof(f1761,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(ennf_transformation,[],[f411]) ).
fof(f1762,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) ) ),
inference(ennf_transformation,[],[f412]) ).
fof(f1763,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ),
inference(ennf_transformation,[],[f413]) ).
fof(f1764,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ),
inference(ennf_transformation,[],[f414]) ).
fof(f1765,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ),
inference(flattening,[],[f1764]) ).
fof(f1766,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(ennf_transformation,[],[f415]) ).
fof(f1767,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) ) ),
inference(ennf_transformation,[],[f416]) ).
fof(f1768,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
inference(ennf_transformation,[],[f417]) ).
fof(f1769,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(ennf_transformation,[],[f418]) ).
fof(f1770,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ),
inference(ennf_transformation,[],[f419]) ).
fof(f1771,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0 ),
inference(ennf_transformation,[],[f420]) ).
fof(f1772,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0 ),
inference(ennf_transformation,[],[f421]) ).
fof(f1773,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__ring__1(X2)
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) ) ),
inference(ennf_transformation,[],[f422]) ).
fof(f1774,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__ring__1(X2)
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) ) ),
inference(ennf_transformation,[],[f423]) ).
fof(f1775,plain,
! [X0] :
( ~ class_Groups_Oab__group__add(X0)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f424]) ).
fof(f1776,plain,
! [X0,X1] :
( ~ class_Groups_Oab__group__add(X1)
| c_Polynomial_Odegree(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0)) = c_Polynomial_Odegree(X1,X0) ),
inference(ennf_transformation,[],[f425]) ).
fof(f1777,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__ring(X2)
| c_Polynomial_Osmult(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) ),
inference(ennf_transformation,[],[f426]) ).
fof(f1778,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(ennf_transformation,[],[f427]) ).
fof(f1779,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(ennf_transformation,[],[f428]) ).
fof(f1780,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(ennf_transformation,[],[f429]) ).
fof(f1781,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(ennf_transformation,[],[f430]) ).
fof(f1782,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(ennf_transformation,[],[f431]) ).
fof(f1783,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(ennf_transformation,[],[f432]) ).
fof(f1784,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(ennf_transformation,[],[f433]) ).
fof(f1785,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(ennf_transformation,[],[f434]) ).
fof(f1787,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| ( X1 = c_Groups_Ouminus__class_Ouminus(X2,X0)
<=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2) ) ),
inference(ennf_transformation,[],[f436]) ).
fof(f1788,plain,
! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f437]) ).
fof(f1789,plain,
! [X0,X1] :
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f438]) ).
fof(f1790,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
<=> X0 = c_Groups_Ouminus__class_Ouminus(X2,X1) ) ),
inference(ennf_transformation,[],[f439]) ).
fof(f1791,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| c_Groups_Ouminus__class_Ouminus(X2,X1) = X0 ),
inference(ennf_transformation,[],[f440]) ).
fof(f1792,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| c_Groups_Ouminus__class_Ouminus(X2,X1) = X0 ),
inference(flattening,[],[f1791]) ).
fof(f1793,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( 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),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( X1 = c_Groups_Ouminus__class_Ouminus(X2,X0)
| X1 = X0 ) ) ),
inference(ennf_transformation,[],[f441]) ).
fof(f1794,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X2),c_Groups_Oplus__class_Oplus(X4,X1,X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(ennf_transformation,[],[f442]) ).
fof(f1795,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1) ),
inference(ennf_transformation,[],[f443]) ).
fof(f1797,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) ),
inference(ennf_transformation,[],[f445]) ).
fof(f1798,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(ennf_transformation,[],[f446]) ).
fof(f1799,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
inference(ennf_transformation,[],[f447]) ).
fof(f1800,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(ennf_transformation,[],[f448]) ).
fof(f1801,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(ennf_transformation,[],[f449]) ).
fof(f1802,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(ennf_transformation,[],[f450]) ).
fof(f1803,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(ennf_transformation,[],[f451]) ).
fof(f1804,plain,
! [X0,X1] :
( ~ 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),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| X1 = X0 ),
inference(ennf_transformation,[],[f452]) ).
fof(f1805,plain,
! [X0,X1] :
( ~ 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),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| X1 = X0 ),
inference(flattening,[],[f1804]) ).
fof(f1806,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(ennf_transformation,[],[f453]) ).
fof(f1807,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(flattening,[],[f1806]) ).
fof(f1808,plain,
! [X0,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,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(ennf_transformation,[],[f454]) ).
fof(f1809,plain,
! [X0,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,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(flattening,[],[f1808]) ).
fof(f1810,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( hAPP(c_Polynomial_Opoly(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1)) ) ),
inference(ennf_transformation,[],[f455]) ).
fof(f1811,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0))
<=> hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) = c_Groups_Ozero__class_Ozero(X2) ) ),
inference(ennf_transformation,[],[f456]) ).
fof(f1812,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(ennf_transformation,[],[f457]) ).
fof(f1813,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(ennf_transformation,[],[f458]) ).
fof(f1814,plain,
! [X0,X1,X2] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
| ( X1 = c_Groups_Oplus__class_Oplus(X2,X1,X0)
<=> X0 = c_Groups_Ozero__class_Ozero(X2) ) ),
inference(ennf_transformation,[],[f459]) ).
fof(f1815,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Ozero__class_Ozero(X1)
<=> X0 = c_Groups_Ozero__class_Ozero(X1) ) ),
inference(ennf_transformation,[],[f460]) ).
fof(f1816,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Oorder(X2,X1,X0))),X0)) ),
inference(ennf_transformation,[],[f461]) ).
fof(f1817,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__ring__1(X2)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Osynthetic__div(X2,X0,X1)),c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X0),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))) = X0 ),
inference(ennf_transformation,[],[f462]) ).
fof(f1818,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
& X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) )
| c_Polynomial_Opos__poly(X2,X0) ) ) ),
inference(ennf_transformation,[],[f464]) ).
fof(f1821,plain,
! [X0,X1,X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ),
inference(ennf_transformation,[],[f466]) ).
fof(f1822,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| 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)),X0) ),
inference(ennf_transformation,[],[f472]) ).
fof(f1823,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
inference(ennf_transformation,[],[f473]) ).
fof(f1824,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0) ),
inference(ennf_transformation,[],[f474]) ).
fof(f1825,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0) ),
inference(flattening,[],[f1824]) ).
fof(f1826,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| X1 = X0 ),
inference(ennf_transformation,[],[f475]) ).
fof(f1827,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| X1 = X0 ),
inference(flattening,[],[f1826]) ).
fof(f1828,plain,
! [X0,X1,X2,X3] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)) ),
inference(ennf_transformation,[],[f476]) ).
fof(f1829,plain,
! [X0,X1,X2,X3] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)) ),
inference(flattening,[],[f1828]) ).
fof(f1830,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| 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),X0)) ),
inference(ennf_transformation,[],[f477]) ).
fof(f1831,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Ocomm__semiring__0(X4)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Polynomial_Omonom(X4,X3,X2)),c_Polynomial_Omonom(X4,X1,X0)) = c_Polynomial_Omonom(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(ennf_transformation,[],[f485]) ).
fof(f1832,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) ),
inference(ennf_transformation,[],[f487]) ).
fof(f1835,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(ennf_transformation,[],[f490]) ).
fof(f1836,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
| ( ( X1 != X0
& X3 != X2 )
<=> c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) != c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X1)) ) ),
inference(ennf_transformation,[],[f491]) ).
fof(f1837,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(ennf_transformation,[],[f492]) ).
fof(f1838,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(ennf_transformation,[],[f495]) ).
fof(f1839,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(ennf_transformation,[],[f496]) ).
fof(f1840,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oring(X2)
| c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(ennf_transformation,[],[f498]) ).
fof(f1841,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oring(X2)
| c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) ),
inference(ennf_transformation,[],[f499]) ).
fof(f1842,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oring(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(ennf_transformation,[],[f500]) ).
fof(f1843,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oring(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),c_Groups_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) ),
inference(ennf_transformation,[],[f501]) ).
fof(f1844,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
<=> ( X1 = c_Groups_Ouminus__class_Ouminus(X2,X0)
| X1 = X0 ) ) ),
inference(ennf_transformation,[],[f502]) ).
fof(f1845,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(ennf_transformation,[],[f503]) ).
fof(f1848,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1) ),
inference(ennf_transformation,[],[f506]) ).
fof(f1850,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) ),
inference(ennf_transformation,[],[f508]) ).
fof(f1851,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(ennf_transformation,[],[f509]) ).
fof(f1852,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) ),
inference(ennf_transformation,[],[f510]) ).
fof(f1853,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(ennf_transformation,[],[f511]) ).
fof(f1854,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f512]) ).
fof(f1855,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f513]) ).
fof(f1856,plain,
! [X0,X1] :
( ~ class_Rings_Omult__zero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f514]) ).
fof(f1857,plain,
! [X0,X1] :
( ~ class_Rings_Omult__zero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f515]) ).
fof(f1858,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oring__no__zero__divisors(X2)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X0 = c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(ennf_transformation,[],[f516]) ).
fof(f1861,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ono__zero__divisors(X2)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)
| X0 = c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ozero__class_Ozero(X2) ),
inference(ennf_transformation,[],[f518]) ).
fof(f1862,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ono__zero__divisors(X2)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)
| X0 = c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ozero__class_Ozero(X2) ),
inference(flattening,[],[f1861]) ).
fof(f1863,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(ennf_transformation,[],[f519]) ).
fof(f1864,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Osemiring(X4)
| c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oplus__class_Oplus(X4,X3,X1)),X2),X0) ),
inference(ennf_transformation,[],[f520]) ).
fof(f1865,plain,
! [X0,X1] :
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(ennf_transformation,[],[f521]) ).
fof(f1866,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__mult(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(ennf_transformation,[],[f522]) ).
fof(f1867,plain,
! [X0,X1] :
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(ennf_transformation,[],[f523]) ).
fof(f1868,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__mult(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(ennf_transformation,[],[f524]) ).
fof(f1869,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))) ),
inference(ennf_transformation,[],[f525]) ).
fof(f1870,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))) ),
inference(ennf_transformation,[],[f526]) ).
fof(f1871,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))) ),
inference(ennf_transformation,[],[f527]) ).
fof(f1872,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))) ),
inference(flattening,[],[f1871]) ).
fof(f1873,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ),
inference(ennf_transformation,[],[f528]) ).
fof(f1874,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ),
inference(flattening,[],[f1873]) ).
fof(f1875,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))) ),
inference(ennf_transformation,[],[f529]) ).
fof(f1876,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))) ),
inference(flattening,[],[f1875]) ).
fof(f1877,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Odvd(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X2)) ),
inference(ennf_transformation,[],[f530]) ).
fof(f1878,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Odvd(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X2)) ),
inference(flattening,[],[f1877]) ).
fof(f1879,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0)) ),
inference(ennf_transformation,[],[f531]) ).
fof(f1880,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0)) ),
inference(flattening,[],[f1879]) ).
fof(f1881,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0)) ),
inference(ennf_transformation,[],[f532]) ).
fof(f1882,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0)) ),
inference(flattening,[],[f1881]) ).
fof(f1883,plain,
! [X0,X1,X2] :
( ~ class_Groups_Omonoid__mult(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(ennf_transformation,[],[f533]) ).
fof(f1884,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocomm__monoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(ennf_transformation,[],[f534]) ).
fof(f1885,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(ennf_transformation,[],[f535]) ).
fof(f1886,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ c_Polynomial_Opos__poly(X2,X0)
| c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) ),
inference(ennf_transformation,[],[f539]) ).
fof(f1887,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ c_Polynomial_Opos__poly(X2,X0)
| c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) ),
inference(flattening,[],[f1886]) ).
fof(f1888,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oab__semigroup__mult(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(ennf_transformation,[],[f540]) ).
fof(f1889,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(ennf_transformation,[],[f541]) ).
fof(f1890,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(ennf_transformation,[],[f542]) ).
fof(f1891,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
inference(ennf_transformation,[],[f543]) ).
fof(f1892,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0) = c_Polynomial_Osmult(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0)) ),
inference(ennf_transformation,[],[f544]) ).
fof(f1893,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0)) ),
inference(ennf_transformation,[],[f545]) ).
fof(f1894,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0)) ),
inference(ennf_transformation,[],[f546]) ).
fof(f1895,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)) ),
inference(ennf_transformation,[],[f547]) ).
fof(f1896,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ) ),
inference(ennf_transformation,[],[f548]) ).
fof(f1897,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ) ),
inference(ennf_transformation,[],[f549]) ).
fof(f1898,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oordered__cancel__semiring(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),X0)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(ennf_transformation,[],[f550]) ).
fof(f1899,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oordered__cancel__semiring(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),X0)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(flattening,[],[f1898]) ).
fof(f1908,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oordered__semiring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(ennf_transformation,[],[f555]) ).
fof(f1909,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oordered__semiring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(flattening,[],[f1908]) ).
fof(f1910,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oordered__semiring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(ennf_transformation,[],[f556]) ).
fof(f1911,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oordered__semiring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(flattening,[],[f1910]) ).
fof(f1912,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oordered__comm__semiring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(ennf_transformation,[],[f557]) ).
fof(f1913,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oordered__comm__semiring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(flattening,[],[f1912]) ).
fof(f1914,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oordered__ring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(ennf_transformation,[],[f558]) ).
fof(f1915,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oordered__ring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(flattening,[],[f1914]) ).
fof(f1916,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oordered__ring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)) ),
inference(ennf_transformation,[],[f559]) ).
fof(f1917,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oordered__ring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)) ),
inference(flattening,[],[f1916]) ).
fof(f1918,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Oordered__semiring(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(ennf_transformation,[],[f560]) ).
fof(f1919,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Oordered__semiring(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(flattening,[],[f1918]) ).
fof(f1920,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Oordered__semiring(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(ennf_transformation,[],[f561]) ).
fof(f1921,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Oordered__semiring(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(flattening,[],[f1920]) ).
fof(f1922,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oordered__ring(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(ennf_transformation,[],[f562]) ).
fof(f1923,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oordered__ring(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(flattening,[],[f1922]) ).
fof(f1924,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oordered__cancel__semiring(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(ennf_transformation,[],[f563]) ).
fof(f1925,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oordered__cancel__semiring(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(flattening,[],[f1924]) ).
fof(f1930,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(ennf_transformation,[],[f566]) ).
fof(f1931,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(flattening,[],[f1930]) ).
fof(f1932,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(ennf_transformation,[],[f567]) ).
fof(f1933,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(flattening,[],[f1932]) ).
fof(f1934,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(ennf_transformation,[],[f568]) ).
fof(f1935,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(flattening,[],[f1934]) ).
fof(f1936,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(ennf_transformation,[],[f569]) ).
fof(f1937,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(flattening,[],[f1936]) ).
fof(f1940,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ),
inference(ennf_transformation,[],[f571]) ).
fof(f1941,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ),
inference(flattening,[],[f1940]) ).
fof(f1942,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ),
inference(ennf_transformation,[],[f572]) ).
fof(f1943,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ),
inference(flattening,[],[f1942]) ).
fof(f1944,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0) ),
inference(ennf_transformation,[],[f573]) ).
fof(f1945,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0) ),
inference(flattening,[],[f1944]) ).
fof(f1946,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),c_Groups_Ozero__class_Ozero(X2)) ),
inference(ennf_transformation,[],[f574]) ).
fof(f1947,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),c_Groups_Ozero__class_Ozero(X2)) ),
inference(flattening,[],[f1946]) ).
fof(f1948,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(ennf_transformation,[],[f575]) ).
fof(f1949,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(flattening,[],[f1948]) ).
fof(f1950,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(ennf_transformation,[],[f576]) ).
fof(f1951,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(flattening,[],[f1950]) ).
fof(f1952,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ),
inference(ennf_transformation,[],[f577]) ).
fof(f1953,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ),
inference(flattening,[],[f1952]) ).
fof(f1954,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X1,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) ) ),
inference(ennf_transformation,[],[f578]) ).
fof(f1955,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
<=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X2,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) ) ),
inference(ennf_transformation,[],[f579]) ).
fof(f1956,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(ennf_transformation,[],[f580]) ).
fof(f1957,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0)) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(ennf_transformation,[],[f581]) ).
fof(f1958,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
| c_Groups_Ozero__class_Ozero(X5) = X4
| X0 = X1
| X2 != X3
| c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X1)) != c_Groups_Oplus__class_Oplus(X5,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X0)) ),
inference(ennf_transformation,[],[f582]) ).
fof(f1959,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
| c_Groups_Ozero__class_Ozero(X5) = X4
| X0 = X1
| X2 != X3
| c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X1)) != c_Groups_Oplus__class_Oplus(X5,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X0)) ),
inference(flattening,[],[f1958]) ).
fof(f1960,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(ennf_transformation,[],[f583]) ).
fof(f1961,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(flattening,[],[f1960]) ).
fof(f1962,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oidom(X3)
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| X2 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
inference(ennf_transformation,[],[f584]) ).
fof(f1963,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oidom(X3)
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| X1 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
inference(ennf_transformation,[],[f585]) ).
fof(f1964,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,X0) = 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))),X0) ),
inference(ennf_transformation,[],[f586]) ).
fof(f1965,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X0,c_Groups_Oone__class_Oone(X2))),X1) ),
inference(ennf_transformation,[],[f587]) ).
fof(f1966,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2))),X0) ),
inference(ennf_transformation,[],[f588]) ).
fof(f1967,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(ennf_transformation,[],[f589]) ).
fof(f1968,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
| c_Polynomial_Opos__poly(X1,X0)
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(ennf_transformation,[],[f590]) ).
fof(f1969,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
| c_Polynomial_Opos__poly(X1,X0)
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(flattening,[],[f1968]) ).
fof(f1970,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__ring__1(X3)
| hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Omonom(X3,c_Groups_Oone__class_Oone(X3),X2)),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(ennf_transformation,[],[f591]) ).
fof(f1971,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__ring__1(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0) ),
inference(ennf_transformation,[],[f592]) ).
fof(f1972,plain,
! [X0,X1] :
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
<=> ( X0 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| X0 = c_Groups_Oone__class_Oone(X1) ) ) ),
inference(ennf_transformation,[],[f593]) ).
fof(f1973,plain,
! [X0,X1,X2] :
( ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(ennf_transformation,[],[f594]) ).
fof(f1974,plain,
! [X0,X1,X2] :
( ~ class_Groups_Omonoid__mult(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) ),
inference(ennf_transformation,[],[f595]) ).
fof(f1976,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) ),
inference(ennf_transformation,[],[f597]) ).
fof(f1977,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) ),
inference(ennf_transformation,[],[f598]) ).
fof(f1978,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) ),
inference(ennf_transformation,[],[f599]) ).
fof(f1979,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(ennf_transformation,[],[f600]) ).
fof(f1980,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ c_Polynomial_Opos__poly(X2,X0)
| c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) ),
inference(ennf_transformation,[],[f601]) ).
fof(f1981,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ c_Polynomial_Opos__poly(X2,X0)
| c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) ),
inference(flattening,[],[f1980]) ).
fof(f1982,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,c_Polynomial_OpCons(X3,X1,X0)) = c_Polynomial_OpCons(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),c_Polynomial_Osmult(X3,X2,X0)) ),
inference(ennf_transformation,[],[f602]) ).
fof(f1983,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(ennf_transformation,[],[f603]) ).
fof(f1984,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
inference(ennf_transformation,[],[f604]) ).
fof(f1985,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ),
inference(ennf_transformation,[],[f605]) ).
fof(f1986,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ),
inference(flattening,[],[f1985]) ).
fof(f1987,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(ennf_transformation,[],[f606]) ).
fof(f1988,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(flattening,[],[f1987]) ).
fof(f1989,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless(X3,X1,X0) ),
inference(ennf_transformation,[],[f607]) ).
fof(f1990,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless(X3,X1,X0) ),
inference(flattening,[],[f1989]) ).
fof(f1991,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless(X3,X1,X0) ),
inference(ennf_transformation,[],[f608]) ).
fof(f1992,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless(X3,X1,X0) ),
inference(flattening,[],[f1991]) ).
fof(f1993,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(ennf_transformation,[],[f609]) ).
fof(f1994,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(flattening,[],[f1993]) ).
fof(f1995,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(ennf_transformation,[],[f610]) ).
fof(f1996,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semiring(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(flattening,[],[f1995]) ).
fof(f1997,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Olinordered__semiring__strict(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(ennf_transformation,[],[f611]) ).
fof(f1998,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Olinordered__semiring__strict(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(flattening,[],[f1997]) ).
fof(f1999,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Olinordered__semiring__strict(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(ennf_transformation,[],[f612]) ).
fof(f2000,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Olinordered__semiring__strict(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(flattening,[],[f1999]) ).
fof(f2001,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Olinordered__semiring__strict(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(ennf_transformation,[],[f613]) ).
fof(f2002,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Olinordered__semiring__strict(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(flattening,[],[f2001]) ).
fof(f2003,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Olinordered__semiring__strict(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(ennf_transformation,[],[f614]) ).
fof(f2004,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Olinordered__semiring__strict(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(flattening,[],[f2003]) ).
fof(f2005,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ) ),
inference(ennf_transformation,[],[f615]) ).
fof(f2006,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ) ),
inference(flattening,[],[f2005]) ).
fof(f2007,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ),
inference(ennf_transformation,[],[f616]) ).
fof(f2008,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ),
inference(flattening,[],[f2007]) ).
fof(f2009,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring(X2)
| c_Orderings_Oord__class_Oless__eq(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),X0),X0))) ),
inference(ennf_transformation,[],[f617]) ).
fof(f2010,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
<=> ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(ennf_transformation,[],[f618]) ).
fof(f2011,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring(X2)
| ~ c_Orderings_Oord__class_Oless(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),X0),X0)),c_Groups_Ozero__class_Ozero(X2)) ),
inference(ennf_transformation,[],[f619]) ).
fof(f2012,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0)))
<=> ( X0 != c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(ennf_transformation,[],[f620]) ).
fof(f2013,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(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),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),X1) ),
inference(ennf_transformation,[],[f621]) ).
fof(f2014,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(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),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),X1) ),
inference(flattening,[],[f2013]) ).
fof(f2015,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(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),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1) ),
inference(ennf_transformation,[],[f622]) ).
fof(f2016,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(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),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1) ),
inference(flattening,[],[f2015]) ).
fof(f2017,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))) ),
inference(ennf_transformation,[],[f623]) ).
fof(f2018,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))) ),
inference(flattening,[],[f2017]) ).
fof(f2019,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))) ),
inference(ennf_transformation,[],[f624]) ).
fof(f2020,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))) ),
inference(flattening,[],[f2019]) ).
fof(f2021,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oring__1(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(ennf_transformation,[],[f625]) ).
fof(f2022,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))) ),
inference(ennf_transformation,[],[f626]) ).
fof(f2023,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)) ),
inference(ennf_transformation,[],[f627]) ).
fof(f2024,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)) ),
inference(flattening,[],[f2023]) ).
fof(f2025,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))) ),
inference(ennf_transformation,[],[f628]) ).
fof(f2026,plain,
! [X0,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
inference(ennf_transformation,[],[f629]) ).
fof(f2027,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ouminus(X3)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0)) ),
inference(ennf_transformation,[],[f630]) ).
fof(f2028,plain,
! [X0,X1,X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0)
<=> X1 = X0 ) ),
inference(ennf_transformation,[],[f631]) ).
fof(f2029,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
inference(ennf_transformation,[],[f632]) ).
fof(f2030,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Olinordered__semiring__1(X5)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| c_Groups_Oplus__class_Oplus(X5,X1,X0) != c_Groups_Oone__class_Oone(X5)
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3) ),
inference(ennf_transformation,[],[f633]) ).
fof(f2031,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Olinordered__semiring__1(X5)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| c_Groups_Oplus__class_Oplus(X5,X1,X0) != c_Groups_Oone__class_Oone(X5)
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3) ),
inference(flattening,[],[f2030]) ).
fof(f2032,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(ennf_transformation,[],[f634]) ).
fof(f2033,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(flattening,[],[f2032]) ).
fof(f2034,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0))) ),
inference(ennf_transformation,[],[f635]) ).
fof(f2035,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0))) ),
inference(ennf_transformation,[],[f636]) ).
fof(f2036,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Olinordered__semiring__1__strict(X5)
| ~ c_Orderings_Oord__class_Oless(X5,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| c_Groups_Oplus__class_Oplus(X5,X1,X0) != c_Groups_Oone__class_Oone(X5)
| c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3) ),
inference(ennf_transformation,[],[f637]) ).
fof(f2037,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Olinordered__semiring__1__strict(X5)
| ~ c_Orderings_Oord__class_Oless(X5,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| c_Groups_Oplus__class_Oplus(X5,X1,X0) != c_Groups_Oone__class_Oone(X5)
| c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3) ),
inference(flattening,[],[f2036]) ).
fof(f2038,plain,
! [X0,X1,X2] :
( ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2)
| ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
<=> ? [X4] :
( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) ) ) ),
inference(ennf_transformation,[],[f1208]) ).
fof(f2039,plain,
! [X0,X1,X2] :
( ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2)
| ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
<=> ? [X4] :
( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) ) ) ),
inference(flattening,[],[f2038]) ).
fof(f2040,plain,
! [X0,X1] :
( ~ 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0)) ),
inference(ennf_transformation,[],[f639]) ).
fof(f2041,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Opcompose(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X0),c_Polynomial_Opcompose(X3,X1,X0))) ),
inference(ennf_transformation,[],[f640]) ).
fof(f2042,plain,
! [X0] :
( ~ class_Power_Opower(X0)
| c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0)) ),
inference(ennf_transformation,[],[f641]) ).
fof(f2043,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(ennf_transformation,[],[f649]) ).
fof(f2044,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0) ),
inference(ennf_transformation,[],[f655]) ).
fof(f2045,plain,
! [X0,X1] :
( ~ 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),X0)
| 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),X0)) ),
inference(ennf_transformation,[],[f657]) ).
fof(f2046,plain,
! [X0,X1] :
( ~ 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),X0)
| 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),X0)) ),
inference(flattening,[],[f2045]) ).
fof(f2047,plain,
! [X0,X1,X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| 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),X2),X0)) ),
inference(ennf_transformation,[],[f660]) ).
fof(f2048,plain,
! [X0,X1,X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| 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),X2),X0)) ),
inference(flattening,[],[f2047]) ).
fof(f2051,plain,
! [X0,X1,X2,X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3))
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X1))) ) ),
inference(ennf_transformation,[],[f669]) ).
fof(f2052,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))) ) ),
inference(ennf_transformation,[],[f675]) ).
fof(f2053,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Opcompose(X2,X1,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),c_Polynomial_Odegree(X2,X0))) ),
inference(ennf_transformation,[],[f676]) ).
fof(f2058,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)) ),
inference(ennf_transformation,[],[f686]) ).
fof(f2059,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)) ),
inference(flattening,[],[f2058]) ).
fof(f2060,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X0 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X1 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
inference(ennf_transformation,[],[f687]) ).
fof(f2061,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(ennf_transformation,[],[f689]) ).
fof(f2062,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(flattening,[],[f2061]) ).
fof(f2063,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(ennf_transformation,[],[f690]) ).
fof(f2064,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(flattening,[],[f2063]) ).
fof(f2065,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(ennf_transformation,[],[f692]) ).
fof(f2066,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Opcompose(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(ennf_transformation,[],[f693]) ).
fof(f2067,plain,
! [X0,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)),X0)
| 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),X0),X1)) ),
inference(ennf_transformation,[],[f696]) ).
fof(f2068,plain,
! [X0,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)),X0)
| 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),X0),X1)) ),
inference(flattening,[],[f2067]) ).
fof(f2069,plain,
! [X0,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)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(ennf_transformation,[],[f697]) ).
fof(f2070,plain,
! [X0,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)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(flattening,[],[f2069]) ).
fof(f2071,plain,
! [X0,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)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(ennf_transformation,[],[f698]) ).
fof(f2072,plain,
! [X0,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)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(flattening,[],[f2071]) ).
fof(f2075,plain,
! [X0,X1,X2] :
( 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),X0),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,X2,X0) ) ),
inference(ennf_transformation,[],[f701]) ).
fof(f2076,plain,
! [X0,X1,X2] :
( 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),X2),X0))
<=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(ennf_transformation,[],[f702]) ).
fof(f2077,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),X0)) ),
inference(ennf_transformation,[],[f703]) ).
fof(f2078,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),X1))
<=> X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(ennf_transformation,[],[f706]) ).
fof(f2079,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X1))
<=> X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(ennf_transformation,[],[f707]) ).
fof(f2082,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != 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,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(ennf_transformation,[],[f711]) ).
fof(f2083,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != 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,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(flattening,[],[f2082]) ).
fof(f2084,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(ennf_transformation,[],[f712]) ).
fof(f2085,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(flattening,[],[f2084]) ).
fof(f2086,plain,
! [X0,X1,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),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,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),X1) ),
inference(ennf_transformation,[],[f713]) ).
fof(f2087,plain,
! [X0,X1,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),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,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),X1) ),
inference(flattening,[],[f2086]) ).
fof(f2088,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3)
| ~ 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),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ 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,X5)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4) ),
inference(ennf_transformation,[],[f718]) ).
fof(f2089,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3)
| ~ 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),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ 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,X5)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4) ),
inference(flattening,[],[f2088]) ).
fof(f2090,plain,
! [X0,X1,X2,X3,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),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
inference(ennf_transformation,[],[f719]) ).
fof(f2091,plain,
! [X0,X1,X2,X3,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),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
inference(flattening,[],[f2090]) ).
fof(f2092,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3)
| ~ 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),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
| ~ 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),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1) ),
inference(ennf_transformation,[],[f720]) ).
fof(f2093,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3)
| ~ 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),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
| ~ 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),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1) ),
inference(flattening,[],[f2092]) ).
fof(f2094,plain,
! [X0,X1,X2,X3,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),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0))
| ~ 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,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1) ),
inference(ennf_transformation,[],[f721]) ).
fof(f2095,plain,
! [X0,X1,X2,X3,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),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0))
| ~ 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,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1) ),
inference(flattening,[],[f2094]) ).
fof(f2096,plain,
! [X0,X1,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),X1),X0),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),X0)
| ~ 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,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(ennf_transformation,[],[f722]) ).
fof(f2097,plain,
! [X0,X1,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),X1),X0),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),X0)
| ~ 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,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(flattening,[],[f2096]) ).
fof(f2098,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ( 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),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(ennf_transformation,[],[f723]) ).
fof(f2099,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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),X2),X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ) ),
inference(ennf_transformation,[],[f724]) ).
fof(f2100,plain,
! [X0,X1,X2] :
( ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(ennf_transformation,[],[f727]) ).
fof(f2101,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
<=> X1 = X0 ) ),
inference(ennf_transformation,[],[f728]) ).
fof(f2102,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Fields_Ofield(X4)
| ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) )
& X3 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) ) ) ),
inference(ennf_transformation,[],[f730]) ).
fof(f2103,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Fields_Ofield(X4)
| ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) )
& X3 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) ) ) ),
inference(flattening,[],[f2102]) ).
fof(f2105,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| ( c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
<=> ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
& X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ) ),
inference(ennf_transformation,[],[f732]) ).
fof(f2106,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| ( c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
<=> ( X0 = X2
& X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ) ),
inference(ennf_transformation,[],[f733]) ).
fof(f2107,plain,
! [X0,X1] :
( ~ class_Fields_Ofield(X1)
| c_Polynomial_Opdivmod__rel(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(ennf_transformation,[],[f734]) ).
fof(f2108,plain,
! [X0,X1] :
( ~ class_Fields_Ofield(X1)
| c_Polynomial_Opdivmod__rel(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
inference(ennf_transformation,[],[f735]) ).
fof(f2109,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Fields_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X5,X4,X3,X2,X1)
| c_Polynomial_Opdivmod__rel(X5,c_Polynomial_Osmult(X5,X0,X4),X3,c_Polynomial_Osmult(X5,X0,X2),c_Polynomial_Osmult(X5,X0,X1)) ),
inference(ennf_transformation,[],[f736]) ).
fof(f2110,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Fields_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X5,X4,X3,X2,X1)
| c_Polynomial_Opdivmod__rel(X5,c_Polynomial_Osmult(X5,X0,X4),X3,c_Polynomial_Osmult(X5,X0,X2),c_Polynomial_Osmult(X5,X0,X1)) ),
inference(flattening,[],[f2109]) ).
fof(f2111,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ class_Fields_Ofield(X6)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
| ( X2 = X0
& X3 = X1 ) ),
inference(ennf_transformation,[],[f737]) ).
fof(f2112,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ class_Fields_Ofield(X6)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
| ( X2 = X0
& X3 = X1 ) ),
inference(flattening,[],[f2111]) ).
fof(f2117,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ class_Fields_Ofield(X7)
| ~ c_Polynomial_Opdivmod__rel(X7,X6,X5,X4,X3)
| ~ c_Polynomial_Opdivmod__rel(X7,X4,X2,X1,X0)
| c_Polynomial_Opdivmod__rel(X7,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X2),X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X0),X3)) ),
inference(ennf_transformation,[],[f740]) ).
fof(f2118,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ class_Fields_Ofield(X7)
| ~ c_Polynomial_Opdivmod__rel(X7,X6,X5,X4,X3)
| ~ c_Polynomial_Opdivmod__rel(X7,X4,X2,X1,X0)
| c_Polynomial_Opdivmod__rel(X7,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X2),X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X0),X3)) ),
inference(flattening,[],[f2117]) ).
fof(f2120,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f742]) ).
fof(f2122,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f744]) ).
fof(f2126,plain,
! [X0,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(ennf_transformation,[],[f748]) ).
fof(f2128,plain,
! [X0,X1,X2] :
( ~ class_RealVector_Oreal__normed__algebra(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(ennf_transformation,[],[f750]) ).
fof(f2129,plain,
! [X0,X1,X2] :
( ~ class_RealVector_Oreal__normed__algebra(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(ennf_transformation,[],[f751]) ).
fof(f2130,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ? [X3] :
( hBOOL(hAPP(X1,X3))
& ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ! [X4] :
( ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)))) ) ),
inference(ennf_transformation,[],[f1209]) ).
fof(f2131,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ? [X3] :
( hBOOL(hAPP(X1,X3))
& ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ! [X4] :
( ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)))) ) ),
inference(flattening,[],[f2130]) ).
fof(f2132,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X0))
| ? [X2] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ hBOOL(hAPP(X1,X3)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ) ),
inference(ennf_transformation,[],[f753]) ).
fof(f2133,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X0))
| ? [X2] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ hBOOL(hAPP(X1,X3)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ) ),
inference(flattening,[],[f2132]) ).
fof(f2134,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(ennf_transformation,[],[f754]) ).
fof(f2135,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(flattening,[],[f2134]) ).
fof(f2136,plain,
! [X0,X1,X2] :
( ~ class_Groups_Omonoid__mult(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) ),
inference(ennf_transformation,[],[f755]) ).
fof(f2137,plain,
! [X0,X1,X2] :
( ~ class_Groups_Omonoid__mult(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) ),
inference(flattening,[],[f2136]) ).
fof(f2138,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1)) != hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X0),X1))
| X1 = X0 ),
inference(ennf_transformation,[],[f756]) ).
fof(f2139,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1)) != hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X0),X1))
| X1 = X0 ),
inference(flattening,[],[f2138]) ).
fof(f2140,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ozero(X3)
| ( ( X1 = X2
| hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) = c_Groups_Ozero__class_Ozero(X3) )
& ( X1 != X2
| hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) = X0 ) ) ),
inference(ennf_transformation,[],[f757]) ).
fof(f2141,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ocomm__monoid__add(X3)
| hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0)) ),
inference(ennf_transformation,[],[f758]) ).
fof(f2142,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,X0,X1) ),
inference(ennf_transformation,[],[f759]) ).
fof(f2143,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
inference(ennf_transformation,[],[f760]) ).
fof(f2144,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
inference(ennf_transformation,[],[f761]) ).
fof(f2145,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ),
inference(ennf_transformation,[],[f767]) ).
fof(f2146,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ),
inference(ennf_transformation,[],[f768]) ).
fof(f2147,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__ring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0))) ),
inference(ennf_transformation,[],[f769]) ).
fof(f2148,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__ring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0))) ),
inference(flattening,[],[f2147]) ).
fof(f2149,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(ennf_transformation,[],[f772]) ).
fof(f2150,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(flattening,[],[f2149]) ).
fof(f2151,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oab__group__add(X3)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Ominus__class_Ominus(X3,X2,X0),X1) ),
inference(ennf_transformation,[],[f773]) ).
fof(f2152,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oab__group__add(X4)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Ominus__class_Ominus(X4,X3,X1),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),X2,X0)) ),
inference(ennf_transformation,[],[f774]) ).
fof(f2153,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__ring(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(ennf_transformation,[],[f775]) ).
fof(f2154,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__ring(X3)
| c_Polynomial_Osmult(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0)) ),
inference(ennf_transformation,[],[f776]) ).
fof(f2155,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oab__group__add(X3)
| hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0)) ),
inference(ennf_transformation,[],[f778]) ).
fof(f2156,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( c_Polynomial_Ocoeff(X2,X1) = c_Polynomial_Ocoeff(X2,X0)
<=> X1 = X0 ) ),
inference(ennf_transformation,[],[f779]) ).
fof(f2157,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( X1 = X0
<=> ! [X3] : hAPP(c_Polynomial_Ocoeff(X2,X1),X3) = hAPP(c_Polynomial_Ocoeff(X2,X0),X3) ) ),
inference(ennf_transformation,[],[f780]) ).
fof(f2158,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ( X3 = X2
<=> X1 = X0 ) ),
inference(ennf_transformation,[],[f781]) ).
fof(f2159,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ( X3 = X2
<=> X1 = X0 ) ),
inference(flattening,[],[f2158]) ).
fof(f2160,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Ominus(X4)
| hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0)) ),
inference(ennf_transformation,[],[f782]) ).
fof(f2161,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ( 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,X0,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(ennf_transformation,[],[f783]) ).
fof(f2162,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ( 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,X0,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(flattening,[],[f2161]) ).
fof(f2163,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f784]) ).
fof(f2164,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f2163]) ).
fof(f2165,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)
<=> X1 = X0 ) ),
inference(ennf_transformation,[],[f785]) ).
fof(f2166,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)
<=> X1 = X0 ) ),
inference(flattening,[],[f2165]) ).
fof(f2167,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1 ),
inference(ennf_transformation,[],[f786]) ).
fof(f2168,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
inference(ennf_transformation,[],[f787]) ).
fof(f2169,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ),
inference(ennf_transformation,[],[f788]) ).
fof(f2170,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ),
inference(ennf_transformation,[],[f790]) ).
fof(f2171,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ),
inference(flattening,[],[f2170]) ).
fof(f2172,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1) ),
inference(ennf_transformation,[],[f791]) ).
fof(f2175,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__ab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ( c_Orderings_Oord__class_Oless(X4,X3,X2)
<=> c_Orderings_Oord__class_Oless(X4,X1,X0) ) ),
inference(ennf_transformation,[],[f796]) ).
fof(f2176,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__ab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ( c_Orderings_Oord__class_Oless(X4,X3,X2)
<=> c_Orderings_Oord__class_Oless(X4,X1,X0) ) ),
inference(flattening,[],[f2175]) ).
fof(f2177,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__ab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
<=> c_Orderings_Oord__class_Oless__eq(X4,X1,X0) ) ),
inference(ennf_transformation,[],[f797]) ).
fof(f2178,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__ab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
<=> c_Orderings_Oord__class_Oless__eq(X4,X1,X0) ) ),
inference(flattening,[],[f2177]) ).
fof(f2179,plain,
! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(ennf_transformation,[],[f798]) ).
fof(f2181,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oab__group__add(X2)
| ( X1 = X0
<=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2) ) ),
inference(ennf_transformation,[],[f800]) ).
fof(f2182,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
<=> X1 = X0 ) ),
inference(ennf_transformation,[],[f801]) ).
fof(f2183,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X2,X1)),c_Nat_OSuc(X0)) = hAPP(c_Polynomial_Ocoeff(X3,X1),X0) ),
inference(ennf_transformation,[],[f802]) ).
fof(f2184,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Ocoeff(X3,X1),X0)) ),
inference(ennf_transformation,[],[f803]) ).
fof(f2185,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ),
inference(ennf_transformation,[],[f804]) ).
fof(f2186,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ),
inference(ennf_transformation,[],[f807]) ).
fof(f2187,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2)) ),
inference(ennf_transformation,[],[f809]) ).
fof(f2190,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ) ),
inference(ennf_transformation,[],[f812]) ).
fof(f2193,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(ennf_transformation,[],[f815]) ).
fof(f2195,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0) ),
inference(ennf_transformation,[],[f817]) ).
fof(f2196,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0)) ),
inference(ennf_transformation,[],[f818]) ).
fof(f2197,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0)) ),
inference(flattening,[],[f2196]) ).
fof(f2198,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(ennf_transformation,[],[f819]) ).
fof(f2199,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(flattening,[],[f2198]) ).
fof(f2200,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ( 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,X0,X2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(ennf_transformation,[],[f820]) ).
fof(f2201,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ( 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,X0,X2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(flattening,[],[f2200]) ).
fof(f2202,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
inference(ennf_transformation,[],[f821]) ).
fof(f2203,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
inference(flattening,[],[f2202]) ).
fof(f2204,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ),
inference(ennf_transformation,[],[f822]) ).
fof(f2205,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f824]) ).
fof(f2207,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(ennf_transformation,[],[f827]) ).
fof(f2208,plain,
! [X0,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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0) ),
inference(ennf_transformation,[],[f830]) ).
fof(f2209,plain,
! [X0,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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0) ),
inference(flattening,[],[f2208]) ).
fof(f2210,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Oplus__class_Oplus(X2,X1,X0) ),
inference(ennf_transformation,[],[f832]) ).
fof(f2211,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__ring__1(X2)
| c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(ennf_transformation,[],[f833]) ).
fof(f2212,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(ennf_transformation,[],[f834]) ).
fof(f2213,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(ennf_transformation,[],[f835]) ).
fof(f2214,plain,
! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ouminus__class_Ouminus(X1,X0) ),
inference(ennf_transformation,[],[f836]) ).
fof(f2215,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Rings_Oring(X4)
| c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0)) ),
inference(ennf_transformation,[],[f837]) ).
fof(f2216,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Oring(X5)
| ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
<=> c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2) = X0 ) ),
inference(ennf_transformation,[],[f838]) ).
fof(f2217,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Oring(X5)
| ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
<=> X2 = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0) ) ),
inference(ennf_transformation,[],[f839]) ).
fof(f2218,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oab__group__add(X2)
| hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Ocoeff(X2,X1),X0)) ),
inference(ennf_transformation,[],[f842]) ).
fof(f2219,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),c_Groups_Ominus__class_Ominus(X4,X2,X0))) ),
inference(ennf_transformation,[],[f843]) ).
fof(f2221,plain,
! [X0,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(ennf_transformation,[],[f845]) ).
fof(f2223,plain,
! [X0,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(ennf_transformation,[],[f847]) ).
fof(f2224,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) ) ),
inference(ennf_transformation,[],[f848]) ).
fof(f2225,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) ) ),
inference(ennf_transformation,[],[f849]) ).
fof(f2226,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) ) ),
inference(ennf_transformation,[],[f850]) ).
fof(f2227,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) ) ),
inference(ennf_transformation,[],[f851]) ).
fof(f2228,plain,
! [X0,X1] :
( ~ class_Rings_Oring__1(X1)
| c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Oone__class_Oone(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Oone__class_Oone(X1))) ),
inference(ennf_transformation,[],[f852]) ).
fof(f2231,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Odvd(X3)
| ~ class_Rings_Ocomm__ring(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ! [X4,X5] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0))) ) ),
inference(ennf_transformation,[],[f854]) ).
fof(f2232,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Odvd(X3)
| ~ class_Rings_Ocomm__ring(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ! [X4,X5] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0))) ) ),
inference(flattening,[],[f2231]) ).
fof(f2234,plain,
! [X0,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,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),X1) ),
inference(ennf_transformation,[],[f856]) ).
fof(f2235,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
inference(ennf_transformation,[],[f857]) ).
fof(f2236,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> ( ! [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1
| hBOOL(hAPP(X2,X3)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
inference(ennf_transformation,[],[f858]) ).
fof(f2237,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Nat_OSuc(X1)) ),
inference(ennf_transformation,[],[f859]) ).
fof(f2238,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(ennf_transformation,[],[f860]) ).
fof(f2239,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| hAPP(c_Polynomial_Ocoeff(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2) ),
inference(ennf_transformation,[],[f861]) ).
fof(f2240,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| hAPP(c_Polynomial_Ocoeff(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2) ),
inference(flattening,[],[f2239]) ).
fof(f2241,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Polynomial_Odegree(X2,X1)) ),
inference(ennf_transformation,[],[f862]) ).
fof(f2242,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Polynomial_Odegree(X2,X1)) ),
inference(flattening,[],[f2241]) ).
fof(f2243,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) ) ),
inference(ennf_transformation,[],[f863]) ).
fof(f2244,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) ),
inference(ennf_transformation,[],[f864]) ).
fof(f2245,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1) = X0 ) ),
inference(ennf_transformation,[],[f865]) ).
fof(f2246,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ) ),
inference(ennf_transformation,[],[f866]) ).
fof(f2247,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ),
inference(ennf_transformation,[],[f867]) ).
fof(f2248,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)
<=> X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0) ) ),
inference(ennf_transformation,[],[f868]) ).
fof(f2251,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| ( hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0)) = c_Groups_Ozero__class_Ozero(X1)
<=> X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ) ),
inference(ennf_transformation,[],[f870]) ).
fof(f2252,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Polynomial_Odegree(X2,c_Polynomial_Osynthetic__div(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(ennf_transformation,[],[f871]) ).
fof(f2254,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0 ),
inference(ennf_transformation,[],[f873]) ).
fof(f2255,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0 ) ),
inference(ennf_transformation,[],[f874]) ).
fof(f2256,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ( 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),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) ) ),
inference(ennf_transformation,[],[f875]) ).
fof(f2257,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ( 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),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ) ),
inference(ennf_transformation,[],[f876]) ).
fof(f2258,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(ennf_transformation,[],[f877]) ).
fof(f2259,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(ennf_transformation,[],[f878]) ).
fof(f2260,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1))),hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))) ),
inference(ennf_transformation,[],[f879]) ).
fof(f2261,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Oone__class_Oone(X1) ) ) ),
inference(ennf_transformation,[],[f880]) ).
fof(f2262,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ( c_Polynomial_Opos__poly(X1,X0)
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))) ) ),
inference(ennf_transformation,[],[f881]) ).
fof(f2263,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)),X0) = c_Groups_Oone__class_Oone(X2) ),
inference(ennf_transformation,[],[f882]) ).
fof(f2264,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__ring__1(X2)
| c_Groups_Ominus__class_Ominus(X2,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),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(X2,X1,X0)) ),
inference(ennf_transformation,[],[f883]) ).
fof(f2265,plain,
! [X0,X1,X2] :
( ~ class_Power_Opower(X2)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = c_Groups_Oone__class_Oone(X2) ) ) ),
inference(ennf_transformation,[],[f884]) ).
fof(f2266,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Omonoid__mult(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),X0) ),
inference(ennf_transformation,[],[f885]) ).
fof(f2267,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Omonoid__mult(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),X0) ),
inference(flattening,[],[f2266]) ).
fof(f2268,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
<=> ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| X1 = X0 ) ) ),
inference(ennf_transformation,[],[f886]) ).
fof(f2269,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
<=> c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1)) ) ),
inference(ennf_transformation,[],[f887]) ).
fof(f2270,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Ocomm__ring(X3)
| c_Polynomial_Osmult(X3,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0)) ),
inference(ennf_transformation,[],[f888]) ).
fof(f2271,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
inference(ennf_transformation,[],[f889]) ).
fof(f2272,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
inference(flattening,[],[f2271]) ).
fof(f2273,plain,
! [X0,X1] :
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 ),
inference(ennf_transformation,[],[f890]) ).
fof(f2274,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oab__group__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ),
inference(ennf_transformation,[],[f893]) ).
fof(f2275,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oab__group__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ),
inference(flattening,[],[f2274]) ).
fof(f2276,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oab__group__add(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ),
inference(ennf_transformation,[],[f894]) ).
fof(f2277,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oab__group__add(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ),
inference(flattening,[],[f2276]) ).
fof(f2278,plain,
! [X0,X1] :
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0) ),
inference(ennf_transformation,[],[f898]) ).
fof(f2279,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ class_Fields_Ofield(X6)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) = X4
| c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))) != X1
| c_Polynomial_Opdivmod__rel(X6,c_Polynomial_OpCons(X6,X0,X5),X4,c_Polynomial_OpCons(X6,X1,X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X0,X2),c_Polynomial_Osmult(X6,X1,X4))) ),
inference(ennf_transformation,[],[f900]) ).
fof(f2280,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ class_Fields_Ofield(X6)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) = X4
| c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))) != X1
| c_Polynomial_Opdivmod__rel(X6,c_Polynomial_OpCons(X6,X0,X5),X4,c_Polynomial_OpCons(X6,X1,X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X0,X2),c_Polynomial_Osmult(X6,X1,X4))) ),
inference(flattening,[],[f2279]) ).
fof(f2281,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ominus__class_Ominus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) ),
inference(ennf_transformation,[],[f901]) ).
fof(f2283,plain,
! [X0,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) ),
inference(ennf_transformation,[],[f903]) ).
fof(f2285,plain,
! [X0,X1] :
( ~ class_Rings_Odivision__ring(X1)
| c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(ennf_transformation,[],[f905]) ).
fof(f2287,plain,
! [X0,X1] :
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| ( ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Rings_Oinverse__class_Odivide(X1,X0,X0) = c_Groups_Oone__class_Oone(X1) )
& ( c_Groups_Ozero__class_Ozero(X1) != X0
| c_Rings_Oinverse__class_Odivide(X1,X0,X0) = c_Groups_Ozero__class_Ozero(X1) ) ) ),
inference(ennf_transformation,[],[f907]) ).
fof(f2290,plain,
! [X0,X1,X2] :
( ~ class_Rings_Odivision__ring(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = c_Groups_Oone__class_Oone(X2)
<=> X0 = X1 ) ),
inference(ennf_transformation,[],[f909]) ).
fof(f2291,plain,
! [X0,X1,X2] :
( ~ class_Rings_Odivision__ring(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = c_Groups_Oone__class_Oone(X2)
<=> X0 = X1 ) ),
inference(flattening,[],[f2290]) ).
fof(f2292,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield__inverse__zero(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X2,X1)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(ennf_transformation,[],[f910]) ).
fof(f2293,plain,
! [X0,X1] :
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f911]) ).
fof(f2295,plain,
! [X0,X1,X2] :
( ~ class_Fields_Ofield__inverse__zero(X2)
| c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),X1)),X0) ),
inference(ennf_transformation,[],[f913]) ).
fof(f2302,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Odivision__ring(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) != X0
| X1 = c_Rings_Oinverse__class_Odivide(X3,X0,X2) ),
inference(ennf_transformation,[],[f917]) ).
fof(f2303,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Odivision__ring(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) != X0
| X1 = c_Rings_Oinverse__class_Odivide(X3,X0,X2) ),
inference(flattening,[],[f2302]) ).
fof(f2306,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Odivision__ring(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ( c_Rings_Oinverse__class_Odivide(X3,X1,X2) = X0
<=> X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2) ) ),
inference(ennf_transformation,[],[f919]) ).
fof(f2307,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Odivision__ring(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ( c_Rings_Oinverse__class_Odivide(X3,X1,X2) = X0
<=> X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2) ) ),
inference(flattening,[],[f2306]) ).
fof(f2310,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Odivision__ring(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
inference(ennf_transformation,[],[f921]) ).
fof(f2311,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X1)
| c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f922]) ).
fof(f2312,plain,
! [X0,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) ),
inference(ennf_transformation,[],[f923]) ).
fof(f2313,plain,
! [X0,X1,X2] :
( ~ class_RealVector_Oreal__normed__field(X2)
| c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) ),
inference(ennf_transformation,[],[f924]) ).
fof(f2314,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)) ),
inference(ennf_transformation,[],[f925]) ).
fof(f2315,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)) ),
inference(flattening,[],[f2314]) ).
fof(f2316,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Fields_Ofield__inverse__zero(X4)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Rings_Oinverse__class_Odivide(X4,X3,X2)),c_Rings_Oinverse__class_Odivide(X4,X1,X0)) = c_Rings_Oinverse__class_Odivide(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(ennf_transformation,[],[f928]) ).
fof(f2317,plain,
! [X0,X1,X2] :
( ~ class_Fields_Ofield__inverse__zero(X2)
| c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) = c_Rings_Oinverse__class_Odivide(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(ennf_transformation,[],[f929]) ).
fof(f2319,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Fields_Ofield(X4)
| c_Groups_Ozero__class_Ozero(X4) = X3
| c_Groups_Ozero__class_Ozero(X4) = X2
| ( c_Rings_Oinverse__class_Odivide(X4,X1,X3) = c_Rings_Oinverse__class_Odivide(X4,X0,X2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3) ) ),
inference(ennf_transformation,[],[f943]) ).
fof(f2320,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Fields_Ofield(X4)
| c_Groups_Ozero__class_Ozero(X4) = X3
| c_Groups_Ozero__class_Ozero(X4) = X2
| ( c_Rings_Oinverse__class_Odivide(X4,X1,X3) = c_Rings_Oinverse__class_Odivide(X4,X0,X2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3) ) ),
inference(flattening,[],[f2319]) ).
fof(f2321,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield__inverse__zero(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) = c_Rings_Oinverse__class_Odivide(X3,X1,X0) ),
inference(ennf_transformation,[],[f944]) ).
fof(f2322,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield__inverse__zero(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) = c_Rings_Oinverse__class_Odivide(X3,X1,X0) ),
inference(flattening,[],[f2321]) ).
fof(f2327,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield__inverse__zero(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2)),X2) ),
inference(ennf_transformation,[],[f965]) ).
fof(f2328,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield__inverse__zero(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2)),X2) ),
inference(flattening,[],[f2327]) ).
fof(f2329,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2) ),
inference(ennf_transformation,[],[f966]) ).
fof(f2330,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2) ),
inference(flattening,[],[f2329]) ).
fof(f2331,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield__inverse__zero(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)),X2) ),
inference(ennf_transformation,[],[f967]) ).
fof(f2332,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield__inverse__zero(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)),X2) ),
inference(flattening,[],[f2331]) ).
fof(f2333,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2) ),
inference(ennf_transformation,[],[f968]) ).
fof(f2334,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2) ),
inference(flattening,[],[f2333]) ).
fof(f2335,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Fields_Ofield(X4)
| c_Groups_Ozero__class_Ozero(X4) = X3
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Oplus__class_Oplus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)) ),
inference(ennf_transformation,[],[f969]) ).
fof(f2336,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Fields_Ofield(X4)
| c_Groups_Ozero__class_Ozero(X4) = X3
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Oplus__class_Oplus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)) ),
inference(flattening,[],[f2335]) ).
fof(f2337,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Fields_Ofield(X4)
| c_Groups_Ozero__class_Ozero(X4) = X3
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ominus__class_Ominus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)) ),
inference(ennf_transformation,[],[f970]) ).
fof(f2338,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Fields_Ofield(X4)
| c_Groups_Ozero__class_Ozero(X4) = X3
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ominus__class_Ominus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)) ),
inference(flattening,[],[f2337]) ).
fof(f2339,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2) ),
inference(ennf_transformation,[],[f971]) ).
fof(f2340,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2) ),
inference(flattening,[],[f2339]) ).
fof(f2341,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ominus__class_Ominus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2) ),
inference(ennf_transformation,[],[f972]) ).
fof(f2342,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ominus__class_Ominus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2) ),
inference(flattening,[],[f2341]) ).
fof(f2343,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_RealVector_Oreal__field(X5)
| c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X1)),X0) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X3,X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X4,X2),X0)),X1)) ),
inference(ennf_transformation,[],[f983]) ).
fof(f2344,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X2
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,X0),X2) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2)),c_Polynomial_Osmult(X3,c_Rings_Oinverse__class_Odivide(X3,hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2))),c_Polynomial_Odegree(X3,X2)),hAPP(c_Polynomial_Ocoeff(X3,X2),c_Polynomial_Odegree(X3,X2))),X2)) ),
inference(ennf_transformation,[],[f984]) ).
fof(f2345,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X2
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,X0),X2) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2)),c_Polynomial_Osmult(X3,c_Rings_Oinverse__class_Odivide(X3,hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2))),c_Polynomial_Odegree(X3,X2)),hAPP(c_Polynomial_Ocoeff(X3,X2),c_Polynomial_Odegree(X3,X2))),X2)) ),
inference(flattening,[],[f2344]) ).
fof(f2346,plain,
! [X0,X1,X2] :
( ~ class_Fields_Ofield(X2)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0) ),
inference(ennf_transformation,[],[f985]) ).
fof(f2347,plain,
! [X0,X1,X2] :
( ~ class_Fields_Ofield(X2)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0)) ),
inference(ennf_transformation,[],[f986]) ).
fof(f2348,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0) = c_Polynomial_Osmult(X3,X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0)) ),
inference(ennf_transformation,[],[f987]) ).
fof(f2349,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0) ),
inference(ennf_transformation,[],[f988]) ).
fof(f2350,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0) ),
inference(flattening,[],[f2349]) ).
fof(f2351,plain,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f989]) ).
fof(f2352,plain,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(ennf_transformation,[],[f990]) ).
fof(f2353,plain,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X0,X0) = c_Groups_Ozero__class_Ozero(X1) ),
inference(ennf_transformation,[],[f991]) ).
fof(f2354,plain,
! [X0,X1,X2] :
( ~ class_Divides_Osemiring__div(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Groups_Ozero__class_Ozero(X2) ),
inference(ennf_transformation,[],[f992]) ).
fof(f2355,plain,
! [X0,X1,X2] :
( ~ class_Divides_Osemiring__div(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Groups_Ozero__class_Ozero(X2) ),
inference(flattening,[],[f2354]) ).
fof(f2356,plain,
! [X0,X1,X2] :
( ~ class_Divides_Osemiring__div(X2)
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
<=> c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Groups_Ozero__class_Ozero(X2) ) ),
inference(ennf_transformation,[],[f993]) ).
fof(f2357,plain,
! [X0,X1,X2] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0) = c_Divides_Odiv__class_Omod(X2,X1,X0) ),
inference(ennf_transformation,[],[f994]) ).
fof(f2358,plain,
! [X0,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1)) ),
inference(ennf_transformation,[],[f995]) ).
fof(f2359,plain,
! [X0,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1)) ),
inference(flattening,[],[f2358]) ).
fof(f2360,plain,
! [X0] :
( ~ class_Groups_Ocancel__comm__monoid__add(X0)
| class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f996]) ).
fof(f2361,plain,
! [X0,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
inference(ennf_transformation,[],[f1000]) ).
fof(f2362,plain,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(ennf_transformation,[],[f1001]) ).
fof(f2363,plain,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(ennf_transformation,[],[f1002]) ).
fof(f2364,plain,
! [X0,X1] :
( ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(ennf_transformation,[],[f1003]) ).
fof(f2365,plain,
! [X0,X1] :
( ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(tc_fun(X0,X1)) ),
inference(ennf_transformation,[],[f1004]) ).
fof(f2366,plain,
! [X0,X1] :
( ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(tc_fun(X0,X1)) ),
inference(ennf_transformation,[],[f1005]) ).
fof(f2367,plain,
! [X0] :
( ~ class_Rings_Oidom(X0)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1147]) ).
fof(f2368,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1148]) ).
fof(f2369,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1149]) ).
fof(f2370,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1150]) ).
fof(f2371,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1151]) ).
fof(f2372,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1152]) ).
fof(f2373,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1153]) ).
fof(f2374,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1154]) ).
fof(f2375,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1155]) ).
fof(f2376,plain,
! [X0] :
( ~ class_Groups_Ocancel__comm__monoid__add(X0)
| class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1156]) ).
fof(f2377,plain,
! [X0] :
( ~ class_Rings_Oidom(X0)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1157]) ).
fof(f2378,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1158]) ).
fof(f2379,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1159]) ).
fof(f2380,plain,
! [X0] :
( ~ class_Rings_Oidom(X0)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1160]) ).
fof(f2381,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1161]) ).
fof(f2382,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1162]) ).
fof(f2383,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1163]) ).
fof(f2384,plain,
! [X0] :
( ~ class_Groups_Ocancel__comm__monoid__add(X0)
| class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1164]) ).
fof(f2385,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1165]) ).
fof(f2386,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1166]) ).
fof(f2387,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1167]) ).
fof(f2388,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1168]) ).
fof(f2389,plain,
! [X0] :
( ~ class_Groups_Ocomm__monoid__add(X0)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1169]) ).
fof(f2390,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1170]) ).
fof(f2391,plain,
! [X0] :
( ~ class_Rings_Oidom(X0)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1171]) ).
fof(f2392,plain,
! [X0] :
( ~ class_Groups_Ocomm__monoid__add(X0)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1172]) ).
fof(f2393,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1173]) ).
fof(f2394,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1174]) ).
fof(f2395,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1175]) ).
fof(f2396,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1176]) ).
fof(f2397,plain,
! [X0] :
( ~ class_Fields_Ofield(X0)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1177]) ).
fof(f2399,plain,
! [X0] :
( ~ class_Groups_Oab__group__add(X0)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1179]) ).
fof(f2400,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1180]) ).
fof(f2401,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1181]) ).
fof(f2402,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1182]) ).
fof(f2403,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1183]) ).
fof(f2404,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1184]) ).
fof(f2405,plain,
! [X0] :
( ~ class_Rings_Ocomm__ring__1(X0)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1185]) ).
fof(f2407,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1187]) ).
fof(f2408,plain,
! [X0] :
( ~ class_Groups_Oab__group__add(X0)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1188]) ).
fof(f2409,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1189]) ).
fof(f2410,plain,
! [X0] :
( ~ class_Rings_Ocomm__ring(X0)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1190]) ).
fof(f2411,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1191]) ).
fof(f2412,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1192]) ).
fof(f2413,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1193]) ).
fof(f2414,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Orderings_Oord(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1194]) ).
fof(f2415,plain,
! [X0] :
( ~ class_Groups_Oab__group__add(X0)
| class_Groups_Ouminus(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1195]) ).
fof(f2416,plain,
! [X0] :
( ~ class_Rings_Ocomm__ring__1(X0)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1196]) ).
fof(f2417,plain,
! [X0] :
( ~ class_Groups_Oab__group__add(X0)
| class_Groups_Ominus(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1197]) ).
fof(f2418,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Power_Opower(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1198]) ).
fof(f2419,plain,
! [X0] :
( ~ class_Groups_Ozero(X0)
| class_Groups_Ozero(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1199]) ).
fof(f2420,plain,
! [X0] :
( ~ class_Rings_Ocomm__ring(X0)
| class_Rings_Oring(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1200]) ).
fof(f2421,plain,
! [X0] :
( ~ class_Rings_Oidom(X0)
| class_Rings_Oidom(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1201]) ).
fof(f2423,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Rings_Odvd(tc_Polynomial_Opoly(X0)) ),
inference(ennf_transformation,[],[f1203]) ).
fof(f2424,plain,
( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<~> ( ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
inference(ennf_transformation,[],[f1207]) ).
fof(f2428,plain,
! [X0,X1] :
( hAPP(X1,sK2(X0,X1)) != hAPP(X0,sK2(X0,X1))
| X1 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f1255]) ).
fof(f2433,plain,
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK4)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK4) )
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f1260]) ).
fof(f2439,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| ( X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(nnf_transformation,[],[f1270]) ).
fof(f2440,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| ( X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(flattening,[],[f2439]) ).
fof(f2441,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),sK6(X1,X2))
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sK6(X1,X2)) )
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X3,sK6(X1,X2))],[f1276]) ).
fof(f2442,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( ( c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0)
| c_Polynomial_Oorder(X2,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 )
| hAPP(c_Polynomial_Opoly(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(nnf_transformation,[],[f1277]) ).
fof(f2443,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( ( c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0)
| c_Polynomial_Oorder(X2,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 )
| hAPP(c_Polynomial_Opoly(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(flattening,[],[f2442]) ).
fof(f2444,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f2445,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(flattening,[],[f2444]) ).
fof(f2446,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ~ class_Int_Oring__char__0(X2)
| ( ( c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X2,X0)
| X1 = X0 )
& ( X0 != X1
| c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0) ) ) ),
inference(nnf_transformation,[],[f1285]) ).
fof(f2447,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f1286]) ).
fof(f2449,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osynthetic__div(X2,X1,X0)
| c_Polynomial_Odegree(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Odegree(X2,X1)
| c_Polynomial_Osynthetic__div(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
inference(nnf_transformation,[],[f1288]) ).
fof(f2458,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(nnf_transformation,[],[f1335]) ).
fof(f2459,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2))) ) ) ),
inference(nnf_transformation,[],[f1338]) ).
fof(f2460,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2))) ) ) ),
inference(nnf_transformation,[],[f1349]) ).
fof(f2461,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
| ( ( c_Groups_Ozero__class_Ozero(X3) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) )
& ( c_Groups_Ozero__class_Ozero(X3) != X2
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ) )
& ( ( c_Groups_Ozero__class_Ozero(X3) != X2
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) )
| ( c_Groups_Ozero__class_Ozero(X3) = X2
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X0 )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0)) ) ) ),
inference(nnf_transformation,[],[f1350]) ).
fof(f2462,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
| ( ( c_Groups_Ozero__class_Ozero(X3) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) )
& ( c_Groups_Ozero__class_Ozero(X3) != X2
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ) )
& ( ( c_Groups_Ozero__class_Ozero(X3) != X2
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) )
| ( c_Groups_Ozero__class_Ozero(X3) = X2
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X0 )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0)) ) ) ),
inference(flattening,[],[f2461]) ).
fof(f2463,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Ozero(X4)
| ( ( c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
| ( X2 = X0
& X3 = X1 ) )
& ( X0 != X2
| X1 != X3
| c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0) ) ) ),
inference(nnf_transformation,[],[f1356]) ).
fof(f2464,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Ozero(X4)
| ( ( c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
| ( X2 = X0
& X3 = X1 ) )
& ( X0 != X2
| X1 != X3
| c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0) ) ) ),
inference(flattening,[],[f2463]) ).
fof(f2465,plain,
! [X0] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(nnf_transformation,[],[f93]) ).
fof(f2466,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f95]) ).
fof(f2467,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| X1 = c_Nat_OSuc(X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ( c_Nat_OSuc(X0) != X1
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f96]) ).
fof(f2468,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| X1 = c_Nat_OSuc(X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ( c_Nat_OSuc(X0) != X1
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(flattening,[],[f2467]) ).
fof(f2469,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f97]) ).
fof(f2470,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
& X1 = c_Groups_Ozero__class_Ozero(X2) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
inference(nnf_transformation,[],[f1373]) ).
fof(f2471,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
& X1 = c_Groups_Ozero__class_Ozero(X2) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
inference(flattening,[],[f2470]) ).
fof(f2472,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osmult(X2,X1,X0)
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_Groups_Ozero__class_Ozero(X2) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
& c_Groups_Ozero__class_Ozero(X2) != X1 )
| c_Polynomial_Osmult(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
inference(nnf_transformation,[],[f1379]) ).
fof(f2473,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osmult(X2,X1,X0)
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_Groups_Ozero__class_Ozero(X2) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
& c_Groups_Ozero__class_Ozero(X2) != X1 )
| c_Polynomial_Osmult(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
inference(flattening,[],[f2472]) ).
fof(f2474,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0))) ) ) ),
inference(nnf_transformation,[],[f1392]) ).
fof(f2476,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)
| X1 = X0 )
& ( X0 != X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0) ) ) ),
inference(nnf_transformation,[],[f1426]) ).
fof(f2477,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Ozero(X3)
| ( ( c_Polynomial_Omonom(X3,X2,X1) != c_Polynomial_Omonom(X3,X0,X1)
| X2 = X0 )
& ( X0 != X2
| c_Polynomial_Omonom(X3,X2,X1) = c_Polynomial_Omonom(X3,X0,X1) ) ) ),
inference(nnf_transformation,[],[f1429]) ).
fof(f2479,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
| X1 = X0
| c_Orderings_Oord__class_Oless(X2,X0,X1) )
& ( ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(X2,X0,X1) )
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(nnf_transformation,[],[f1469]) ).
fof(f2480,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
| X1 = X0
| c_Orderings_Oord__class_Oless(X2,X0,X1) )
& ( ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(X2,X0,X1) )
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(flattening,[],[f2479]) ).
fof(f2481,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| ( ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) )
& ( ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
& ~ c_Orderings_Oord__class_Oless(X2,X1,X0) )
| X1 != X0 ) ) ),
inference(nnf_transformation,[],[f1470]) ).
fof(f2482,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| ( ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) )
& ( ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
& ~ c_Orderings_Oord__class_Oless(X2,X1,X0) )
| X1 != X0 ) ) ),
inference(flattening,[],[f2481]) ).
fof(f2486,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X1 = X0 )
& ( X0 != X1
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
inference(nnf_transformation,[],[f1512]) ).
fof(f2489,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Opreorder(X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
& ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(nnf_transformation,[],[f1518]) ).
fof(f2490,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Opreorder(X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
& ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(flattening,[],[f2489]) ).
fof(f2491,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(nnf_transformation,[],[f1519]) ).
fof(f2492,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(flattening,[],[f2491]) ).
fof(f2494,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(X2)
| ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(nnf_transformation,[],[f1523]) ).
fof(f2495,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(nnf_transformation,[],[f218]) ).
fof(f2498,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| X1 = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f229]) ).
fof(f2499,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| X1 = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(flattening,[],[f2498]) ).
fof(f2500,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f230]) ).
fof(f2501,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f231]) ).
fof(f2502,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(flattening,[],[f2501]) ).
fof(f2505,plain,
! [X0] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(nnf_transformation,[],[f239]) ).
fof(f2506,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) ) ) ),
inference(nnf_transformation,[],[f1568]) ).
fof(f2507,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ? [X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& X1 = c_Nat_OSuc(X2) )
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f255]) ).
fof(f2508,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ? [X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& X1 = c_Nat_OSuc(X2) )
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(flattening,[],[f2507]) ).
fof(f2509,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ? [X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0)
& c_Nat_OSuc(X3) = X1 )
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(rectify,[],[f2508]) ).
fof(f2510,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK8(X0,X1),X0)
& c_Nat_OSuc(sK8(X0,X1)) = X1 )
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1))],[f2509]) ).
fof(f2511,plain,
! [X0] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(nnf_transformation,[],[f256]) ).
fof(f2512,plain,
! [X0] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ? [X1] : X0 = c_Nat_OSuc(X1) )
& ( ! [X1] : c_Nat_OSuc(X1) != X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(nnf_transformation,[],[f257]) ).
fof(f2513,plain,
! [X0] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ? [X2] : c_Nat_OSuc(X2) = X0 )
& ( ! [X1] : c_Nat_OSuc(X1) != X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(rectify,[],[f2512]) ).
fof(f2514,plain,
! [X0] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Nat_OSuc(sK9(X0)) = X0 )
& ( ! [X1] : c_Nat_OSuc(X1) != X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0))],[f2513]) ).
fof(f2516,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f261]) ).
fof(f2519,plain,
! [X0,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),X0))
| X0 = 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_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ 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),X0)) ) ),
inference(nnf_transformation,[],[f271]) ).
fof(f2520,plain,
! [X0,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),X0))
| X0 = 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_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ 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),X0)) ) ),
inference(flattening,[],[f2519]) ).
fof(f2521,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
inference(nnf_transformation,[],[f1596]) ).
fof(f2522,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Omonom(X2,X1,X0)
| X1 = c_Groups_Ozero__class_Ozero(X2) )
& ( c_Groups_Ozero__class_Ozero(X2) != X1
| c_Polynomial_Omonom(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
inference(nnf_transformation,[],[f1599]) ).
fof(f2524,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X2)
| ( ( X0 != X1
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X1 = X0 ) ) ),
inference(nnf_transformation,[],[f1637]) ).
fof(f2525,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X2)
| ( ( X0 != X1
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X1 = X0 ) ) ),
inference(flattening,[],[f2524]) ).
fof(f2526,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oord(X3)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) )
& ( ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) ) ),
inference(nnf_transformation,[],[f1640]) ).
fof(f2527,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oord(X3)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ! [X5] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5)) )
& ( ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) ) ),
inference(rectify,[],[f2526]) ).
fof(f2528,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oord(X3)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ! [X5] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK10(X0,X1,X3)),hAPP(X0,sK10(X0,X1,X3)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X4,sK10(X0,X1,X3))],[f2527]) ).
fof(f2529,plain,
! [X0,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),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X0 = 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_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
| 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),X0)) ) ),
inference(nnf_transformation,[],[f307]) ).
fof(f2530,plain,
! [X0,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),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X0 = 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_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
| 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),X0)) ) ),
inference(flattening,[],[f2529]) ).
fof(f2531,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oord(X3)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0) ) ) ),
inference(nnf_transformation,[],[f1659]) ).
fof(f2532,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oord(X3)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0) ) ) ),
inference(flattening,[],[f2531]) ).
fof(f2533,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ( X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(nnf_transformation,[],[f312]) ).
fof(f2534,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ( X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(flattening,[],[f2533]) ).
fof(f2535,plain,
! [X0,X1,X2] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
inference(nnf_transformation,[],[f325]) ).
fof(f2536,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) ) ),
inference(nnf_transformation,[],[f328]) ).
fof(f2537,plain,
! [X0,X1,X2] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
inference(nnf_transformation,[],[f336]) ).
fof(f2538,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ? [X2] : X0 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) )
& ( ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f337]) ).
fof(f2539,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0 )
& ( ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f2538]) ).
fof(f2540,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK11(X0,X1)) = X0 )
& ( ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f2539]) ).
fof(f2541,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ( X0 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X0 = 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)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(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,X0) ) ),
inference(nnf_transformation,[],[f340]) ).
fof(f2542,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ( X0 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X0 = 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)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(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,X0) ) ),
inference(flattening,[],[f2541]) ).
fof(f2545,plain,
! [X0,X1] :
( ( ~ 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,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| 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),X0)
& ~ 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ) ),
inference(nnf_transformation,[],[f342]) ).
fof(f2546,plain,
! [X0,X1] :
( ( ~ 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,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| 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),X0)
& ~ 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ) ),
inference(flattening,[],[f2545]) ).
fof(f2547,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ? [X2] : X0 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) )
& ( ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f345]) ).
fof(f2548,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ? [X3] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = X0 )
& ( ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f2547]) ).
fof(f2549,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK12(X0,X1))) = X0 )
& ( ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X3,sK12(X0,X1))],[f2548]) ).
fof(f2555,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) ) ),
inference(nnf_transformation,[],[f1693]) ).
fof(f2556,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| c_Orderings_Oord__class_Oless__eq(X3,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
inference(nnf_transformation,[],[f1694]) ).
fof(f2557,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| c_Orderings_Oord__class_Oless(X3,X2,X0) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) ) ),
inference(nnf_transformation,[],[f1705]) ).
fof(f2558,plain,
! [X0,X1,X2,X3] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| c_Orderings_Oord__class_Oless(X3,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
inference(nnf_transformation,[],[f1706]) ).
fof(f2559,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(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),X0)
| ( ( c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) )
& ( c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(nnf_transformation,[],[f1724]) ).
fof(f2560,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(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),X0)
| ( ( c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) )
& ( c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(flattening,[],[f2559]) ).
fof(f2561,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1)) ) ) ),
inference(nnf_transformation,[],[f1727]) ).
fof(f2562,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0)) ) ) ),
inference(nnf_transformation,[],[f1728]) ).
fof(f2563,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1)) ) ) ),
inference(nnf_transformation,[],[f1733]) ).
fof(f2564,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0)) ) ) ),
inference(nnf_transformation,[],[f1734]) ).
fof(f2565,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ( ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1)) ) ) ),
inference(nnf_transformation,[],[f1740]) ).
fof(f2566,plain,
! [X0,X1,X2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)
| X1 = X0 )
& ( X0 != X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0) ) ),
inference(nnf_transformation,[],[f395]) ).
fof(f2567,plain,
! [X0,X1,X2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| X2 = X0 )
& ( X0 != X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ) ),
inference(nnf_transformation,[],[f396]) ).
fof(f2569,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| ( ( c_Groups_Ouminus__class_Ouminus(X2,X1) != X0
| c_Groups_Ouminus__class_Ouminus(X2,X0) = X1 )
& ( c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
| c_Groups_Ouminus__class_Ouminus(X2,X1) = X0 ) ) ),
inference(nnf_transformation,[],[f1749]) ).
fof(f2570,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1)
| X1 = X0 )
& ( X0 != X1
| c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0) ) ) ),
inference(nnf_transformation,[],[f1750]) ).
fof(f2573,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( ( c_Groups_Ouminus__class_Ouminus(X1,X0) != X0
| X0 = c_Groups_Ozero__class_Ozero(X1) )
& ( c_Groups_Ozero__class_Ozero(X1) != X0
| X0 = c_Groups_Ouminus__class_Ouminus(X1,X0) ) ) ),
inference(nnf_transformation,[],[f1758]) ).
fof(f2574,plain,
! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| ( ( c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0 )
& ( c_Groups_Ozero__class_Ozero(X1) != X0
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X0) ) ) ),
inference(nnf_transformation,[],[f1759]) ).
fof(f2575,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ) ) ),
inference(nnf_transformation,[],[f1761]) ).
fof(f2576,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ) ) ),
inference(nnf_transformation,[],[f1762]) ).
fof(f2577,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ) ) ),
inference(nnf_transformation,[],[f1763]) ).
fof(f2578,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ) ) ),
inference(nnf_transformation,[],[f1766]) ).
fof(f2579,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ) ) ),
inference(nnf_transformation,[],[f1767]) ).
fof(f2580,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| c_Orderings_Oord__class_Oless(X2,X0,X1) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ) ) ),
inference(nnf_transformation,[],[f1768]) ).
fof(f2581,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__ring__1(X2)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0))) ) ) ),
inference(nnf_transformation,[],[f1773]) ).
fof(f2582,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__ring__1(X2)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)) ) ) ),
inference(nnf_transformation,[],[f1774]) ).
fof(f2583,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1,X0,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,X0)) ) ) ),
inference(nnf_transformation,[],[f1778]) ).
fof(f2584,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ) ) ),
inference(nnf_transformation,[],[f1779]) ).
fof(f2585,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) ) ),
inference(nnf_transformation,[],[f1780]) ).
fof(f2586,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ) ) ),
inference(nnf_transformation,[],[f1781]) ).
fof(f2587,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ( ( ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ) ) ),
inference(nnf_transformation,[],[f1782]) ).
fof(f2588,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ( ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0)) ) ) ),
inference(nnf_transformation,[],[f1783]) ).
fof(f2589,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ( ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) ) ),
inference(nnf_transformation,[],[f1784]) ).
fof(f2590,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ) ) ),
inference(nnf_transformation,[],[f1785]) ).
fof(f2591,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2) )
& ( c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| X1 = c_Groups_Ouminus__class_Ouminus(X2,X0) ) ) ),
inference(nnf_transformation,[],[f1787]) ).
fof(f2592,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| ( ( c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| X0 = c_Groups_Ouminus__class_Ouminus(X2,X1) )
& ( c_Groups_Ouminus__class_Ouminus(X2,X1) != X0
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(nnf_transformation,[],[f1790]) ).
fof(f2593,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( ( 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),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X1 = c_Groups_Ouminus__class_Ouminus(X2,X0)
| X1 = X0 )
& ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
& X0 != X1 )
| 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),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ),
inference(nnf_transformation,[],[f1793]) ).
fof(f2594,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( ( 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),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X1 = c_Groups_Ouminus__class_Ouminus(X2,X0)
| X1 = X0 )
& ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
& X0 != X1 )
| 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),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ),
inference(flattening,[],[f2593]) ).
fof(f2595,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( ( c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1))
| hAPP(c_Polynomial_Opoly(X2,X1),X0) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(nnf_transformation,[],[f1810]) ).
fof(f2596,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0))
| hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) = c_Groups_Ozero__class_Ozero(X2) )
& ( c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) ) ) ),
inference(nnf_transformation,[],[f1811]) ).
fof(f2597,plain,
! [X0,X1,X2] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
| ( ( c_Groups_Oplus__class_Oplus(X2,X1,X0) != X1
| X0 = c_Groups_Ozero__class_Ozero(X2) )
& ( c_Groups_Ozero__class_Ozero(X2) != X0
| X1 = c_Groups_Oplus__class_Oplus(X2,X1,X0) ) ) ),
inference(nnf_transformation,[],[f1814]) ).
fof(f2598,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ( ( c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oplus__class_Oplus(X1,X0,X0)
| X0 = c_Groups_Ozero__class_Ozero(X1) )
& ( c_Groups_Ozero__class_Ozero(X1) != X0
| c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Ozero__class_Ozero(X1) ) ) ),
inference(nnf_transformation,[],[f1815]) ).
fof(f2599,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ? [X2] : X0 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) )
& ( ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f463]) ).
fof(f2600,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0 )
& ( ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f2599]) ).
fof(f2601,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK13(X0,X1)) = X0 )
& ( ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X3,sK13(X0,X1))],[f2600]) ).
fof(f2602,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| ( ( ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
& X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) )
| c_Polynomial_Opos__poly(X2,X0) )
& ( ( ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 )
& ~ c_Polynomial_Opos__poly(X2,X0) )
| c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0)) ) ) ),
inference(nnf_transformation,[],[f1818]) ).
fof(f2603,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| ( ( ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
& X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) )
| c_Polynomial_Opos__poly(X2,X0) )
& ( ( ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 )
& ~ c_Polynomial_Opos__poly(X2,X0) )
| c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0)) ) ) ),
inference(flattening,[],[f2602]) ).
fof(f2604,plain,
! [X0,X1,X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ) ) ),
inference(nnf_transformation,[],[f1821]) ).
fof(f2605,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f469]) ).
fof(f2606,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(flattening,[],[f2605]) ).
fof(f2607,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(nnf_transformation,[],[f470]) ).
fof(f2608,plain,
! [X0,X1] :
( ( ~ 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)),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| 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)),X0) ) ),
inference(nnf_transformation,[],[f471]) ).
fof(f2609,plain,
! [X0] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ),
inference(nnf_transformation,[],[f478]) ).
fof(f2610,plain,
! [X0] :
( ( ~ 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),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,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),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(nnf_transformation,[],[f486]) ).
fof(f2613,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
| ( ( X0 = X1
| X2 = X3
| c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) != c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X1)) )
& ( c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X1))
| ( X1 != X0
& X3 != X2 ) ) ) ),
inference(nnf_transformation,[],[f1836]) ).
fof(f2614,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
| ( ( X0 = X1
| X2 = X3
| c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) != c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X1)) )
& ( c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X1))
| ( X1 != X0
& X3 != X2 ) ) ) ),
inference(flattening,[],[f2613]) ).
fof(f2615,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 = X0
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
& ( ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(nnf_transformation,[],[f493]) ).
fof(f2616,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 = X0
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
& ( ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(flattening,[],[f2615]) ).
fof(f2617,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
| X1 = c_Groups_Ouminus__class_Ouminus(X2,X0)
| X1 = X0 )
& ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
& X0 != X1 )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0) ) ) ),
inference(nnf_transformation,[],[f1844]) ).
fof(f2618,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oidom(X2)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
| X1 = c_Groups_Ouminus__class_Ouminus(X2,X0)
| X1 = X0 )
& ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
& X0 != X1 )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0) ) ) ),
inference(flattening,[],[f2617]) ).
fof(f2619,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oring__no__zero__divisors(X2)
| ( ( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)
| X0 = c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ozero__class_Ozero(X2) )
& ( ( c_Groups_Ozero__class_Ozero(X2) != X0
& c_Groups_Ozero__class_Ozero(X2) != X1 )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(nnf_transformation,[],[f1858]) ).
fof(f2620,plain,
! [X0,X1,X2] :
( ~ class_Rings_Oring__no__zero__divisors(X2)
| ( ( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)
| X0 = c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ozero__class_Ozero(X2) )
& ( ( c_Groups_Ozero__class_Ozero(X2) != X0
& c_Groups_Ozero__class_Ozero(X2) != X1 )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(flattening,[],[f2619]) ).
fof(f2621,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) )
& ( ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ) ),
inference(nnf_transformation,[],[f1896]) ).
fof(f2622,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) )
& ( ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ) ),
inference(flattening,[],[f2621]) ).
fof(f2623,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,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),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(nnf_transformation,[],[f1897]) ).
fof(f2624,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,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),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(flattening,[],[f2623]) ).
fof(f2625,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ( ( ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Orderings_Oord__class_Oless(X3,X0,X1) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) ) ),
inference(nnf_transformation,[],[f1941]) ).
fof(f2626,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Orderings_Oord__class_Oless(X3,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) ) ),
inference(nnf_transformation,[],[f1953]) ).
fof(f2627,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ( c_Orderings_Oord__class_Oless(X3,X0,X1)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X1,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) )
& ( ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) )
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) ) ),
inference(nnf_transformation,[],[f1954]) ).
fof(f2628,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ( c_Orderings_Oord__class_Oless(X3,X0,X1)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X1,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) )
& ( ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) )
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) ) ),
inference(flattening,[],[f2627]) ).
fof(f2629,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ( c_Orderings_Oord__class_Oless(X3,X0,X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X2,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
& ( ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ) ),
inference(nnf_transformation,[],[f1955]) ).
fof(f2630,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ( c_Orderings_Oord__class_Oless(X3,X0,X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X2,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
& ( ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ) ),
inference(flattening,[],[f2629]) ).
fof(f2631,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0))
| ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) )
& ( c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(nnf_transformation,[],[f1957]) ).
fof(f2632,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0))
| ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) )
& ( c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(flattening,[],[f2631]) ).
fof(f2633,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oidom(X3)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| X2 = c_Groups_Ozero__class_Ozero(X3) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
& c_Groups_Ozero__class_Ozero(X3) != X2 )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))) ) ) ),
inference(nnf_transformation,[],[f1962]) ).
fof(f2634,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oidom(X3)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| X2 = c_Groups_Ozero__class_Ozero(X3) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
& c_Groups_Ozero__class_Ozero(X3) != X2 )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))) ) ) ),
inference(flattening,[],[f2633]) ).
fof(f2635,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oidom(X3)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| X1 = c_Groups_Ozero__class_Ozero(X3) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
& c_Groups_Ozero__class_Ozero(X3) != X1 )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ) ) ),
inference(nnf_transformation,[],[f1963]) ).
fof(f2636,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Oidom(X3)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| X1 = c_Groups_Ozero__class_Ozero(X3) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
& c_Groups_Ozero__class_Ozero(X3) != X1 )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ) ) ),
inference(flattening,[],[f2635]) ).
fof(f2637,plain,
! [X0,X1] :
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| ( ( c_Groups_Oone__class_Oone(X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)
| X0 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| X0 = c_Groups_Oone__class_Oone(X1) )
& ( ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) != X0
& c_Groups_Oone__class_Oone(X1) != X0 )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1) ) ) ),
inference(nnf_transformation,[],[f1972]) ).
fof(f2638,plain,
! [X0,X1] :
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| ( ( c_Groups_Oone__class_Oone(X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)
| X0 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| X0 = c_Groups_Oone__class_Oone(X1) )
& ( ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) != X0
& c_Groups_Oone__class_Oone(X1) != X0 )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1) ) ) ),
inference(flattening,[],[f2637]) ).
fof(f2639,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Orderings_Oord__class_Oless__eq(X3,X0,X1) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) ) ),
inference(nnf_transformation,[],[f2006]) ).
fof(f2640,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Orderings_Oord__class_Oless__eq(X3,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) ) ),
inference(nnf_transformation,[],[f2008]) ).
fof(f2641,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) )
& ( c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| 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),X0),X0)),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(nnf_transformation,[],[f2010]) ).
fof(f2642,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| ( X0 = c_Groups_Ozero__class_Ozero(X2)
& X1 = c_Groups_Ozero__class_Ozero(X2) ) )
& ( c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| 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),X0),X0)),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(flattening,[],[f2641]) ).
fof(f2643,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0)))
| X0 != c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2) )
& ( ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| 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),X0),X0))) ) ) ),
inference(nnf_transformation,[],[f2012]) ).
fof(f2644,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0)))
| X0 != c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2) )
& ( ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| 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),X0),X0))) ) ) ),
inference(flattening,[],[f2643]) ).
fof(f2645,plain,
! [X0,X1,X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1)
| X1 = X0 )
& ( X0 != X1
| c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0) ) ) ),
inference(nnf_transformation,[],[f2028]) ).
fof(f2646,plain,
! [X0,X1,X2] :
( ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2)
| ( ( ! [X3] : ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
| ? [X4] :
( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) ) )
& ( ! [X4] :
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) )
| ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3))) ) ) ),
inference(nnf_transformation,[],[f2039]) ).
fof(f2647,plain,
! [X0,X1,X2] :
( ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2)
| ( ( ! [X6] : ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6)))
| ? [X5] :
( hBOOL(hAPP(X1,X5))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X5,c_Groups_Ozero__class_Ozero(X2)))) ) )
& ( ! [X4] :
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) )
| ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3))) ) ) ),
inference(rectify,[],[f2646]) ).
fof(f2648,plain,
! [X0,X1,X2] :
( ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2)
| ( ( ! [X6] : ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6)))
| ( hBOOL(hAPP(X1,sK15(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,sK15(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2)))) ) )
& ( ! [X4] :
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) )
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),sK14(X0,X1,X2)))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X3,sK14(X0,X1,X2)),skolemize(X5,sK15(X0,X1,X2))],[f2647]) ).
fof(f2649,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = X0 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& X0 != X2 )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) ) ),
inference(nnf_transformation,[],[f650]) ).
fof(f2650,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = X0 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& X0 != X2 )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) ) ),
inference(flattening,[],[f2649]) ).
fof(f2653,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(nnf_transformation,[],[f652]) ).
fof(f2654,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(flattening,[],[f2653]) ).
fof(f2655,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0)
| X1 = X0 )
& ( X0 != X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0) ) ),
inference(nnf_transformation,[],[f656]) ).
fof(f2658,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| ( X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(nnf_transformation,[],[f668]) ).
fof(f2659,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| ( X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(flattening,[],[f2658]) ).
fof(f2660,plain,
! [X0,X1,X2,X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3))
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X1))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X1)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))) ) ) ),
inference(nnf_transformation,[],[f2051]) ).
fof(f2661,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))) ) ),
inference(nnf_transformation,[],[f670]) ).
fof(f2662,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ) ),
inference(nnf_transformation,[],[f2052]) ).
fof(f2665,plain,
! [X0,X1,X2] :
( ( ~ 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),X0),X1))
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& 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,X0)
| ~ 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),X0),X1)) ) ),
inference(nnf_transformation,[],[f680]) ).
fof(f2666,plain,
! [X0,X1,X2] :
( ( ~ 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),X0),X1))
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& 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,X0)
| ~ 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),X0),X1)) ) ),
inference(flattening,[],[f2665]) ).
fof(f2667,plain,
! [X0,X1,X2] :
( ( ~ 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),X2),X0))
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
& 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,X1,X0)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
inference(nnf_transformation,[],[f681]) ).
fof(f2668,plain,
! [X0,X1,X2] :
( ( ~ 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),X2),X0))
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
& 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,X1,X0)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
inference(flattening,[],[f2667]) ).
fof(f2669,plain,
! [X0,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),X0))
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
& 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),X0)
| ~ 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),X0)) ) ),
inference(nnf_transformation,[],[f682]) ).
fof(f2670,plain,
! [X0,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),X0))
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
& 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),X0)
| ~ 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),X0)) ) ),
inference(flattening,[],[f2669]) ).
fof(f2671,plain,
! [X0,X1,X2] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0)) ) ),
inference(nnf_transformation,[],[f683]) ).
fof(f2672,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| ( X0 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X1 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
inference(nnf_transformation,[],[f2060]) ).
fof(f2673,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| ( X0 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X1 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
inference(flattening,[],[f2672]) ).
fof(f2674,plain,
! [X0,X1,X2] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0)) ) ),
inference(nnf_transformation,[],[f688]) ).
fof(f2675,plain,
! [X0,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),X0))
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
& 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)),X0)
| ~ 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),X0)) ) ),
inference(nnf_transformation,[],[f699]) ).
fof(f2676,plain,
! [X0,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),X0))
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
& 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)),X0)
| ~ 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),X0)) ) ),
inference(flattening,[],[f2675]) ).
fof(f2677,plain,
! [X0,X1,X2] :
( ( ~ 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),X0),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,X2,X0) )
& ( ( 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,X2,X0) )
| 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),X0),X1)) ) ),
inference(nnf_transformation,[],[f2075]) ).
fof(f2678,plain,
! [X0,X1,X2] :
( ( ~ 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),X0),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,X2,X0) )
& ( ( 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,X2,X0) )
| 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),X0),X1)) ) ),
inference(flattening,[],[f2677]) ).
fof(f2679,plain,
! [X0,X1,X2] :
( ( ~ 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),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| 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),X2),X0)) ) ),
inference(nnf_transformation,[],[f2076]) ).
fof(f2680,plain,
! [X0,X1,X2] :
( ( ~ 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),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| 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),X2),X0)) ) ),
inference(flattening,[],[f2679]) ).
fof(f2681,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ),
inference(nnf_transformation,[],[f704]) ).
fof(f2682,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ),
inference(nnf_transformation,[],[f705]) ).
fof(f2683,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),X1))
| X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),X1)) ) ) ),
inference(nnf_transformation,[],[f2078]) ).
fof(f2684,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X1))
| X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X1)) ) ) ),
inference(nnf_transformation,[],[f2079]) ).
fof(f2685,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ( ( ~ 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),X2),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| 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),X2),X0)) ) ) ),
inference(nnf_transformation,[],[f2098]) ).
fof(f2686,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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),X2),X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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),X2),X0))) ) ) ),
inference(nnf_transformation,[],[f2099]) ).
fof(f2687,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
| X1 = X0
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( X0 != X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ) ),
inference(nnf_transformation,[],[f725]) ).
fof(f2688,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
| X1 = X0
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( X0 != X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ) ),
inference(flattening,[],[f2687]) ).
fof(f2689,plain,
! [X0,X1,X2] :
( ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| 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),X2),X0)) ) ) ),
inference(nnf_transformation,[],[f2100]) ).
fof(f2690,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
| X1 = X0 )
& ( X0 != X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ) ) ),
inference(nnf_transformation,[],[f2101]) ).
fof(f2691,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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),X2),X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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),X2),X0))) ) ),
inference(nnf_transformation,[],[f729]) ).
fof(f2692,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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),X2),X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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),X2),X0))) ) ),
inference(flattening,[],[f2691]) ).
fof(f2693,plain,
! [X4,X1,X2,X0,X3] :
( ~ sP1(X4,X1,X2,X0,X3)
| ( ( ~ c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
| sP0(X3,X0,X2,X1,X4) )
& ( ~ sP0(X3,X0,X2,X1,X4)
| c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0) ) ) ),
inference(nnf_transformation,[],[f2426]) ).
fof(f2694,plain,
! [X0,X1,X2,X3,X4] :
( ~ sP1(X0,X1,X2,X3,X4)
| ( ( ~ c_Polynomial_Opdivmod__rel(X0,X4,X2,X1,X3)
| sP0(X4,X3,X2,X1,X0) )
& ( ~ sP0(X4,X3,X2,X1,X0)
| c_Polynomial_Opdivmod__rel(X0,X4,X2,X1,X3) ) ) ),
inference(rectify,[],[f2693]) ).
fof(f2698,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| ( ( ~ c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
| ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
& X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X1
| c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0) ) ) ),
inference(nnf_transformation,[],[f2105]) ).
fof(f2699,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| ( ( ~ c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
| ( X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
& X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X1
| c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0) ) ) ),
inference(flattening,[],[f2698]) ).
fof(f2700,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| ( ( ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
| ( X0 = X2
& X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) )
& ( X0 != X2
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X1
| c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0) ) ) ),
inference(nnf_transformation,[],[f2106]) ).
fof(f2701,plain,
! [X0,X1,X2,X3] :
( ~ class_Fields_Ofield(X3)
| ( ( ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
| ( X0 = X2
& X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) )
& ( X0 != X2
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X1
| c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0) ) ) ),
inference(flattening,[],[f2700]) ).
fof(f2702,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ? [X4] :
( hBOOL(hAPP(X1,X4))
& ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,X2))) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)))) ) ),
inference(rectify,[],[f2131]) ).
fof(f2703,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ( hBOOL(hAPP(X1,sK16(X1,X2)))
& ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK16(X1,X2),X2))) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X4,sK16(X1,X2))],[f2702]) ).
fof(f2704,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X0))
| ( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK17(X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,sK17(X0,X1))
| ~ hBOOL(hAPP(X1,X3)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK17(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X2,sK17(X0,X1))],[f2133]) ).
fof(f2705,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
inference(nnf_transformation,[],[f2145]) ).
fof(f2706,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(nnf_transformation,[],[f2146]) ).
fof(f2707,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( ( c_Polynomial_Ocoeff(X2,X1) != c_Polynomial_Ocoeff(X2,X0)
| X1 = X0 )
& ( X0 != X1
| c_Polynomial_Ocoeff(X2,X1) = c_Polynomial_Ocoeff(X2,X0) ) ) ),
inference(nnf_transformation,[],[f2156]) ).
fof(f2708,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( ( X0 != X1
| ! [X3] : hAPP(c_Polynomial_Ocoeff(X2,X1),X3) = hAPP(c_Polynomial_Ocoeff(X2,X0),X3) )
& ( ? [X3] : hAPP(c_Polynomial_Ocoeff(X2,X1),X3) != hAPP(c_Polynomial_Ocoeff(X2,X0),X3)
| X1 = X0 ) ) ),
inference(nnf_transformation,[],[f2157]) ).
fof(f2709,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( ( X0 != X1
| ! [X4] : hAPP(c_Polynomial_Ocoeff(X2,X1),X4) = hAPP(c_Polynomial_Ocoeff(X2,X0),X4) )
& ( ? [X3] : hAPP(c_Polynomial_Ocoeff(X2,X1),X3) != hAPP(c_Polynomial_Ocoeff(X2,X0),X3)
| X1 = X0 ) ) ),
inference(rectify,[],[f2708]) ).
fof(f2710,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ozero(X2)
| ( ( X0 != X1
| ! [X4] : hAPP(c_Polynomial_Ocoeff(X2,X1),X4) = hAPP(c_Polynomial_Ocoeff(X2,X0),X4) )
& ( hAPP(c_Polynomial_Ocoeff(X2,X1),sK18(X0,X1,X2)) != hAPP(c_Polynomial_Ocoeff(X2,X0),sK18(X0,X1,X2))
| X1 = X0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X3,sK18(X0,X1,X2))],[f2709]) ).
fof(f2711,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ( ( X2 != X3
| X1 = X0 )
& ( X0 != X1
| X3 = X2 ) ) ),
inference(nnf_transformation,[],[f2159]) ).
fof(f2712,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ( ( ~ 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,X0,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| 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,X0,X2)) ) ) ),
inference(nnf_transformation,[],[f2162]) ).
fof(f2713,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)
| X1 = X0 )
& ( X0 != X1
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) ) ) ),
inference(nnf_transformation,[],[f2166]) ).
fof(f2714,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__ab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ( ( ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| c_Orderings_Oord__class_Oless(X4,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| c_Orderings_Oord__class_Oless(X4,X3,X2) ) ) ),
inference(nnf_transformation,[],[f2176]) ).
fof(f2715,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Groups_Oordered__ab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| c_Orderings_Oord__class_Oless__eq(X4,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X4,X3,X2) ) ) ),
inference(nnf_transformation,[],[f2178]) ).
fof(f2716,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oab__group__add(X2)
| ( ( X0 != X1
| c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2) )
& ( c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
| X1 = X0 ) ) ),
inference(nnf_transformation,[],[f2181]) ).
fof(f2717,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X2)
| ( ( c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
| X1 = X0 )
& ( X0 != X1
| c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(nnf_transformation,[],[f2182]) ).
fof(f2718,plain,
! [X0,X1,X2] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) ) ),
inference(nnf_transformation,[],[f808]) ).
fof(f2719,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ) ) ),
inference(nnf_transformation,[],[f2190]) ).
fof(f2721,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ( ( ~ 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,X0,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| 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,X0,X2)) ) ) ),
inference(nnf_transformation,[],[f2201]) ).
fof(f2722,plain,
! [X0,X1,X2] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
inference(nnf_transformation,[],[f823]) ).
fof(f2723,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(nnf_transformation,[],[f826]) ).
fof(f2724,plain,
! [X0,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,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,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,X0)) ) ),
inference(nnf_transformation,[],[f831]) ).
fof(f2725,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Oring(X5)
| ( ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) != c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2) = X0 )
& ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2) != X0
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0) ) ) ),
inference(nnf_transformation,[],[f2216]) ).
fof(f2726,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Oring(X5)
| ( ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) != c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
| X2 = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0) )
& ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0) != X2
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0) ) ) ),
inference(nnf_transformation,[],[f2217]) ).
fof(f2727,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)) ) ) ),
inference(nnf_transformation,[],[f2224]) ).
fof(f2728,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)) ) ) ),
inference(nnf_transformation,[],[f2225]) ).
fof(f2729,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ( ( ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) )
& ( ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)) ) ) ),
inference(nnf_transformation,[],[f2226]) ).
fof(f2730,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ( ( ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) )
& ( ~ c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)) ) ) ),
inference(nnf_transformation,[],[f2227]) ).
fof(f2732,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Odvd(X3)
| ~ class_Rings_Ocomm__ring(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ! [X4,X5] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0))) ) ) ),
inference(nnf_transformation,[],[f2232]) ).
fof(f2733,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) )
& ( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f2235]) ).
fof(f2734,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) )
& ( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(flattening,[],[f2733]) ).
fof(f2735,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ( ! [X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X4) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) )
& ( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(rectify,[],[f2734]) ).
fof(f2736,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ( ! [X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X4) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) )
& ( ( ~ hBOOL(hAPP(X2,sK19(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK19(X0,X1,X2)) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X3,sK19(X0,X1,X2))],[f2735]) ).
fof(f2737,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ( ! [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1
| hBOOL(hAPP(X2,X3)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) )
& ( ? [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1
& ~ hBOOL(hAPP(X2,X3)) )
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
& ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f2236]) ).
fof(f2738,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ( ! [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1
| hBOOL(hAPP(X2,X3)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) )
& ( ? [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1
& ~ hBOOL(hAPP(X2,X3)) )
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
& ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(flattening,[],[f2737]) ).
fof(f2739,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ( ! [X4] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X4) != X1
| hBOOL(hAPP(X2,X4)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) )
& ( ? [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1
& ~ hBOOL(hAPP(X2,X3)) )
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
& ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(rectify,[],[f2738]) ).
fof(f2740,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ( ! [X4] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X4) != X1
| hBOOL(hAPP(X2,X4)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) )
& ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK20(X0,X1,X2)) = X1
& ~ hBOOL(hAPP(X2,sK20(X0,X1,X2))) )
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
& ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X3,sK20(X0,X1,X2))],[f2739]) ).
fof(f2741,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) ) ) ),
inference(nnf_transformation,[],[f2243]) ).
fof(f2742,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1) = X0 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1) != X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0) ) ) ),
inference(nnf_transformation,[],[f2245]) ).
fof(f2743,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) ) ) ),
inference(nnf_transformation,[],[f2246]) ).
fof(f2744,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0) != X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0) ) ) ),
inference(nnf_transformation,[],[f2248]) ).
fof(f2745,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| ( ( c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0
| hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0)) = c_Groups_Ozero__class_Ozero(X1) ) ) ),
inference(nnf_transformation,[],[f2251]) ).
fof(f2746,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ( ( ~ 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),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| 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),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) ) ) ),
inference(nnf_transformation,[],[f2256]) ).
fof(f2747,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ( ( ~ 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),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| 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),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) ) ) ),
inference(nnf_transformation,[],[f2257]) ).
fof(f2748,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ( ( ~ c_Polynomial_Opos__poly(X1,X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))) )
& ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0)))
| c_Polynomial_Opos__poly(X1,X0) ) ) ),
inference(nnf_transformation,[],[f2262]) ).
fof(f2749,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
| c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| X1 = X0 )
& ( ( ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
& X0 != X1 )
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0) ) ) ),
inference(nnf_transformation,[],[f2268]) ).
fof(f2750,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
| c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| X1 = X0 )
& ( ( ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
& X0 != X1 )
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0) ) ) ),
inference(flattening,[],[f2749]) ).
fof(f2751,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X2)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
| c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1)) )
& ( ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0) ) ) ),
inference(nnf_transformation,[],[f2269]) ).
fof(f2752,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f895]) ).
fof(f2753,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(nnf_transformation,[],[f899]) ).
fof(f2754,plain,
! [X0,X1,X2] :
( ~ class_Rings_Odivision__ring(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ( ( c_Groups_Oone__class_Oone(X2) != c_Rings_Oinverse__class_Odivide(X2,X0,X1)
| X0 = X1 )
& ( X0 != X1
| c_Rings_Oinverse__class_Odivide(X2,X0,X1) = c_Groups_Oone__class_Oone(X2) ) ) ),
inference(nnf_transformation,[],[f2291]) ).
fof(f2755,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Odivision__ring(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ( ( c_Rings_Oinverse__class_Odivide(X3,X1,X2) != X0
| X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2) != X1
| c_Rings_Oinverse__class_Odivide(X3,X1,X2) = X0 ) ) ),
inference(nnf_transformation,[],[f2307]) ).
fof(f2757,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Fields_Ofield(X4)
| c_Groups_Ozero__class_Ozero(X4) = X3
| c_Groups_Ozero__class_Ozero(X4) = X2
| ( ( c_Rings_Oinverse__class_Odivide(X4,X1,X3) != c_Rings_Oinverse__class_Odivide(X4,X0,X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)
| c_Rings_Oinverse__class_Odivide(X4,X1,X3) = c_Rings_Oinverse__class_Odivide(X4,X0,X2) ) ) ),
inference(nnf_transformation,[],[f2320]) ).
fof(f2762,plain,
! [X0,X1,X2] :
( ~ class_Divides_Osemiring__div(X2)
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Groups_Ozero__class_Ozero(X2) )
& ( c_Groups_Ozero__class_Ozero(X2) != c_Divides_Odiv__class_Omod(X2,X0,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) ) ) ),
inference(nnf_transformation,[],[f2356]) ).
fof(f2763,plain,
( ( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) )
& ( ? [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) )
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ) ),
inference(nnf_transformation,[],[f2424]) ).
fof(f2764,plain,
( ( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) )
& ( ? [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) )
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ) ),
inference(flattening,[],[f2763]) ).
fof(f2765,plain,
( ( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1) )
| ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) )
& ( ? [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) )
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ) ),
inference(rectify,[],[f2764]) ).
fof(f2766,plain,
( ( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1) )
| ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK21)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK21) )
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X0,sK21)],[f2765]) ).
fof(f2767,plain,
! [X0,X1] :
( hAPP(X1,sK2(X0,X1)) != hAPP(X0,sK2(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f2428]) ).
fof(f2768,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[],[f2]) ).
fof(f2769,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f3]) ).
fof(f2770,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(v_n____),
inference(cnf_transformation,[],[f4]) ).
fof(f2777,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) ),
inference(cnf_transformation,[],[f1258]) ).
fof(f2778,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK4)
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(cnf_transformation,[],[f2433]) ).
fof(f2779,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK4)
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(cnf_transformation,[],[f2433]) ).
fof(f2786,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1))) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f2787,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),X1) ),
inference(cnf_transformation,[],[f1263]) ).
fof(f2788,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
inference(cnf_transformation,[],[f1264]) ).
fof(f2791,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))) ),
inference(cnf_transformation,[],[f1268]) ).
fof(f2792,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f2440]) ).
fof(f2793,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1 ),
inference(cnf_transformation,[],[f2440]) ).
fof(f2794,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2) ),
inference(cnf_transformation,[],[f2440]) ).
fof(f2795,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oring__1__no__zero__divisors(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ),
inference(cnf_transformation,[],[f1272]) ).
fof(f2796,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| c_Groups_Ozero__class_Ozero(X1) = X0 ),
inference(cnf_transformation,[],[f1274]) ).
fof(f2797,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),sK6(X1,X2))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0))) ),
inference(cnf_transformation,[],[f2441]) ).
fof(f2798,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sK6(X1,X2))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0))) ),
inference(cnf_transformation,[],[f2441]) ).
fof(f2799,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ),
inference(cnf_transformation,[],[f2443]) ).
fof(f2800,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0) ),
inference(cnf_transformation,[],[f2443]) ).
fof(f2801,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0) ),
inference(cnf_transformation,[],[f2443]) ).
fof(f2802,plain,
! [X0] : c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
inference(cnf_transformation,[],[f19]) ).
fof(f2803,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2445]) ).
fof(f2806,plain,
! [X0,X1] :
( ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f1279]) ).
fof(f2807,plain,
! [X0] :
( ~ class_Groups_Ozero(X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(cnf_transformation,[],[f1280]) ).
fof(f2808,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1282]) ).
fof(f2809,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0)) ),
inference(cnf_transformation,[],[f1283]) ).
fof(f2810,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| ~ class_Int_Oring__char__0(X2)
| c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2446]) ).
fof(f2812,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(sK7),
inference(cnf_transformation,[],[f2447]) ).
fof(f2814,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Nat_OSuc(c_Polynomial_Odegree(X1,X0)) ),
inference(cnf_transformation,[],[f1287]) ).
fof(f2823,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
inference(cnf_transformation,[],[f35]) ).
fof(f2824,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osynthetic__div(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,X1) ),
inference(cnf_transformation,[],[f2449]) ).
fof(f2825,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Odegree(X2,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osynthetic__div(X2,X1,X0) ),
inference(cnf_transformation,[],[f2449]) ).
fof(f2840,plain,
! [X0,X1] :
( X0 != X1
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f1291]) ).
fof(f2850,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f1304]) ).
fof(f2851,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0)) ),
inference(cnf_transformation,[],[f1306]) ).
fof(f2870,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
inference(cnf_transformation,[],[f1333]) ).
fof(f2875,plain,
! [X0] : c_Nat_OSuc(X0) != X0,
inference(cnf_transformation,[],[f68]) ).
fof(f2876,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 ),
inference(cnf_transformation,[],[f2458]) ).
fof(f2877,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) ),
inference(cnf_transformation,[],[f2458]) ).
fof(f2879,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f2459]) ).
fof(f2880,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2))) ),
inference(cnf_transformation,[],[f2459]) ).
fof(f2881,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f72]) ).
fof(f2882,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ozero(X3)
| hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) != X1
| c_Polynomial_Opoly__rec(X0,X3,X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X1 ),
inference(cnf_transformation,[],[f1340]) ).
fof(f2885,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(X2,X0,X1),c_Polynomial_Odegree(X2,X1)) ),
inference(cnf_transformation,[],[f1343]) ).
fof(f2886,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)) ),
inference(cnf_transformation,[],[f1345]) ).
fof(f2887,plain,
! [X0,X1] :
( ~ 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_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f1346]) ).
fof(f2889,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f2460]) ).
fof(f2890,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2))) ),
inference(cnf_transformation,[],[f2460]) ).
fof(f2891,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) ),
inference(cnf_transformation,[],[f2462]) ).
fof(f2892,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
| c_Groups_Ozero__class_Ozero(X3) != X2
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0 ),
inference(cnf_transformation,[],[f2462]) ).
fof(f2894,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f2462]) ).
fof(f2895,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) != X2
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X0
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f2462]) ).
fof(f2896,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X0
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f2462]) ).
fof(f2899,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(cnf_transformation,[],[f1354]) ).
fof(f2903,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Ozero(X4)
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
| X0 = X2 ),
inference(cnf_transformation,[],[f2464]) ).
fof(f2904,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Ozero(X4)
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
| X1 = X3 ),
inference(cnf_transformation,[],[f2464]) ).
fof(f2906,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,X1) != c_Polynomial_OpCons(X3,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ),
inference(cnf_transformation,[],[f1358]) ).
fof(f2907,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0)) ),
inference(cnf_transformation,[],[f1359]) ).
fof(f2908,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Groups_Ozero(X5)
| c_Polynomial_Opoly__rec(X4,X5,X3,X2,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X2,X1),X0),c_If(X4,c_fequal(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3,c_Polynomial_Opoly__rec(X4,X5,X3,X2,X0))) ),
inference(cnf_transformation,[],[f1360]) ).
fof(f2909,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Nat_OSuc(c_Polynomial_Odegree(X2,X0))) ),
inference(cnf_transformation,[],[f1361]) ).
fof(f2910,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f92]) ).
fof(f2911,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2465]) ).
fof(f2913,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
inference(cnf_transformation,[],[f94]) ).
fof(f2914,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) ),
inference(cnf_transformation,[],[f2466]) ).
fof(f2916,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Nat_OSuc(X0) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2468]) ).
fof(f2919,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2469]) ).
fof(f2924,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(cnf_transformation,[],[f1366]) ).
fof(f2925,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Groups_Ozero(X5)
| hAPP(hAPP(hAPP(X4,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3) != X3
| c_Polynomial_Opoly__rec(X2,X5,X3,X4,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X4,X1),X0),c_Polynomial_Opoly__rec(X2,X5,X3,X4,X0)) ),
inference(cnf_transformation,[],[f1368]) ).
fof(f2926,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) ),
inference(cnf_transformation,[],[f1370]) ).
fof(f2927,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X0,X1))) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2928,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0 ),
inference(cnf_transformation,[],[f2471]) ).
fof(f2929,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(X2) = X1 ),
inference(cnf_transformation,[],[f2471]) ).
fof(f2931,plain,
! [X0] :
( ~ class_Groups_Ozero(X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(cnf_transformation,[],[f1374]) ).
fof(f2932,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1376]) ).
fof(f2933,plain,
! [X2,X0,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),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1378]) ).
fof(f2934,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osmult(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1 ),
inference(cnf_transformation,[],[f2473]) ).
fof(f2935,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0) ),
inference(cnf_transformation,[],[f2473]) ).
fof(f2936,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0) ),
inference(cnf_transformation,[],[f2473]) ).
fof(f2937,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f1380]) ).
fof(f2938,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X2)),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X0)),X1)) ),
inference(cnf_transformation,[],[f1382]) ).
fof(f2939,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X0))) ),
inference(cnf_transformation,[],[f1384]) ).
fof(f2940,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))) ),
inference(cnf_transformation,[],[f1386]) ).
fof(f2941,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X1,X0)))
| c_Groups_Ozero__class_Ozero(X3) = X1
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X0)) ),
inference(cnf_transformation,[],[f1388]) ).
fof(f2944,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0))) ),
inference(cnf_transformation,[],[f2474]) ).
fof(f2945,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osynthetic__div(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Polynomial_OpCons(X3,hAPP(c_Polynomial_Opoly(X3,X1),X0),c_Polynomial_Osynthetic__div(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1393]) ).
fof(f2946,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) ),
inference(cnf_transformation,[],[f1394]) ).
fof(f2947,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Nat_OSuc(c_Polynomial_Odegree(X2,X1)) ),
inference(cnf_transformation,[],[f1396]) ).
fof(f2948,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| X0 = X2 ),
inference(cnf_transformation,[],[f1398]) ).
fof(f2949,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1)))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(cnf_transformation,[],[f1400]) ).
fof(f2950,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)) ),
inference(cnf_transformation,[],[f1401]) ).
fof(f2951,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)) ),
inference(cnf_transformation,[],[f1401]) ).
fof(f2953,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Ocomm__semiring__0(X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X3,c_Polynomial_Osmult(X4,X2,X1)) != c_Polynomial_OpCons(X4,X0,X1)
| c_Polynomial_Osynthetic__div(X4,X3,X2) = X1 ),
inference(cnf_transformation,[],[f1404]) ).
fof(f2954,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Ocomm__semiring__0(X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X3,c_Polynomial_Osmult(X4,X2,X1)) != c_Polynomial_OpCons(X4,X0,X1)
| hAPP(c_Polynomial_Opoly(X4,X3),X2) = X0 ),
inference(cnf_transformation,[],[f1404]) ).
fof(f2955,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,c_Polynomial_Osmult(X2,X0,c_Polynomial_Osynthetic__div(X2,X1,X0))) = c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0),c_Polynomial_Osynthetic__div(X2,X1,X0)) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2956,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) = X0 ),
inference(cnf_transformation,[],[f1406]) ).
fof(f2957,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) ),
inference(cnf_transformation,[],[f1407]) ).
fof(f2958,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(cnf_transformation,[],[f1408]) ).
fof(f2959,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f1410]) ).
fof(f2960,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)) ),
inference(cnf_transformation,[],[f1412]) ).
fof(f2961,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Polynomial_Omonom(X2,X1,c_Nat_OSuc(X0)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0)) ),
inference(cnf_transformation,[],[f1413]) ).
fof(f2968,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1418]) ).
fof(f2969,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
inference(cnf_transformation,[],[f1420]) ).
fof(f2970,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(cnf_transformation,[],[f1422]) ).
fof(f2971,plain,
! [X0] :
( ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f1423]) ).
fof(f2972,plain,
! [X0] :
( ~ class_Rings_Olinordered__semidom(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(cnf_transformation,[],[f1424]) ).
fof(f2973,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f2476]) ).
fof(f2975,plain,
! [X0] :
( ~ class_Rings_Olinordered__semidom(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))) ),
inference(cnf_transformation,[],[f1427]) ).
fof(f2976,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))) ),
inference(cnf_transformation,[],[f1428]) ).
fof(f2977,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ozero(X3)
| c_Polynomial_Omonom(X3,X2,X1) != c_Polynomial_Omonom(X3,X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f2477]) ).
fof(f2979,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X3)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1) ),
inference(cnf_transformation,[],[f1430]) ).
fof(f2980,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1) ),
inference(cnf_transformation,[],[f1432]) ).
fof(f2983,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,X0,X1) ),
inference(cnf_transformation,[],[f1438]) ).
fof(f2984,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(cnf_transformation,[],[f1440]) ).
fof(f2989,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ),
inference(cnf_transformation,[],[f1450]) ).
fof(f2994,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ),
inference(cnf_transformation,[],[f1460]) ).
fof(f3002,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ),
inference(cnf_transformation,[],[f2480]) ).
fof(f3003,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X2)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ),
inference(cnf_transformation,[],[f2482]) ).
fof(f3004,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f2482]) ).
fof(f3006,plain,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X0,X0) ),
inference(cnf_transformation,[],[f1471]) ).
fof(f3011,plain,
! [X0,X1] :
( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f1473]) ).
fof(f3023,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Ocomm__monoid__add(X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X2,X0)) ),
inference(cnf_transformation,[],[f1478]) ).
fof(f3024,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X0,X1)) ),
inference(cnf_transformation,[],[f1480]) ).
fof(f3025,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) ),
inference(cnf_transformation,[],[f1482]) ).
fof(f3026,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ),
inference(cnf_transformation,[],[f1484]) ).
fof(f3027,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(cnf_transformation,[],[f1485]) ).
fof(f3028,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1486]) ).
fof(f3029,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,X0,X1) ),
inference(cnf_transformation,[],[f1488]) ).
fof(f3030,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(cnf_transformation,[],[f1490]) ).
fof(f3031,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,X0,X1) ),
inference(cnf_transformation,[],[f1492]) ).
fof(f3032,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(cnf_transformation,[],[f1494]) ).
fof(f3042,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2486]) ).
fof(f3043,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 != X1
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ),
inference(cnf_transformation,[],[f2486]) ).
fof(f3049,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ),
inference(cnf_transformation,[],[f2490]) ).
fof(f3050,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ),
inference(cnf_transformation,[],[f2490]) ).
fof(f3051,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X2)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ),
inference(cnf_transformation,[],[f2490]) ).
fof(f3052,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f2492]) ).
fof(f3053,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ),
inference(cnf_transformation,[],[f2492]) ).
fof(f3054,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X2)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ),
inference(cnf_transformation,[],[f2492]) ).
fof(f3058,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ),
inference(cnf_transformation,[],[f2494]) ).
fof(f3059,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ),
inference(cnf_transformation,[],[f2494]) ).
fof(f3060,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) ),
inference(cnf_transformation,[],[f1524]) ).
fof(f3061,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Oone__class_Oone(X3))
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)) ),
inference(cnf_transformation,[],[f1526]) ).
fof(f3062,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1528]) ).
fof(f3063,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1529]) ).
fof(f3064,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0))) ),
inference(cnf_transformation,[],[f1531]) ).
fof(f3065,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(cnf_transformation,[],[f1532]) ).
fof(f3067,plain,
! [X0] :
( ~ class_Rings_Ozero__neq__one(X0)
| c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ),
inference(cnf_transformation,[],[f1534]) ).
fof(f3068,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0))) ),
inference(cnf_transformation,[],[f1536]) ).
fof(f3069,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0)) ),
inference(cnf_transformation,[],[f1537]) ).
fof(f3070,plain,
! [X0,X1] :
( ~ class_Groups_Omonoid__mult(X1)
| c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0) ),
inference(cnf_transformation,[],[f1538]) ).
fof(f3074,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f2495]) ).
fof(f3076,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f219]) ).
fof(f3078,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1542]) ).
fof(f3080,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0) ),
inference(cnf_transformation,[],[f1546]) ).
fof(f3081,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Nat_OSuc(X1) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(cnf_transformation,[],[f1548]) ).
fof(f3089,plain,
! [X0,X1] :
( X0 != X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f2499]) ).
fof(f3090,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f2499]) ).
fof(f3091,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
inference(cnf_transformation,[],[f2500]) ).
fof(f3092,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2500]) ).
fof(f3093,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f2502]) ).
fof(f3101,plain,
! [X0,X1] :
( X0 != X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1556]) ).
fof(f3103,plain,
! [X0,X1] :
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
inference(cnf_transformation,[],[f1557]) ).
fof(f3104,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0 ),
inference(cnf_transformation,[],[f1558]) ).
fof(f3105,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 ),
inference(cnf_transformation,[],[f1559]) ).
fof(f3106,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2505]) ).
fof(f3108,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)),
inference(cnf_transformation,[],[f240]) ).
fof(f3109,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0)) ),
inference(cnf_transformation,[],[f1560]) ).
fof(f3110,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0 ),
inference(cnf_transformation,[],[f1561]) ).
fof(f3111,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0))) ),
inference(cnf_transformation,[],[f1562]) ).
fof(f3112,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),c_Groups_Oone__class_Oone(X2)) ),
inference(cnf_transformation,[],[f1564]) ).
fof(f3114,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2506]) ).
fof(f3115,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) ),
inference(cnf_transformation,[],[f2506]) ).
fof(f3117,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))) ),
inference(cnf_transformation,[],[f1570]) ).
fof(f3118,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1572]) ).
fof(f3119,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1574]) ).
fof(f3120,plain,
! [X0] :
( ~ class_Rings_Olinordered__semidom(X0)
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(cnf_transformation,[],[f1575]) ).
fof(f3121,plain,
! [X0] :
( ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f1576]) ).
fof(f3122,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1578]) ).
fof(f3123,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1580]) ).
fof(f3125,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK8(X0,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(cnf_transformation,[],[f2510]) ).
fof(f3126,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Nat_OSuc(sK8(X0,X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(cnf_transformation,[],[f2510]) ).
fof(f3129,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2511]) ).
fof(f3131,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Nat_OSuc(sK9(X0)) = X0 ),
inference(cnf_transformation,[],[f2514]) ).
fof(f3132,plain,
! [X0,X1] :
( c_Nat_OSuc(X1) != X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f2514]) ).
fof(f3133,plain,
! [X0,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,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f1583]) ).
fof(f3134,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f1585]) ).
fof(f3137,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2516]) ).
fof(f3141,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f1586]) ).
fof(f3142,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(cnf_transformation,[],[f1587]) ).
fof(f3145,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1589]) ).
fof(f3146,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ),
inference(cnf_transformation,[],[f1591]) ).
fof(f3148,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))) ),
inference(cnf_transformation,[],[f1592]) ).
fof(f3149,plain,
! [X2,X0,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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f3151,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| 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),X0)) ),
inference(cnf_transformation,[],[f2520]) ).
fof(f3154,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ),
inference(cnf_transformation,[],[f2521]) ).
fof(f3155,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0) ),
inference(cnf_transformation,[],[f2521]) ).
fof(f3156,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Polynomial_Odegree(X2,X1) = c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)) ),
inference(cnf_transformation,[],[f1597]) ).
fof(f3158,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Omonom(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(X2) = X1 ),
inference(cnf_transformation,[],[f2522]) ).
fof(f3159,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Omonom(X2,X1,X0) ),
inference(cnf_transformation,[],[f2522]) ).
fof(f3160,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0 ),
inference(cnf_transformation,[],[f1601]) ).
fof(f3161,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)),X0) ),
inference(cnf_transformation,[],[f1602]) ).
fof(f3162,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(cnf_transformation,[],[f1604]) ).
fof(f3163,plain,
! [X0,X1] :
( ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
inference(cnf_transformation,[],[f1606]) ).
fof(f3165,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
inference(cnf_transformation,[],[f1608]) ).
fof(f3169,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ),
inference(cnf_transformation,[],[f1616]) ).
fof(f3171,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(cnf_transformation,[],[f1620]) ).
fof(f3180,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X2)
| X0 != X1
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ),
inference(cnf_transformation,[],[f1636]) ).
fof(f3181,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X2)
| X0 != X1
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ),
inference(cnf_transformation,[],[f2525]) ).
fof(f3183,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2525]) ).
fof(f3184,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ),
inference(cnf_transformation,[],[f1639]) ).
fof(f3185,plain,
! [X2,X3,X0,X1,X5] :
( ~ class_Orderings_Oord(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5)) ),
inference(cnf_transformation,[],[f2528]) ).
fof(f3186,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oord(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK10(X0,X1,X3)),hAPP(X0,sK10(X0,X1,X3)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ),
inference(cnf_transformation,[],[f2528]) ).
fof(f3187,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ),
inference(cnf_transformation,[],[f1642]) ).
fof(f3188,plain,
! [X2,X0,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,X1,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),X1) ),
inference(cnf_transformation,[],[f1644]) ).
fof(f3191,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(cnf_transformation,[],[f1650]) ).
fof(f3192,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(cnf_transformation,[],[f1652]) ).
fof(f3193,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f1654]) ).
fof(f3194,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f1656]) ).
fof(f3195,plain,
! [X0,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),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2530]) ).
fof(f3196,plain,
! [X0,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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f2530]) ).
fof(f3198,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f1658]) ).
fof(f3199,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oord(X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1) ),
inference(cnf_transformation,[],[f2532]) ).
fof(f3200,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oord(X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ),
inference(cnf_transformation,[],[f2532]) ).
fof(f3201,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oord(X3)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0) ),
inference(cnf_transformation,[],[f2532]) ).
fof(f3203,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f311]) ).
fof(f3204,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2534]) ).
fof(f3205,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(cnf_transformation,[],[f2534]) ).
fof(f3207,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f1660]) ).
fof(f3211,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f317]) ).
fof(f3213,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
inference(cnf_transformation,[],[f1661]) ).
fof(f3214,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f3215,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| 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,X2,X0)) ),
inference(cnf_transformation,[],[f1665]) ).
fof(f3216,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f1666]) ).
fof(f3219,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2535]) ).
fof(f3220,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(cnf_transformation,[],[f2535]) ).
fof(f3221,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
inference(cnf_transformation,[],[f326]) ).
fof(f3222,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
inference(cnf_transformation,[],[f327]) ).
fof(f3223,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f2536]) ).
fof(f3224,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) ),
inference(cnf_transformation,[],[f2536]) ).
fof(f3227,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(cnf_transformation,[],[f1670]) ).
fof(f3228,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1671]) ).
fof(f3229,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| 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,X2,X0)) ),
inference(cnf_transformation,[],[f1673]) ).
fof(f3230,plain,
! [X2,X0,X1] :
( ~ 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,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f1674]) ).
fof(f3233,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2537]) ).
fof(f3234,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(cnf_transformation,[],[f2537]) ).
fof(f3235,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK11(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f2540]) ).
fof(f3238,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(cnf_transformation,[],[f339]) ).
fof(f3239,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2542]) ).
fof(f3240,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2542]) ).
fof(f3241,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ),
inference(cnf_transformation,[],[f2542]) ).
fof(f3242,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ),
inference(cnf_transformation,[],[f2542]) ).
fof(f3251,plain,
! [X0,X1] :
( ~ 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,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f2546]) ).
fof(f3255,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(cnf_transformation,[],[f344]) ).
fof(f3256,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK12(X0,X1))) = X0 ),
inference(cnf_transformation,[],[f2549]) ).
fof(f3257,plain,
! [X2,X0,X1] :
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2549]) ).
fof(f3260,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oab__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1678]) ).
fof(f3265,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ocancel__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,X0) != c_Groups_Oplus__class_Oplus(X3,X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1682]) ).
fof(f3266,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,X0) != c_Groups_Oplus__class_Oplus(X3,X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1684]) ).
fof(f3267,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ocancel__semigroup__add(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f1686]) ).
fof(f3270,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(cnf_transformation,[],[f1688]) ).
fof(f3271,plain,
! [X0,X1] :
( ~ class_Groups_Omonoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(cnf_transformation,[],[f1689]) ).
fof(f3274,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(cnf_transformation,[],[f1691]) ).
fof(f3275,plain,
! [X0,X1] :
( ~ class_Groups_Omonoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(cnf_transformation,[],[f1692]) ).
fof(f3277,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ),
inference(cnf_transformation,[],[f2555]) ).
fof(f3279,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(cnf_transformation,[],[f2556]) ).
fof(f3280,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1696]) ).
fof(f3281,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ),
inference(cnf_transformation,[],[f1698]) ).
fof(f3282,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Oordered__ab__semigroup__add(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(cnf_transformation,[],[f1700]) ).
fof(f3283,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(cnf_transformation,[],[f1702]) ).
fof(f3284,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ),
inference(cnf_transformation,[],[f1704]) ).
fof(f3286,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ),
inference(cnf_transformation,[],[f2557]) ).
fof(f3288,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(cnf_transformation,[],[f2558]) ).
fof(f3289,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1708]) ).
fof(f3290,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ),
inference(cnf_transformation,[],[f1710]) ).
fof(f3291,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(cnf_transformation,[],[f1712]) ).
fof(f3292,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(cnf_transformation,[],[f1714]) ).
fof(f3293,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| c_Orderings_Oord__class_Oless(X3,X1,X0) ),
inference(cnf_transformation,[],[f1716]) ).
fof(f3294,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f1718]) ).
fof(f3295,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2)) ),
inference(cnf_transformation,[],[f1720]) ).
fof(f3296,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oordered__comm__monoid__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(cnf_transformation,[],[f1722]) ).
fof(f3297,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__comm__monoid__add(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),X0)
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(X2) = X0 ),
inference(cnf_transformation,[],[f2560]) ).
fof(f3298,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__comm__monoid__add(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),X0)
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(X2) = X1 ),
inference(cnf_transformation,[],[f2560]) ).
fof(f3301,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2561]) ).
fof(f3302,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2561]) ).
fof(f3303,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f2562]) ).
fof(f3304,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0)) ),
inference(cnf_transformation,[],[f2562]) ).
fof(f3305,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f1730]) ).
fof(f3306,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__comm__monoid__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0)) ),
inference(cnf_transformation,[],[f1732]) ).
fof(f3307,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2563]) ).
fof(f3308,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2563]) ).
fof(f3309,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f2564]) ).
fof(f3310,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0)) ),
inference(cnf_transformation,[],[f2564]) ).
fof(f3311,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(cnf_transformation,[],[f1736]) ).
fof(f3312,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(cnf_transformation,[],[f1738]) ).
fof(f3313,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(cnf_transformation,[],[f1739]) ).
fof(f3314,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2565]) ).
fof(f3315,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2565]) ).
fof(f3318,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Nat_OSuc(c_Polynomial_Oorder(X2,X0,X1)))),X1)) ),
inference(cnf_transformation,[],[f1744]) ).
fof(f3319,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
inference(cnf_transformation,[],[f1745]) ).
fof(f3321,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(cnf_transformation,[],[f392]) ).
fof(f3322,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
inference(cnf_transformation,[],[f393]) ).
fof(f3323,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0),
inference(cnf_transformation,[],[f394]) ).
fof(f3324,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2566]) ).
fof(f3326,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f2567]) ).
fof(f3331,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ouminus__class_Ouminus(X2,X1) != X0
| c_Groups_Ouminus__class_Ouminus(X2,X0) = X1 ),
inference(cnf_transformation,[],[f2569]) ).
fof(f3333,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f2570]) ).
fof(f3335,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__ring(X2)
| c_Polynomial_Osmult(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) ),
inference(cnf_transformation,[],[f1751]) ).
fof(f3336,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__ring(X2)
| hAPP(c_Polynomial_Opoly(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0)) ),
inference(cnf_transformation,[],[f1752]) ).
fof(f3338,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_OpCons(X2,X1,X0)) = c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) ),
inference(cnf_transformation,[],[f1754]) ).
fof(f3339,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ),
inference(cnf_transformation,[],[f1755]) ).
fof(f3344,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X0) != X0
| c_Groups_Ozero__class_Ozero(X1) = X0 ),
inference(cnf_transformation,[],[f2573]) ).
fof(f3345,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) != X0
| c_Groups_Ouminus__class_Ouminus(X1,X0) = X0 ),
inference(cnf_transformation,[],[f2573]) ).
fof(f3346,plain,
! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0 ),
inference(cnf_transformation,[],[f2574]) ).
fof(f3348,plain,
! [X0] :
( ~ class_Groups_Ogroup__add(X0)
| c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f1760]) ).
fof(f3349,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ),
inference(cnf_transformation,[],[f2575]) ).
fof(f3351,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) ),
inference(cnf_transformation,[],[f2576]) ).
fof(f3353,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ),
inference(cnf_transformation,[],[f2577]) ).
fof(f3355,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ),
inference(cnf_transformation,[],[f1765]) ).
fof(f3356,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ),
inference(cnf_transformation,[],[f2578]) ).
fof(f3358,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) ),
inference(cnf_transformation,[],[f2579]) ).
fof(f3360,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| c_Orderings_Oord__class_Oless(X2,X0,X1) ),
inference(cnf_transformation,[],[f2580]) ).
fof(f3361,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(cnf_transformation,[],[f2580]) ).
fof(f3362,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(cnf_transformation,[],[f1769]) ).
fof(f3363,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ),
inference(cnf_transformation,[],[f1770]) ).
fof(f3364,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0 ),
inference(cnf_transformation,[],[f1771]) ).
fof(f3365,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0 ),
inference(cnf_transformation,[],[f1772]) ).
fof(f3366,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__ring__1(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) ),
inference(cnf_transformation,[],[f2581]) ).
fof(f3367,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__ring__1(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0))) ),
inference(cnf_transformation,[],[f2581]) ).
fof(f3368,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__ring__1(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) ),
inference(cnf_transformation,[],[f2582]) ).
fof(f3369,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__ring__1(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)) ),
inference(cnf_transformation,[],[f2582]) ).
fof(f3370,plain,
! [X0] :
( ~ class_Groups_Oab__group__add(X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(cnf_transformation,[],[f1775]) ).
fof(f3371,plain,
! [X0,X1] :
( ~ class_Groups_Oab__group__add(X1)
| c_Polynomial_Odegree(X1,X0) = c_Polynomial_Odegree(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0)) ),
inference(cnf_transformation,[],[f1776]) ).
fof(f3372,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__ring(X2)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) ),
inference(cnf_transformation,[],[f1777]) ).
fof(f3373,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2583]) ).
fof(f3374,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,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,X0)) ),
inference(cnf_transformation,[],[f2583]) ).
fof(f3375,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2584]) ).
fof(f3376,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ),
inference(cnf_transformation,[],[f2584]) ).
fof(f3377,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f2585]) ).
fof(f3378,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2585]) ).
fof(f3379,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f2586]) ).
fof(f3380,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ),
inference(cnf_transformation,[],[f2586]) ).
fof(f3381,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2587]) ).
fof(f3382,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ),
inference(cnf_transformation,[],[f2587]) ).
fof(f3383,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2588]) ).
fof(f3384,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0)) ),
inference(cnf_transformation,[],[f2588]) ).
fof(f3385,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f2589]) ).
fof(f3386,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2589]) ).
fof(f3387,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f2590]) ).
fof(f3388,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ),
inference(cnf_transformation,[],[f2590]) ).
fof(f3391,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| c_Groups_Ouminus__class_Ouminus(X2,X0) = X1 ),
inference(cnf_transformation,[],[f2591]) ).
fof(f3392,plain,
! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ),
inference(cnf_transformation,[],[f1788]) ).
fof(f3393,plain,
! [X0,X1] :
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ),
inference(cnf_transformation,[],[f1789]) ).
fof(f3395,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ouminus__class_Ouminus(X2,X1) != X0
| c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0) ),
inference(cnf_transformation,[],[f2592]) ).
fof(f3396,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| c_Groups_Ouminus__class_Ouminus(X2,X1) = X0 ),
inference(cnf_transformation,[],[f1792]) ).
fof(f3397,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| 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),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1 ),
inference(cnf_transformation,[],[f2594]) ).
fof(f3398,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
| 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),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(cnf_transformation,[],[f2594]) ).
fof(f3400,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X2),c_Groups_Oplus__class_Oplus(X4,X1,X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(cnf_transformation,[],[f1794]) ).
fof(f3401,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1) ),
inference(cnf_transformation,[],[f1795]) ).
fof(f3403,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1797]) ).
fof(f3404,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(cnf_transformation,[],[f1798]) ).
fof(f3405,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
inference(cnf_transformation,[],[f1799]) ).
fof(f3406,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f1800]) ).
fof(f3407,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(cnf_transformation,[],[f1801]) ).
fof(f3408,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f1802]) ).
fof(f3409,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(cnf_transformation,[],[f1803]) ).
fof(f3410,plain,
! [X0,X1] :
( ~ 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),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f1805]) ).
fof(f3411,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f1807]) ).
fof(f3412,plain,
! [X0,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,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(cnf_transformation,[],[f1809]) ).
fof(f3413,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1)) ),
inference(cnf_transformation,[],[f2595]) ).
fof(f3414,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1))
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0) ),
inference(cnf_transformation,[],[f2595]) ).
fof(f3415,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0))
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ),
inference(cnf_transformation,[],[f2596]) ).
fof(f3416,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) ),
inference(cnf_transformation,[],[f2596]) ).
fof(f3417,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(cnf_transformation,[],[f1812]) ).
fof(f3418,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(cnf_transformation,[],[f1813]) ).
fof(f3419,plain,
! [X2,X0,X1] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X0) != X1
| c_Groups_Ozero__class_Ozero(X2) = X0 ),
inference(cnf_transformation,[],[f2597]) ).
fof(f3420,plain,
! [X2,X0,X1] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = X1 ),
inference(cnf_transformation,[],[f2597]) ).
fof(f3421,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oplus__class_Oplus(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0 ),
inference(cnf_transformation,[],[f2598]) ).
fof(f3422,plain,
! [X0,X1] :
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) != X0
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,X0) ),
inference(cnf_transformation,[],[f2598]) ).
fof(f3423,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Oorder(X2,X1,X0))),X0)) ),
inference(cnf_transformation,[],[f1816]) ).
fof(f3424,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__ring__1(X2)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Osynthetic__div(X2,X0,X1)),c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X0),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))) = X0 ),
inference(cnf_transformation,[],[f1817]) ).
fof(f3425,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK13(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f2601]) ).
fof(f3426,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2601]) ).
fof(f3427,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Polynomial_Opos__poly(X2,X0) ),
inference(cnf_transformation,[],[f2603]) ).
fof(f3428,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Polynomial_Opos__poly(X2,X0) ),
inference(cnf_transformation,[],[f2603]) ).
fof(f3429,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0)) ),
inference(cnf_transformation,[],[f2603]) ).
fof(f3430,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Polynomial_Opos__poly(X2,X0)
| c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0)) ),
inference(cnf_transformation,[],[f2603]) ).
fof(f3432,plain,
! [X2,X0,X1] :
( ~ class_Lattices_Oboolean__algebra(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ),
inference(cnf_transformation,[],[f2604]) ).
fof(f3433,plain,
! [X2,X0,X1] :
( ~ class_Lattices_Oboolean__algebra(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(cnf_transformation,[],[f2604]) ).
fof(f3434,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f467]) ).
fof(f3435,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f468]) ).
fof(f3436,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f2606]) ).
fof(f3437,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2606]) ).
fof(f3438,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2606]) ).
fof(f3439,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2607]) ).
fof(f3440,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f2607]) ).
fof(f3441,plain,
! [X0,X1] :
( ~ 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)),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2608]) ).
fof(f3443,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| 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)),X0) ),
inference(cnf_transformation,[],[f1822]) ).
fof(f3444,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
inference(cnf_transformation,[],[f1823]) ).
fof(f3445,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0) ),
inference(cnf_transformation,[],[f1825]) ).
fof(f3446,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1827]) ).
fof(f3447,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)) ),
inference(cnf_transformation,[],[f1829]) ).
fof(f3448,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| 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),X0)) ),
inference(cnf_transformation,[],[f1830]) ).
fof(f3449,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f2609]) ).
fof(f3450,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f2609]) ).
fof(f3451,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f479]) ).
fof(f3452,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f480]) ).
fof(f3453,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(cnf_transformation,[],[f481]) ).
fof(f3454,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[],[f482]) ).
fof(f3455,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f483]) ).
fof(f3456,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0),
inference(cnf_transformation,[],[f484]) ).
fof(f3457,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Ocomm__semiring__0(X4)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Polynomial_Omonom(X4,X3,X2)),c_Polynomial_Omonom(X4,X1,X0)) = c_Polynomial_Omonom(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(cnf_transformation,[],[f1831]) ).
fof(f3458,plain,
! [X0] :
( ~ 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),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f2610]) ).
fof(f3459,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,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),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f2610]) ).
fof(f3460,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) ),
inference(cnf_transformation,[],[f1832]) ).
fof(f3465,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1835]) ).
fof(f3466,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
| X0 = X1
| X2 = X3
| c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) != c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X1)) ),
inference(cnf_transformation,[],[f2614]) ).
fof(f3468,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
| c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X1))
| X2 != X3 ),
inference(cnf_transformation,[],[f2614]) ).
fof(f3469,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1837]) ).
fof(f3471,plain,
! [X0,X1] :
( X0 != X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f2616]) ).
fof(f3473,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f494]) ).
fof(f3474,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(cnf_transformation,[],[f1838]) ).
fof(f3475,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(cnf_transformation,[],[f1839]) ).
fof(f3476,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f497]) ).
fof(f3477,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oring(X2)
| c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(cnf_transformation,[],[f1840]) ).
fof(f3478,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oring(X2)
| c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) ),
inference(cnf_transformation,[],[f1841]) ).
fof(f3479,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oring(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) ),
inference(cnf_transformation,[],[f1842]) ).
fof(f3480,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oring(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(cnf_transformation,[],[f1843]) ).
fof(f3481,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
| c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1 ),
inference(cnf_transformation,[],[f2618]) ).
fof(f3482,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0) ),
inference(cnf_transformation,[],[f2618]) ).
fof(f3484,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(cnf_transformation,[],[f1845]) ).
fof(f3487,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1) ),
inference(cnf_transformation,[],[f1848]) ).
fof(f3489,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1850]) ).
fof(f3490,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1851]) ).
fof(f3491,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) ),
inference(cnf_transformation,[],[f1852]) ).
fof(f3492,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1853]) ).
fof(f3493,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f1854]) ).
fof(f3494,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
inference(cnf_transformation,[],[f1855]) ).
fof(f3495,plain,
! [X0,X1] :
( ~ class_Rings_Omult__zero(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
inference(cnf_transformation,[],[f1856]) ).
fof(f3496,plain,
! [X0,X1] :
( ~ class_Rings_Omult__zero(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f1857]) ).
fof(f3497,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oring__no__zero__divisors(X2)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)
| c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1 ),
inference(cnf_transformation,[],[f2620]) ).
fof(f3498,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oring__no__zero__divisors(X2)
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) ),
inference(cnf_transformation,[],[f2620]) ).
fof(f3499,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oring__no__zero__divisors(X2)
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) ),
inference(cnf_transformation,[],[f2620]) ).
fof(f3501,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ono__zero__divisors(X2)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)
| c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1 ),
inference(cnf_transformation,[],[f1862]) ).
fof(f3502,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1863]) ).
fof(f3503,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Osemiring(X4)
| c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oplus__class_Oplus(X4,X3,X1)),X2),X0) ),
inference(cnf_transformation,[],[f1864]) ).
fof(f3504,plain,
! [X0,X1] :
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(cnf_transformation,[],[f1865]) ).
fof(f3505,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__mult(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(cnf_transformation,[],[f1866]) ).
fof(f3506,plain,
! [X0,X1] :
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(cnf_transformation,[],[f1867]) ).
fof(f3507,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__mult(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(cnf_transformation,[],[f1868]) ).
fof(f3508,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))) ),
inference(cnf_transformation,[],[f1869]) ).
fof(f3509,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))) ),
inference(cnf_transformation,[],[f1870]) ).
fof(f3510,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))) ),
inference(cnf_transformation,[],[f1872]) ).
fof(f3511,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ),
inference(cnf_transformation,[],[f1874]) ).
fof(f3512,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))) ),
inference(cnf_transformation,[],[f1876]) ).
fof(f3513,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Odvd(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X2)) ),
inference(cnf_transformation,[],[f1878]) ).
fof(f3514,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1880]) ).
fof(f3515,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1882]) ).
fof(f3516,plain,
! [X2,X0,X1] :
( ~ class_Groups_Omonoid__mult(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1883]) ).
fof(f3517,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ocomm__monoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1884]) ).
fof(f3518,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(cnf_transformation,[],[f1885]) ).
fof(f3519,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ c_Polynomial_Opos__poly(X2,X0)
| c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) ),
inference(cnf_transformation,[],[f1887]) ).
fof(f3520,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oab__semigroup__mult(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1888]) ).
fof(f3521,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(cnf_transformation,[],[f1889]) ).
fof(f3522,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
inference(cnf_transformation,[],[f1890]) ).
fof(f3523,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
inference(cnf_transformation,[],[f1891]) ).
fof(f3524,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0) = c_Polynomial_Osmult(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0)) ),
inference(cnf_transformation,[],[f1892]) ).
fof(f3525,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0)) ),
inference(cnf_transformation,[],[f1893]) ).
fof(f3526,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0)) ),
inference(cnf_transformation,[],[f1894]) ).
fof(f3527,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)) ),
inference(cnf_transformation,[],[f1895]) ).
fof(f3528,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0) ),
inference(cnf_transformation,[],[f2622]) ).
fof(f3529,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0) ),
inference(cnf_transformation,[],[f2622]) ).
fof(f3530,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ),
inference(cnf_transformation,[],[f2622]) ).
fof(f3531,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ),
inference(cnf_transformation,[],[f2622]) ).
fof(f3532,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(cnf_transformation,[],[f2622]) ).
fof(f3533,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(cnf_transformation,[],[f2622]) ).
fof(f3534,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f2624]) ).
fof(f3535,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f2624]) ).
fof(f3536,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ),
inference(cnf_transformation,[],[f2624]) ).
fof(f3537,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ),
inference(cnf_transformation,[],[f2624]) ).
fof(f3538,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f2624]) ).
fof(f3539,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f2624]) ).
fof(f3540,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oordered__cancel__semiring(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),X0)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1899]) ).
fof(f3545,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Oordered__semiring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1909]) ).
fof(f3546,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Oordered__semiring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(cnf_transformation,[],[f1911]) ).
fof(f3547,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Oordered__comm__semiring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(cnf_transformation,[],[f1913]) ).
fof(f3548,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Oordered__ring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1915]) ).
fof(f3549,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Oordered__ring(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)) ),
inference(cnf_transformation,[],[f1917]) ).
fof(f3550,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Oordered__semiring(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(cnf_transformation,[],[f1919]) ).
fof(f3551,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Oordered__semiring(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(cnf_transformation,[],[f1921]) ).
fof(f3552,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oordered__ring(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1923]) ).
fof(f3553,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oordered__ring(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1923]) ).
fof(f3554,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oordered__cancel__semiring(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f1925]) ).
fof(f3555,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oordered__cancel__semiring(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f1925]) ).
fof(f3558,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(cnf_transformation,[],[f1931]) ).
fof(f3559,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(cnf_transformation,[],[f1933]) ).
fof(f3560,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1935]) ).
fof(f3561,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1937]) ).
fof(f3563,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Orderings_Oord__class_Oless(X3,X0,X1) ),
inference(cnf_transformation,[],[f2625]) ).
fof(f3565,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ),
inference(cnf_transformation,[],[f1943]) ).
fof(f3566,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0) ),
inference(cnf_transformation,[],[f1945]) ).
fof(f3567,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f1947]) ).
fof(f3568,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f1949]) ).
fof(f3569,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semiring__strict(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1951]) ).
fof(f3570,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Orderings_Oord__class_Oless(X3,X1,X0) ),
inference(cnf_transformation,[],[f2626]) ).
fof(f3572,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Orderings_Oord__class_Oless(X3,X0,X1)
| c_Orderings_Oord__class_Oless(X3,X1,X0) ),
inference(cnf_transformation,[],[f2628]) ).
fof(f3573,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,X1,X0) ),
inference(cnf_transformation,[],[f2628]) ).
fof(f3574,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Orderings_Oord__class_Oless(X3,X0,X1)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ),
inference(cnf_transformation,[],[f2628]) ).
fof(f3575,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ),
inference(cnf_transformation,[],[f2628]) ).
fof(f3576,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f2628]) ).
fof(f3577,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f2628]) ).
fof(f3578,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| c_Orderings_Oord__class_Oless(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(cnf_transformation,[],[f2630]) ).
fof(f3579,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(cnf_transformation,[],[f2630]) ).
fof(f3580,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| c_Orderings_Oord__class_Oless(X3,X0,X2)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ),
inference(cnf_transformation,[],[f2630]) ).
fof(f3581,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ),
inference(cnf_transformation,[],[f2630]) ).
fof(f3582,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(cnf_transformation,[],[f2630]) ).
fof(f3583,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ),
inference(cnf_transformation,[],[f2630]) ).
fof(f3584,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f1956]) ).
fof(f3585,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0))
| c_Groups_Ozero__class_Ozero(X2) = X0 ),
inference(cnf_transformation,[],[f2632]) ).
fof(f3586,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0))
| c_Groups_Ozero__class_Ozero(X2) = X1 ),
inference(cnf_transformation,[],[f2632]) ).
fof(f3587,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != 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),X0),X0)) ),
inference(cnf_transformation,[],[f2632]) ).
fof(f3588,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
| c_Groups_Ozero__class_Ozero(X5) = X4
| X0 = X1
| X2 != X3
| c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X1)) != c_Groups_Oplus__class_Oplus(X5,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X0)) ),
inference(cnf_transformation,[],[f1959]) ).
fof(f3589,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1961]) ).
fof(f3590,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Oidom(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2 ),
inference(cnf_transformation,[],[f2634]) ).
fof(f3591,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Oidom(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))) ),
inference(cnf_transformation,[],[f2634]) ).
fof(f3592,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Oidom(X3)
| c_Groups_Ozero__class_Ozero(X3) != X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))) ),
inference(cnf_transformation,[],[f2634]) ).
fof(f3593,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Oidom(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X1 ),
inference(cnf_transformation,[],[f2636]) ).
fof(f3594,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Oidom(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ),
inference(cnf_transformation,[],[f2636]) ).
fof(f3595,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Oidom(X3)
| c_Groups_Ozero__class_Ozero(X3) != X1
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ),
inference(cnf_transformation,[],[f2636]) ).
fof(f3596,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,X0) = 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))),X0) ),
inference(cnf_transformation,[],[f1964]) ).
fof(f3597,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X0,c_Groups_Oone__class_Oone(X2))),X1) ),
inference(cnf_transformation,[],[f1965]) ).
fof(f3598,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2))),X0) ),
inference(cnf_transformation,[],[f1966]) ).
fof(f3599,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(cnf_transformation,[],[f1967]) ).
fof(f3600,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
| c_Polynomial_Opos__poly(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 ),
inference(cnf_transformation,[],[f1969]) ).
fof(f3601,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__ring__1(X3)
| hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Omonom(X3,c_Groups_Oone__class_Oone(X3),X2)),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(cnf_transformation,[],[f1970]) ).
fof(f3602,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__ring__1(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0) ),
inference(cnf_transformation,[],[f1971]) ).
fof(f3603,plain,
! [X0,X1] :
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| c_Groups_Oone__class_Oone(X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0 ),
inference(cnf_transformation,[],[f2638]) ).
fof(f3604,plain,
! [X0,X1] :
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) != X0
| c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) ),
inference(cnf_transformation,[],[f2638]) ).
fof(f3605,plain,
! [X0,X1] :
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| c_Groups_Oone__class_Oone(X1) != X0
| c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) ),
inference(cnf_transformation,[],[f2638]) ).
fof(f3606,plain,
! [X2,X0,X1] :
( ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1973]) ).
fof(f3607,plain,
! [X2,X0,X1] :
( ~ class_Groups_Omonoid__mult(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) ),
inference(cnf_transformation,[],[f1974]) ).
fof(f3609,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1976]) ).
fof(f3610,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) ),
inference(cnf_transformation,[],[f1977]) ).
fof(f3611,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1978]) ).
fof(f3612,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1979]) ).
fof(f3613,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ c_Polynomial_Opos__poly(X2,X0)
| c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) ),
inference(cnf_transformation,[],[f1981]) ).
fof(f3614,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,c_Polynomial_OpCons(X3,X1,X0)) = c_Polynomial_OpCons(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),c_Polynomial_Osmult(X3,X2,X0)) ),
inference(cnf_transformation,[],[f1982]) ).
fof(f3615,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(cnf_transformation,[],[f1983]) ).
fof(f3616,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
inference(cnf_transformation,[],[f1984]) ).
fof(f3617,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ),
inference(cnf_transformation,[],[f1986]) ).
fof(f3618,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(cnf_transformation,[],[f1988]) ).
fof(f3619,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless(X3,X1,X0) ),
inference(cnf_transformation,[],[f1990]) ).
fof(f3620,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semiring(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless(X3,X1,X0) ),
inference(cnf_transformation,[],[f1992]) ).
fof(f3621,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semiring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(cnf_transformation,[],[f1994]) ).
fof(f3622,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semiring(X3)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| c_Orderings_Oord__class_Oless(X3,X2,X0) ),
inference(cnf_transformation,[],[f1996]) ).
fof(f3623,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Olinordered__semiring__strict(X4)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(cnf_transformation,[],[f1998]) ).
fof(f3624,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Olinordered__semiring__strict(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(cnf_transformation,[],[f2000]) ).
fof(f3625,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Olinordered__semiring__strict(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(cnf_transformation,[],[f2002]) ).
fof(f3626,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Olinordered__semiring__strict(X4)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(cnf_transformation,[],[f2004]) ).
fof(f3627,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ),
inference(cnf_transformation,[],[f2639]) ).
fof(f3628,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f2639]) ).
fof(f3629,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ),
inference(cnf_transformation,[],[f2640]) ).
fof(f3630,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f2640]) ).
fof(f3631,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring(X2)
| c_Orderings_Oord__class_Oless__eq(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),X0),X0))) ),
inference(cnf_transformation,[],[f2009]) ).
fof(f3632,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| c_Groups_Ozero__class_Ozero(X2) = X0 ),
inference(cnf_transformation,[],[f2642]) ).
fof(f3633,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| c_Groups_Ozero__class_Ozero(X2) = X1 ),
inference(cnf_transformation,[],[f2642]) ).
fof(f3634,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| 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),X0),X0)),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f2642]) ).
fof(f3635,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring(X2)
| ~ c_Orderings_Oord__class_Oless(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),X0),X0)),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f2011]) ).
fof(f3636,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(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),X0),X0)))
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 ),
inference(cnf_transformation,[],[f2644]) ).
fof(f3637,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| c_Groups_Ozero__class_Ozero(X2) = X0
| 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),X0),X0))) ),
inference(cnf_transformation,[],[f2644]) ).
fof(f3638,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| 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),X0),X0))) ),
inference(cnf_transformation,[],[f2644]) ).
fof(f3639,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(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),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),X1) ),
inference(cnf_transformation,[],[f2014]) ).
fof(f3640,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(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),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1) ),
inference(cnf_transformation,[],[f2016]) ).
fof(f3641,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))) ),
inference(cnf_transformation,[],[f2018]) ).
fof(f3642,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))) ),
inference(cnf_transformation,[],[f2020]) ).
fof(f3643,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oring__1(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(cnf_transformation,[],[f2021]) ).
fof(f3644,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))) ),
inference(cnf_transformation,[],[f2022]) ).
fof(f3645,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)) ),
inference(cnf_transformation,[],[f2024]) ).
fof(f3646,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))) ),
inference(cnf_transformation,[],[f2025]) ).
fof(f3647,plain,
! [X0,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f2026]) ).
fof(f3648,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ouminus(X3)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0)) ),
inference(cnf_transformation,[],[f2027]) ).
fof(f3649,plain,
! [X2,X0,X1] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f2645]) ).
fof(f3651,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
inference(cnf_transformation,[],[f2029]) ).
fof(f3652,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Olinordered__semiring__1(X5)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| c_Groups_Oplus__class_Oplus(X5,X1,X0) != c_Groups_Oone__class_Oone(X5)
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3) ),
inference(cnf_transformation,[],[f2031]) ).
fof(f3653,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(cnf_transformation,[],[f2033]) ).
fof(f3654,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0))) ),
inference(cnf_transformation,[],[f2034]) ).
fof(f3655,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0))) ),
inference(cnf_transformation,[],[f2035]) ).
fof(f3656,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Olinordered__semiring__1__strict(X5)
| ~ c_Orderings_Oord__class_Oless(X5,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| c_Groups_Oplus__class_Oplus(X5,X1,X0) != c_Groups_Oone__class_Oone(X5)
| c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3) ),
inference(cnf_transformation,[],[f2037]) ).
fof(f3657,plain,
! [X2,X0,X1,X6] :
( ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2)
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6)))
| hBOOL(hAPP(X1,sK15(X0,X1,X2))) ),
inference(cnf_transformation,[],[f2648]) ).
fof(f3658,plain,
! [X2,X0,X1,X6] :
( ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2)
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,sK15(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2)))) ),
inference(cnf_transformation,[],[f2648]) ).
fof(f3659,plain,
! [X2,X0,X1,X4] :
( ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2)
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2))))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),sK14(X0,X1,X2)))) ),
inference(cnf_transformation,[],[f2648]) ).
fof(f3660,plain,
! [X0,X1] :
( ~ 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f2040]) ).
fof(f3661,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Opcompose(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X0),c_Polynomial_Opcompose(X3,X1,X0))) ),
inference(cnf_transformation,[],[f2041]) ).
fof(f3662,plain,
! [X0] :
( ~ class_Power_Opower(X0)
| c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0)) ),
inference(cnf_transformation,[],[f2042]) ).
fof(f3663,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
inference(cnf_transformation,[],[f642]) ).
fof(f3664,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)),
inference(cnf_transformation,[],[f643]) ).
fof(f3665,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f644]) ).
fof(f3666,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(cnf_transformation,[],[f645]) ).
fof(f3667,plain,
! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = 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,X0)),
inference(cnf_transformation,[],[f646]) ).
fof(f3668,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
inference(cnf_transformation,[],[f647]) ).
fof(f3669,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
inference(cnf_transformation,[],[f648]) ).
fof(f3670,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f2043]) ).
fof(f3671,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f2650]) ).
fof(f3677,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(cnf_transformation,[],[f2654]) ).
fof(f3680,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f653]) ).
fof(f3682,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f2044]) ).
fof(f3683,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2655]) ).
fof(f3685,plain,
! [X0,X1] :
( ~ 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),X0)
| 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),X0)) ),
inference(cnf_transformation,[],[f2046]) ).
fof(f3686,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f658]) ).
fof(f3687,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(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),X2),X0)),
inference(cnf_transformation,[],[f659]) ).
fof(f3688,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| 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),X2),X0)) ),
inference(cnf_transformation,[],[f2048]) ).
fof(f3691,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))),
inference(cnf_transformation,[],[f663]) ).
fof(f3692,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f664]) ).
fof(f3693,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f665]) ).
fof(f3697,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f667]) ).
fof(f3698,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2659]) ).
fof(f3699,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 ),
inference(cnf_transformation,[],[f2659]) ).
fof(f3701,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X1))) ),
inference(cnf_transformation,[],[f2660]) ).
fof(f3702,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X1)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))) ),
inference(cnf_transformation,[],[f2660]) ).
fof(f3703,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
inference(cnf_transformation,[],[f2661]) ).
fof(f3704,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))) ),
inference(cnf_transformation,[],[f2661]) ).
fof(f3705,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f671]) ).
fof(f3706,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0),
inference(cnf_transformation,[],[f672]) ).
fof(f3707,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
inference(cnf_transformation,[],[f673]) ).
fof(f3708,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
inference(cnf_transformation,[],[f674]) ).
fof(f3709,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))) ),
inference(cnf_transformation,[],[f2662]) ).
fof(f3711,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Opcompose(X2,X1,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),c_Polynomial_Odegree(X2,X0))) ),
inference(cnf_transformation,[],[f2053]) ).
fof(f3717,plain,
! [X2,X0,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),X0),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
inference(cnf_transformation,[],[f2666]) ).
fof(f3718,plain,
! [X2,X0,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),X0),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f2666]) ).
fof(f3719,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ 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),X0),X1)) ),
inference(cnf_transformation,[],[f2666]) ).
fof(f3720,plain,
! [X2,X0,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),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2668]) ).
fof(f3721,plain,
! [X2,X0,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),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(cnf_transformation,[],[f2668]) ).
fof(f3723,plain,
! [X0,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),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f2670]) ).
fof(f3724,plain,
! [X0,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),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f2670]) ).
fof(f3725,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ 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),X0)) ),
inference(cnf_transformation,[],[f2670]) ).
fof(f3727,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0)) ),
inference(cnf_transformation,[],[f2671]) ).
fof(f3728,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f684]) ).
fof(f3729,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f685]) ).
fof(f3730,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)) ),
inference(cnf_transformation,[],[f2059]) ).
fof(f3731,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 ),
inference(cnf_transformation,[],[f2673]) ).
fof(f3732,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 ),
inference(cnf_transformation,[],[f2673]) ).
fof(f3734,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2674]) ).
fof(f3736,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2062]) ).
fof(f3737,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f2064]) ).
fof(f3738,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X0)),
inference(cnf_transformation,[],[f691]) ).
fof(f3739,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
inference(cnf_transformation,[],[f2065]) ).
fof(f3740,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Opcompose(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(cnf_transformation,[],[f2066]) ).
fof(f3741,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(cnf_transformation,[],[f694]) ).
fof(f3742,plain,
! [X2,X3,X0,X1,X4] : hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(X2,X1),hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),X0)),
inference(cnf_transformation,[],[f695]) ).
fof(f3743,plain,
! [X0,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)),X0)
| 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),X0),X1)) ),
inference(cnf_transformation,[],[f2068]) ).
fof(f3744,plain,
! [X0,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)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f2070]) ).
fof(f3745,plain,
! [X0,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)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f2072]) ).
fof(f3746,plain,
! [X0,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),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
inference(cnf_transformation,[],[f2676]) ).
fof(f3747,plain,
! [X0,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),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(cnf_transformation,[],[f2676]) ).
fof(f3748,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ 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),X0)) ),
inference(cnf_transformation,[],[f2676]) ).
fof(f3750,plain,
! [X2,X0,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),X0),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,X2,X0) ),
inference(cnf_transformation,[],[f2678]) ).
fof(f3751,plain,
! [X2,X0,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),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f2678]) ).
fof(f3752,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| 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),X0),X1)) ),
inference(cnf_transformation,[],[f2678]) ).
fof(f3754,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| 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),X2),X0)) ),
inference(cnf_transformation,[],[f2680]) ).
fof(f3755,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| 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),X2),X0)) ),
inference(cnf_transformation,[],[f2680]) ).
fof(f3756,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),X0)) ),
inference(cnf_transformation,[],[f2077]) ).
fof(f3757,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))) ),
inference(cnf_transformation,[],[f2681]) ).
fof(f3758,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f2681]) ).
fof(f3759,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0)) ),
inference(cnf_transformation,[],[f2682]) ).
fof(f3760,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f2682]) ).
fof(f3761,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),X1))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2683]) ).
fof(f3763,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X1))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2684]) ).
fof(f3766,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(cnf_transformation,[],[f709]) ).
fof(f3768,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != 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,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f2083]) ).
fof(f3769,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f2085]) ).
fof(f3770,plain,
! [X2,X0,X1] :
( ~ 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),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,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),X1) ),
inference(cnf_transformation,[],[f2087]) ).
fof(f3771,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
inference(cnf_transformation,[],[f714]) ).
fof(f3772,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),
inference(cnf_transformation,[],[f715]) ).
fof(f3773,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f716]) ).
fof(f3774,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
inference(cnf_transformation,[],[f717]) ).
fof(f3775,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3)
| ~ 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),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ 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,X5)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4) ),
inference(cnf_transformation,[],[f2089]) ).
fof(f3776,plain,
! [X2,X3,X0,X1,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),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
inference(cnf_transformation,[],[f2091]) ).
fof(f3777,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3)
| ~ 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),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
| ~ 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),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1) ),
inference(cnf_transformation,[],[f2093]) ).
fof(f3778,plain,
! [X2,X3,X0,X1,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),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0))
| ~ 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,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1) ),
inference(cnf_transformation,[],[f2095]) ).
fof(f3779,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0),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),X0)
| ~ 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,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f2097]) ).
fof(f3780,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ 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),X2),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2685]) ).
fof(f3782,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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),X2),X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f2686]) ).
fof(f3784,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
| X0 = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
inference(cnf_transformation,[],[f2688]) ).
fof(f3787,plain,
! [X2,X3,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X0)) = 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,X3,X1)),X2),X0),
inference(cnf_transformation,[],[f726]) ).
fof(f3789,plain,
! [X2,X0,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,X1,X0)
| 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),X2),X0)) ),
inference(cnf_transformation,[],[f2689]) ).
fof(f3790,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2690]) ).
fof(f3792,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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),X2),X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
inference(cnf_transformation,[],[f2692]) ).
fof(f3793,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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),X2),X0))) ),
inference(cnf_transformation,[],[f2692]) ).
fof(f3795,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2,X3,X4)
| ~ c_Polynomial_Opdivmod__rel(X0,X4,X2,X1,X3)
| sP0(X4,X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f2694]) ).
fof(f3796,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2,X3,X4)
| ~ sP0(X4,X3,X2,X1,X0)
| c_Polynomial_Opdivmod__rel(X0,X4,X2,X1,X3) ),
inference(cnf_transformation,[],[f2694]) ).
fof(f3806,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Fields_Ofield(X4)
| sP1(X4,X1,X2,X0,X3) ),
inference(cnf_transformation,[],[f2427]) ).
fof(f3808,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| ~ c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0 ),
inference(cnf_transformation,[],[f2699]) ).
fof(f3809,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| ~ c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ),
inference(cnf_transformation,[],[f2699]) ).
fof(f3811,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
| X0 = X2 ),
inference(cnf_transformation,[],[f2701]) ).
fof(f3812,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ),
inference(cnf_transformation,[],[f2701]) ).
fof(f3814,plain,
! [X0,X1] :
( ~ class_Fields_Ofield(X1)
| c_Polynomial_Opdivmod__rel(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(cnf_transformation,[],[f2107]) ).
fof(f3815,plain,
! [X0,X1] :
( ~ class_Fields_Ofield(X1)
| c_Polynomial_Opdivmod__rel(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
inference(cnf_transformation,[],[f2108]) ).
fof(f3816,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Fields_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X5,X4,X3,X2,X1)
| c_Polynomial_Opdivmod__rel(X5,c_Polynomial_Osmult(X5,X0,X4),X3,c_Polynomial_Osmult(X5,X0,X2),c_Polynomial_Osmult(X5,X0,X1)) ),
inference(cnf_transformation,[],[f2110]) ).
fof(f3817,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ class_Fields_Ofield(X6)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
| X0 = X2 ),
inference(cnf_transformation,[],[f2112]) ).
fof(f3818,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ class_Fields_Ofield(X6)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
| X1 = X3 ),
inference(cnf_transformation,[],[f2112]) ).
fof(f3821,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ class_Fields_Ofield(X7)
| ~ c_Polynomial_Opdivmod__rel(X7,X6,X5,X4,X3)
| ~ c_Polynomial_Opdivmod__rel(X7,X4,X2,X1,X0)
| c_Polynomial_Opdivmod__rel(X7,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X2),X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X0),X3)) ),
inference(cnf_transformation,[],[f2118]) ).
fof(f3823,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
inference(cnf_transformation,[],[f2120]) ).
fof(f3825,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2122]) ).
fof(f3829,plain,
! [X2,X3,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f2126]) ).
fof(f3831,plain,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X2)
| c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) ),
inference(cnf_transformation,[],[f2128]) ).
fof(f3832,plain,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X2)
| c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(cnf_transformation,[],[f2129]) ).
fof(f3833,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| hBOOL(hAPP(X1,sK16(X1,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)))) ),
inference(cnf_transformation,[],[f2703]) ).
fof(f3834,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK16(X1,X2),X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)))) ),
inference(cnf_transformation,[],[f2703]) ).
fof(f3835,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK17(X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(cnf_transformation,[],[f2704]) ).
fof(f3836,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,sK17(X0,X1))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(cnf_transformation,[],[f2704]) ).
fof(f3837,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK17(X0,X1),X0) ),
inference(cnf_transformation,[],[f2704]) ).
fof(f3838,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ),
inference(cnf_transformation,[],[f2135]) ).
fof(f3839,plain,
! [X2,X0,X1] :
( ~ class_Groups_Omonoid__mult(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) ),
inference(cnf_transformation,[],[f2137]) ).
fof(f3840,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1)) != hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X0),X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f2139]) ).
fof(f3841,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ozero(X3)
| X1 = X2
| c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) ),
inference(cnf_transformation,[],[f2140]) ).
fof(f3842,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ozero(X3)
| X1 != X2
| hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) = X0 ),
inference(cnf_transformation,[],[f2140]) ).
fof(f3843,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X3)
| hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0)) ),
inference(cnf_transformation,[],[f2141]) ).
fof(f3844,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,X0,X1) ),
inference(cnf_transformation,[],[f2142]) ).
fof(f3845,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f2143]) ).
fof(f3846,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f2144]) ).
fof(f3847,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),
inference(cnf_transformation,[],[f762]) ).
fof(f3848,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),
inference(cnf_transformation,[],[f763]) ).
fof(f3849,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(cnf_transformation,[],[f764]) ).
fof(f3850,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0,
inference(cnf_transformation,[],[f765]) ).
fof(f3851,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
inference(cnf_transformation,[],[f766]) ).
fof(f3852,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f2705]) ).
fof(f3853,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ),
inference(cnf_transformation,[],[f2705]) ).
fof(f3854,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f2706]) ).
fof(f3855,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oordered__ab__group__add(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,X1,X0) ),
inference(cnf_transformation,[],[f2706]) ).
fof(f3856,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__ring__1(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0))) ),
inference(cnf_transformation,[],[f2148]) ).
fof(f3859,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f2150]) ).
fof(f3860,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oab__group__add(X3)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Ominus__class_Ominus(X3,X2,X0),X1) ),
inference(cnf_transformation,[],[f2151]) ).
fof(f3861,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Oab__group__add(X4)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Ominus__class_Ominus(X4,X3,X1),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),X2,X0)) ),
inference(cnf_transformation,[],[f2152]) ).
fof(f3862,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__ring(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(cnf_transformation,[],[f2153]) ).
fof(f3863,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__ring(X3)
| c_Polynomial_Osmult(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0)) ),
inference(cnf_transformation,[],[f2154]) ).
fof(f3864,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1),
inference(cnf_transformation,[],[f777]) ).
fof(f3865,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oab__group__add(X3)
| hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0)) ),
inference(cnf_transformation,[],[f2155]) ).
fof(f3866,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Polynomial_Ocoeff(X2,X1) != c_Polynomial_Ocoeff(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2707]) ).
fof(f3869,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| hAPP(c_Polynomial_Ocoeff(X2,X1),sK18(X0,X1,X2)) != hAPP(c_Polynomial_Ocoeff(X2,X0),sK18(X0,X1,X2))
| X0 = X1 ),
inference(cnf_transformation,[],[f2710]) ).
fof(f3870,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Oab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| X2 != X3
| X0 = X1 ),
inference(cnf_transformation,[],[f2711]) ).
fof(f3872,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Ominus(X4)
| hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0)) ),
inference(cnf_transformation,[],[f2160]) ).
fof(f3873,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ 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,X0,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2712]) ).
fof(f3875,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ),
inference(cnf_transformation,[],[f2164]) ).
fof(f3876,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f2713]) ).
fof(f3878,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1 ),
inference(cnf_transformation,[],[f2167]) ).
fof(f3879,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f2168]) ).
fof(f3880,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ),
inference(cnf_transformation,[],[f2169]) ).
fof(f3881,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1),
inference(cnf_transformation,[],[f789]) ).
fof(f3882,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ),
inference(cnf_transformation,[],[f2171]) ).
fof(f3883,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1) ),
inference(cnf_transformation,[],[f2172]) ).
fof(f3884,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f792]) ).
fof(f3885,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f793]) ).
fof(f3886,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f794]) ).
fof(f3888,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Oordered__ab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| c_Orderings_Oord__class_Oless(X4,X1,X0) ),
inference(cnf_transformation,[],[f2714]) ).
fof(f3889,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Oordered__ab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| c_Orderings_Oord__class_Oless(X4,X3,X2) ),
inference(cnf_transformation,[],[f2714]) ).
fof(f3890,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Oordered__ab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| c_Orderings_Oord__class_Oless__eq(X4,X1,X0) ),
inference(cnf_transformation,[],[f2715]) ).
fof(f3891,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Groups_Oordered__ab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X4,X3,X2) ),
inference(cnf_transformation,[],[f2715]) ).
fof(f3892,plain,
! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(cnf_transformation,[],[f2179]) ).
fof(f3894,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oab__group__add(X2)
| X0 != X1
| c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0) ),
inference(cnf_transformation,[],[f2716]) ).
fof(f3895,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2716]) ).
fof(f3896,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2717]) ).
fof(f3897,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| X0 != X1
| c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0) ),
inference(cnf_transformation,[],[f2717]) ).
fof(f3898,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(X3,X1),X0) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X2,X1)),c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f2183]) ).
fof(f3899,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Ocoeff(X3,X1),X0)) ),
inference(cnf_transformation,[],[f2184]) ).
fof(f3900,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ),
inference(cnf_transformation,[],[f2185]) ).
fof(f3903,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ),
inference(cnf_transformation,[],[f2186]) ).
fof(f3904,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(cnf_transformation,[],[f2718]) ).
fof(f3905,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) ),
inference(cnf_transformation,[],[f2718]) ).
fof(f3906,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2)) ),
inference(cnf_transformation,[],[f2187]) ).
fof(f3909,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ),
inference(cnf_transformation,[],[f2719]) ).
fof(f3910,plain,
! [X2,X0,X1] :
( ~ 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,X0,X2),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(cnf_transformation,[],[f2719]) ).
fof(f3914,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(cnf_transformation,[],[f2193]) ).
fof(f3916,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0) ),
inference(cnf_transformation,[],[f2195]) ).
fof(f3917,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0)) ),
inference(cnf_transformation,[],[f2197]) ).
fof(f3918,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(cnf_transformation,[],[f2199]) ).
fof(f3919,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ 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,X0,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2721]) ).
fof(f3921,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f2203]) ).
fof(f3922,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ),
inference(cnf_transformation,[],[f2204]) ).
fof(f3923,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) ),
inference(cnf_transformation,[],[f2722]) ).
fof(f3924,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f2722]) ).
fof(f3925,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
inference(cnf_transformation,[],[f2205]) ).
fof(f3927,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2723]) ).
fof(f3929,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2207]) ).
fof(f3930,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(cnf_transformation,[],[f828]) ).
fof(f3931,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Nat_OSuc(X1)),
inference(cnf_transformation,[],[f829]) ).
fof(f3932,plain,
! [X0,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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0) ),
inference(cnf_transformation,[],[f2209]) ).
fof(f3933,plain,
! [X0,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,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f2724]) ).
fof(f3934,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,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,X0)) ),
inference(cnf_transformation,[],[f2724]) ).
fof(f3935,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(cnf_transformation,[],[f2210]) ).
fof(f3936,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__ring__1(X2)
| c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(cnf_transformation,[],[f2211]) ).
fof(f3937,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(cnf_transformation,[],[f2212]) ).
fof(f3938,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(cnf_transformation,[],[f2213]) ).
fof(f3939,plain,
! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f2214]) ).
fof(f3940,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Oring(X4)
| c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0)) ),
inference(cnf_transformation,[],[f2215]) ).
fof(f3941,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Oring(X5)
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) != c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2) = X0 ),
inference(cnf_transformation,[],[f2725]) ).
fof(f3943,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Oring(X5)
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) != c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0) = X2 ),
inference(cnf_transformation,[],[f2726]) ).
fof(f3944,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Oring(X5)
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0) != X2
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0) ),
inference(cnf_transformation,[],[f2726]) ).
fof(f3945,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(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),X2),X0)),
inference(cnf_transformation,[],[f840]) ).
fof(f3946,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f841]) ).
fof(f3947,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oab__group__add(X2)
| hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Ocoeff(X2,X1),X0)) ),
inference(cnf_transformation,[],[f2218]) ).
fof(f3948,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),c_Groups_Ominus__class_Ominus(X4,X2,X0))) ),
inference(cnf_transformation,[],[f2219]) ).
fof(f3950,plain,
! [X2,X3,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f2221]) ).
fof(f3952,plain,
! [X2,X3,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(cnf_transformation,[],[f2223]) ).
fof(f3953,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) ),
inference(cnf_transformation,[],[f2727]) ).
fof(f3954,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)) ),
inference(cnf_transformation,[],[f2727]) ).
fof(f3955,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) ),
inference(cnf_transformation,[],[f2728]) ).
fof(f3956,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)) ),
inference(cnf_transformation,[],[f2728]) ).
fof(f3957,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) ),
inference(cnf_transformation,[],[f2729]) ).
fof(f3958,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)) ),
inference(cnf_transformation,[],[f2729]) ).
fof(f3959,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) ),
inference(cnf_transformation,[],[f2730]) ).
fof(f3960,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Oordered__ring(X5)
| ~ c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)) ),
inference(cnf_transformation,[],[f2730]) ).
fof(f3961,plain,
! [X0,X1] :
( ~ class_Rings_Oring__1(X1)
| c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Oone__class_Oone(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Oone__class_Oone(X1))) ),
inference(cnf_transformation,[],[f2228]) ).
fof(f3964,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Odvd(X3)
| ~ class_Rings_Ocomm__ring(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0))) ),
inference(cnf_transformation,[],[f2732]) ).
fof(f3965,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_Rings_Odvd(X3)
| ~ class_Rings_Ocomm__ring(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0))) ),
inference(cnf_transformation,[],[f2732]) ).
fof(f3967,plain,
! [X0,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,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),X1) ),
inference(cnf_transformation,[],[f2234]) ).
fof(f3970,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,sK19(X0,X1,X2)))
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f2736]) ).
fof(f3971,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK19(X0,X1,X2)) = X1
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f2736]) ).
fof(f3972,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,sK19(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f2736]) ).
fof(f3973,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK19(X0,X1,X2)) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f2736]) ).
fof(f3975,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f2740]) ).
fof(f3976,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK20(X0,X1,X2)) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f2740]) ).
fof(f3977,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,sK20(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f2740]) ).
fof(f3978,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK20(X0,X1,X2)) = X1
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f2740]) ).
fof(f3979,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,sK20(X0,X1,X2)))
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f2740]) ).
fof(f3980,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Nat_OSuc(X1)) ),
inference(cnf_transformation,[],[f2237]) ).
fof(f3981,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(cnf_transformation,[],[f2238]) ).
fof(f3982,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0) ),
inference(cnf_transformation,[],[f2240]) ).
fof(f3983,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Polynomial_Odegree(X2,X1)) ),
inference(cnf_transformation,[],[f2242]) ).
fof(f3984,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) ),
inference(cnf_transformation,[],[f2741]) ).
fof(f3985,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) ),
inference(cnf_transformation,[],[f2741]) ).
fof(f3986,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) ),
inference(cnf_transformation,[],[f2244]) ).
fof(f3987,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1) = X0 ),
inference(cnf_transformation,[],[f2742]) ).
fof(f3989,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ),
inference(cnf_transformation,[],[f2743]) ).
fof(f3990,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) ),
inference(cnf_transformation,[],[f2743]) ).
fof(f3991,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ),
inference(cnf_transformation,[],[f2247]) ).
fof(f3992,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0) = X1 ),
inference(cnf_transformation,[],[f2744]) ).
fof(f3993,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0) != X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0) ),
inference(cnf_transformation,[],[f2744]) ).
fof(f3995,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 ),
inference(cnf_transformation,[],[f2745]) ).
fof(f3997,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Polynomial_Odegree(X2,c_Polynomial_Osynthetic__div(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(cnf_transformation,[],[f2252]) ).
fof(f3999,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0 ),
inference(cnf_transformation,[],[f2254]) ).
fof(f4000,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) ),
inference(cnf_transformation,[],[f2255]) ).
fof(f4001,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0 ),
inference(cnf_transformation,[],[f2255]) ).
fof(f4002,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ 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),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) ),
inference(cnf_transformation,[],[f2746]) ).
fof(f4003,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| 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),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) ),
inference(cnf_transformation,[],[f2746]) ).
fof(f4004,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ 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),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ),
inference(cnf_transformation,[],[f2747]) ).
fof(f4005,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| 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),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) ),
inference(cnf_transformation,[],[f2747]) ).
fof(f4006,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)) ),
inference(cnf_transformation,[],[f2258]) ).
fof(f4007,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
inference(cnf_transformation,[],[f2258]) ).
fof(f4008,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(cnf_transformation,[],[f2259]) ).
fof(f4009,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(cnf_transformation,[],[f2259]) ).
fof(f4010,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1))),hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))) ),
inference(cnf_transformation,[],[f2260]) ).
fof(f4011,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) ),
inference(cnf_transformation,[],[f2261]) ).
fof(f4012,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) ),
inference(cnf_transformation,[],[f2261]) ).
fof(f4013,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))) ),
inference(cnf_transformation,[],[f2748]) ).
fof(f4014,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0)))
| c_Polynomial_Opos__poly(X1,X0) ),
inference(cnf_transformation,[],[f2748]) ).
fof(f4015,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oone__class_Oone(X2) = hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)),X0) ),
inference(cnf_transformation,[],[f2263]) ).
fof(f4016,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__ring__1(X2)
| c_Groups_Ominus__class_Ominus(X2,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),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(X2,X1,X0)) ),
inference(cnf_transformation,[],[f2264]) ).
fof(f4017,plain,
! [X2,X0,X1] :
( ~ class_Power_Opower(X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(cnf_transformation,[],[f2265]) ).
fof(f4018,plain,
! [X2,X0,X1] :
( ~ class_Power_Opower(X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Oone__class_Oone(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) ),
inference(cnf_transformation,[],[f2265]) ).
fof(f4019,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Omonoid__mult(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),X0) ),
inference(cnf_transformation,[],[f2267]) ).
fof(f4020,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
| c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f2750]) ).
fof(f4021,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0) ),
inference(cnf_transformation,[],[f2750]) ).
fof(f4022,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| X0 != X1
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0) ),
inference(cnf_transformation,[],[f2750]) ).
fof(f4023,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
| c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1)) ),
inference(cnf_transformation,[],[f2751]) ).
fof(f4024,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0) ),
inference(cnf_transformation,[],[f2751]) ).
fof(f4025,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__ring(X3)
| c_Polynomial_Osmult(X3,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0)) ),
inference(cnf_transformation,[],[f2270]) ).
fof(f4026,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
inference(cnf_transformation,[],[f2272]) ).
fof(f4027,plain,
! [X0,X1] :
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 ),
inference(cnf_transformation,[],[f2273]) ).
fof(f4028,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(cnf_transformation,[],[f891]) ).
fof(f4029,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(cnf_transformation,[],[f892]) ).
fof(f4030,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oab__group__add(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ),
inference(cnf_transformation,[],[f2275]) ).
fof(f4031,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oab__group__add(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ),
inference(cnf_transformation,[],[f2277]) ).
fof(f4032,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f2752]) ).
fof(f4033,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2752]) ).
fof(f4034,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)),
inference(cnf_transformation,[],[f896]) ).
fof(f4035,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
inference(cnf_transformation,[],[f897]) ).
fof(f4036,plain,
! [X0,X1] :
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
inference(cnf_transformation,[],[f2278]) ).
fof(f4037,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2753]) ).
fof(f4038,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f2753]) ).
fof(f4039,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ class_Fields_Ofield(X6)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) = X4
| c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))) != X1
| c_Polynomial_Opdivmod__rel(X6,c_Polynomial_OpCons(X6,X0,X5),X4,c_Polynomial_OpCons(X6,X1,X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X0,X2),c_Polynomial_Osmult(X6,X1,X4))) ),
inference(cnf_transformation,[],[f2280]) ).
fof(f4040,plain,
! [X2,X0,X1] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(cnf_transformation,[],[f2281]) ).
fof(f4042,plain,
! [X2,X3,X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) ),
inference(cnf_transformation,[],[f2283]) ).
fof(f4044,plain,
! [X0,X1] :
( ~ class_Rings_Odivision__ring(X1)
| c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(cnf_transformation,[],[f2285]) ).
fof(f4046,plain,
! [X0,X1] :
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,X0) ),
inference(cnf_transformation,[],[f2287]) ).
fof(f4049,plain,
! [X2,X0,X1] :
( ~ class_Rings_Odivision__ring(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Oone__class_Oone(X2) != c_Rings_Oinverse__class_Odivide(X2,X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f2754]) ).
fof(f4051,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield__inverse__zero(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X2,X1)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(cnf_transformation,[],[f2292]) ).
fof(f4052,plain,
! [X0,X1] :
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f2293]) ).
fof(f4054,plain,
! [X2,X0,X1] :
( ~ class_Fields_Ofield__inverse__zero(X2)
| c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),X1)),X0) ),
inference(cnf_transformation,[],[f2295]) ).
fof(f4058,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Odivision__ring(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) != X0
| c_Rings_Oinverse__class_Odivide(X3,X0,X2) = X1 ),
inference(cnf_transformation,[],[f2303]) ).
fof(f4060,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Odivision__ring(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Rings_Oinverse__class_Odivide(X3,X1,X2) != X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2) = X1 ),
inference(cnf_transformation,[],[f2755]) ).
fof(f4064,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Odivision__ring(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
inference(cnf_transformation,[],[f2310]) ).
fof(f4065,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f2311]) ).
fof(f4066,plain,
! [X2,X3,X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) ),
inference(cnf_transformation,[],[f2312]) ).
fof(f4067,plain,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X2)
| c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ),
inference(cnf_transformation,[],[f2313]) ).
fof(f4068,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)) ),
inference(cnf_transformation,[],[f2315]) ).
fof(f4069,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Fields_Ofield__inverse__zero(X4)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Rings_Oinverse__class_Odivide(X4,X3,X2)),c_Rings_Oinverse__class_Odivide(X4,X1,X0)) = c_Rings_Oinverse__class_Odivide(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(cnf_transformation,[],[f2316]) ).
fof(f4070,plain,
! [X2,X0,X1] :
( ~ class_Fields_Ofield__inverse__zero(X2)
| c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) = c_Rings_Oinverse__class_Odivide(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(cnf_transformation,[],[f2317]) ).
fof(f4072,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Fields_Ofield(X4)
| c_Groups_Ozero__class_Ozero(X4) = X3
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Rings_Oinverse__class_Odivide(X4,X1,X3) != c_Rings_Oinverse__class_Odivide(X4,X0,X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3) ),
inference(cnf_transformation,[],[f2757]) ).
fof(f4073,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Fields_Ofield(X4)
| c_Groups_Ozero__class_Ozero(X4) = X3
| c_Groups_Ozero__class_Ozero(X4) = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)
| c_Rings_Oinverse__class_Odivide(X4,X1,X3) = c_Rings_Oinverse__class_Odivide(X4,X0,X2) ),
inference(cnf_transformation,[],[f2757]) ).
fof(f4074,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield__inverse__zero(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Rings_Oinverse__class_Odivide(X3,X1,X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f2322]) ).
fof(f4088,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield__inverse__zero(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2)),X2) ),
inference(cnf_transformation,[],[f2328]) ).
fof(f4089,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2) ),
inference(cnf_transformation,[],[f2330]) ).
fof(f4090,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield__inverse__zero(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)),X2) ),
inference(cnf_transformation,[],[f2332]) ).
fof(f4091,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2) ),
inference(cnf_transformation,[],[f2334]) ).
fof(f4092,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Fields_Ofield(X4)
| c_Groups_Ozero__class_Ozero(X4) = X3
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Oplus__class_Oplus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)) ),
inference(cnf_transformation,[],[f2336]) ).
fof(f4093,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Fields_Ofield(X4)
| c_Groups_Ozero__class_Ozero(X4) = X3
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ominus__class_Ominus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)) ),
inference(cnf_transformation,[],[f2338]) ).
fof(f4094,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2) ),
inference(cnf_transformation,[],[f2340]) ).
fof(f4095,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ominus__class_Ominus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2) ),
inference(cnf_transformation,[],[f2342]) ).
fof(f4096,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ class_RealVector_Oreal__field(X5)
| c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X1)),X0) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X3,X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X4,X2),X0)),X1)) ),
inference(cnf_transformation,[],[f2343]) ).
fof(f4097,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X2
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,X0),X2) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2)),c_Polynomial_Osmult(X3,c_Rings_Oinverse__class_Odivide(X3,hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2))),c_Polynomial_Odegree(X3,X2)),hAPP(c_Polynomial_Ocoeff(X3,X2),c_Polynomial_Odegree(X3,X2))),X2)) ),
inference(cnf_transformation,[],[f2345]) ).
fof(f4098,plain,
! [X2,X0,X1] :
( ~ class_Fields_Ofield(X2)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0) ),
inference(cnf_transformation,[],[f2346]) ).
fof(f4099,plain,
! [X2,X0,X1] :
( ~ class_Fields_Ofield(X2)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0)) ),
inference(cnf_transformation,[],[f2347]) ).
fof(f4100,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0) = c_Polynomial_Osmult(X3,X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0)) ),
inference(cnf_transformation,[],[f2348]) ).
fof(f4101,plain,
! [X2,X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0)) ),
inference(cnf_transformation,[],[f2350]) ).
fof(f4102,plain,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f2351]) ).
fof(f4103,plain,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(cnf_transformation,[],[f2352]) ).
fof(f4104,plain,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0) ),
inference(cnf_transformation,[],[f2353]) ).
fof(f4105,plain,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1) ),
inference(cnf_transformation,[],[f2355]) ).
fof(f4107,plain,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X2)
| c_Groups_Ozero__class_Ozero(X2) != c_Divides_Odiv__class_Omod(X2,X0,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) ),
inference(cnf_transformation,[],[f2762]) ).
fof(f4108,plain,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0) ),
inference(cnf_transformation,[],[f2357]) ).
fof(f4109,plain,
! [X2,X3,X0,X1] :
( ~ class_Divides_Osemiring__div(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1)) ),
inference(cnf_transformation,[],[f2359]) ).
fof(f4110,plain,
! [X0] :
( ~ class_Groups_Ocancel__comm__monoid__add(X0)
| class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2360]) ).
fof(f4111,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f997]) ).
fof(f4112,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f998]) ).
fof(f4113,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f999]) ).
fof(f4114,plain,
! [X0,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
inference(cnf_transformation,[],[f2361]) ).
fof(f4115,plain,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(cnf_transformation,[],[f2362]) ).
fof(f4116,plain,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(cnf_transformation,[],[f2363]) ).
fof(f4117,plain,
! [X0,X1] :
( ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(cnf_transformation,[],[f2364]) ).
fof(f4118,plain,
! [X0,X1] :
( ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(tc_fun(X0,X1)) ),
inference(cnf_transformation,[],[f2365]) ).
fof(f4119,plain,
! [X0,X1] :
( ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(tc_fun(X0,X1)) ),
inference(cnf_transformation,[],[f2366]) ).
fof(f4120,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[],[f1006]) ).
fof(f4121,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1007]) ).
fof(f4122,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f1008]) ).
fof(f4124,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1010]) ).
fof(f4125,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1011]) ).
fof(f4126,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1012]) ).
fof(f4127,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1013]) ).
fof(f4128,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1014]) ).
fof(f4129,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1015]) ).
fof(f4130,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1016]) ).
fof(f4131,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1017]) ).
fof(f4132,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1018]) ).
fof(f4133,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1019]) ).
fof(f4134,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1020]) ).
fof(f4135,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1021]) ).
fof(f4136,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1022]) ).
fof(f4137,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1023]) ).
fof(f4138,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1024]) ).
fof(f4139,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f1025]) ).
fof(f4140,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1026]) ).
fof(f4141,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1027]) ).
fof(f4142,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1028]) ).
fof(f4143,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1029]) ).
fof(f4144,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1030]) ).
fof(f4145,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1031]) ).
fof(f4146,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1032]) ).
fof(f4147,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f1033]) ).
fof(f4148,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1034]) ).
fof(f4149,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1035]) ).
fof(f4150,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f1036]) ).
fof(f4152,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1038]) ).
fof(f4153,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f1039]) ).
fof(f4154,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1040]) ).
fof(f4155,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1041]) ).
fof(f4156,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1042]) ).
fof(f4157,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1043]) ).
fof(f4158,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1044]) ).
fof(f4160,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1046]) ).
fof(f4161,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1047]) ).
fof(f4162,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f1048]) ).
fof(f4163,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1049]) ).
fof(f4164,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1050]) ).
fof(f4165,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1051]) ).
fof(f4166,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1052]) ).
fof(f4167,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f1053]) ).
fof(f4168,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(cnf_transformation,[],[f1054]) ).
fof(f4169,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1055]) ).
fof(f4170,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(cnf_transformation,[],[f1056]) ).
fof(f4171,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f1057]) ).
fof(f4172,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f1058]) ).
fof(f4173,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f1059]) ).
fof(f4174,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f1060]) ).
fof(f4176,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(cnf_transformation,[],[f1062]) ).
fof(f4177,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f1063]) ).
fof(f4178,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1064]) ).
fof(f4179,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f1065]) ).
fof(f4181,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f1067]) ).
fof(f4182,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1068]) ).
fof(f4183,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1069]) ).
fof(f4184,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1070]) ).
fof(f4185,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1071]) ).
fof(f4186,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1072]) ).
fof(f4187,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1073]) ).
fof(f4188,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1074]) ).
fof(f4189,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f1075]) ).
fof(f4190,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1076]) ).
fof(f4191,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1077]) ).
fof(f4192,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1078]) ).
fof(f4193,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1079]) ).
fof(f4194,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f1080]) ).
fof(f4195,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1081]) ).
fof(f4196,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f1082]) ).
fof(f4197,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f1083]) ).
fof(f4198,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f1084]) ).
fof(f4200,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f1086]) ).
fof(f4201,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1087]) ).
fof(f4202,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1088]) ).
fof(f4203,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1089]) ).
fof(f4205,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f1091]) ).
fof(f4206,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f1092]) ).
fof(f4207,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1093]) ).
fof(f4208,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1094]) ).
fof(f4209,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f1095]) ).
fof(f4210,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f1096]) ).
fof(f4211,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f1097]) ).
fof(f4212,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f1098]) ).
fof(f4214,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(cnf_transformation,[],[f1100]) ).
fof(f4215,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(cnf_transformation,[],[f1101]) ).
fof(f4216,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f1102]) ).
fof(f4217,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f1103]) ).
fof(f4218,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f1104]) ).
fof(f4219,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(cnf_transformation,[],[f1105]) ).
fof(f4220,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f1106]) ).
fof(f4221,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1107]) ).
fof(f4222,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1108]) ).
fof(f4223,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1109]) ).
fof(f4224,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1110]) ).
fof(f4225,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1111]) ).
fof(f4226,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1112]) ).
fof(f4227,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1113]) ).
fof(f4228,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1114]) ).
fof(f4229,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1115]) ).
fof(f4230,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1116]) ).
fof(f4231,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1117]) ).
fof(f4232,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1118]) ).
fof(f4233,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1119]) ).
fof(f4234,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1120]) ).
fof(f4235,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1121]) ).
fof(f4236,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1122]) ).
fof(f4237,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1123]) ).
fof(f4238,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1124]) ).
fof(f4239,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1125]) ).
fof(f4240,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1126]) ).
fof(f4241,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1127]) ).
fof(f4242,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1128]) ).
fof(f4243,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1129]) ).
fof(f4244,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1130]) ).
fof(f4245,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1131]) ).
fof(f4246,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1132]) ).
fof(f4247,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1133]) ).
fof(f4248,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1134]) ).
fof(f4249,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1135]) ).
fof(f4250,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1136]) ).
fof(f4251,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1137]) ).
fof(f4252,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1138]) ).
fof(f4253,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1139]) ).
fof(f4254,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1140]) ).
fof(f4255,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1141]) ).
fof(f4256,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1142]) ).
fof(f4257,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1143]) ).
fof(f4258,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1144]) ).
fof(f4260,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1146]) ).
fof(f4261,plain,
! [X0] :
( ~ class_Rings_Oidom(X0)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2367]) ).
fof(f4262,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2368]) ).
fof(f4263,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2369]) ).
fof(f4264,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2370]) ).
fof(f4265,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2371]) ).
fof(f4266,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2372]) ).
fof(f4267,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2373]) ).
fof(f4268,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2374]) ).
fof(f4269,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2375]) ).
fof(f4270,plain,
! [X0] :
( ~ class_Groups_Ocancel__comm__monoid__add(X0)
| class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2376]) ).
fof(f4271,plain,
! [X0] :
( ~ class_Rings_Oidom(X0)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2377]) ).
fof(f4272,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2378]) ).
fof(f4273,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2379]) ).
fof(f4274,plain,
! [X0] :
( ~ class_Rings_Oidom(X0)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2380]) ).
fof(f4275,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2381]) ).
fof(f4276,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2382]) ).
fof(f4277,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2383]) ).
fof(f4278,plain,
! [X0] :
( ~ class_Groups_Ocancel__comm__monoid__add(X0)
| class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2384]) ).
fof(f4279,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2385]) ).
fof(f4280,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2386]) ).
fof(f4281,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2387]) ).
fof(f4282,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2388]) ).
fof(f4283,plain,
! [X0] :
( ~ class_Groups_Ocomm__monoid__add(X0)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2389]) ).
fof(f4284,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2390]) ).
fof(f4285,plain,
! [X0] :
( ~ class_Rings_Oidom(X0)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2391]) ).
fof(f4286,plain,
! [X0] :
( ~ class_Groups_Ocomm__monoid__add(X0)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2392]) ).
fof(f4287,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2393]) ).
fof(f4288,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2394]) ).
fof(f4289,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2395]) ).
fof(f4290,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2396]) ).
fof(f4291,plain,
! [X0] :
( ~ class_Fields_Ofield(X0)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2397]) ).
fof(f4293,plain,
! [X0] :
( ~ class_Groups_Oab__group__add(X0)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2399]) ).
fof(f4294,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2400]) ).
fof(f4295,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2401]) ).
fof(f4296,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2402]) ).
fof(f4297,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2403]) ).
fof(f4298,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2404]) ).
fof(f4299,plain,
! [X0] :
( ~ class_Rings_Ocomm__ring__1(X0)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2405]) ).
fof(f4301,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2407]) ).
fof(f4302,plain,
! [X0] :
( ~ class_Groups_Oab__group__add(X0)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2408]) ).
fof(f4303,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2409]) ).
fof(f4304,plain,
! [X0] :
( ~ class_Rings_Ocomm__ring(X0)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2410]) ).
fof(f4305,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2411]) ).
fof(f4306,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2412]) ).
fof(f4307,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2413]) ).
fof(f4308,plain,
! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| class_Orderings_Oord(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2414]) ).
fof(f4309,plain,
! [X0] :
( ~ class_Groups_Oab__group__add(X0)
| class_Groups_Ouminus(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2415]) ).
fof(f4310,plain,
! [X0] :
( ~ class_Rings_Ocomm__ring__1(X0)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2416]) ).
fof(f4311,plain,
! [X0] :
( ~ class_Groups_Oab__group__add(X0)
| class_Groups_Ominus(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2417]) ).
fof(f4312,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Power_Opower(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2418]) ).
fof(f4313,plain,
! [X0] :
( ~ class_Groups_Ozero(X0)
| class_Groups_Ozero(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2419]) ).
fof(f4314,plain,
! [X0] :
( ~ class_Rings_Ocomm__ring(X0)
| class_Rings_Oring(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2420]) ).
fof(f4315,plain,
! [X0] :
( ~ class_Rings_Oidom(X0)
| class_Rings_Oidom(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2421]) ).
fof(f4317,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Rings_Odvd(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2423]) ).
fof(f4318,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(c_fequal(X1,X0)) ),
inference(cnf_transformation,[],[f1204]) ).
fof(f4319,plain,
! [X0,X1] :
( hBOOL(c_fequal(X1,X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f1205]) ).
fof(f4320,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(cnf_transformation,[],[f2766]) ).
fof(f4321,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(cnf_transformation,[],[f2766]) ).
fof(f4324,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK21)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(cnf_transformation,[],[f2766]) ).
fof(f4325,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK21)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(cnf_transformation,[],[f2766]) ).
fof(f4326,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____),
inference(definition_unfolding,[],[f2770,f3211]) ).
fof(f4327,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) ),
inference(definition_unfolding,[],[f2777,f3211]) ).
fof(f4328,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
inference(definition_unfolding,[],[f2802,f3211,f3211]) ).
fof(f4331,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(definition_unfolding,[],[f2803,f3211,f3211]) ).
fof(f4332,plain,
! [X0,X1] :
( ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(definition_unfolding,[],[f2806,f3211]) ).
fof(f4333,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK7),
inference(definition_unfolding,[],[f2812,f3211]) ).
fof(f4335,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X1,X0)) ),
inference(definition_unfolding,[],[f2814,f3211]) ).
fof(f4343,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(definition_unfolding,[],[f2823,f3211]) ).
fof(f4348,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != X0,
inference(definition_unfolding,[],[f2875,f3211]) ).
fof(f4350,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ),
inference(definition_unfolding,[],[f2887,f3211,f3211]) ).
fof(f4351,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X2,X0))) ),
inference(definition_unfolding,[],[f2909,f3211]) ).
fof(f4352,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X0),
inference(definition_unfolding,[],[f2913,f3211]) ).
fof(f4354,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(definition_unfolding,[],[f2914,f3211]) ).
fof(f4357,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f2916,f3211,f3211]) ).
fof(f4359,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f2919,f3211,f3211]) ).
fof(f4363,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)) ),
inference(definition_unfolding,[],[f2947,f3211]) ).
fof(f4364,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| X0 = X2 ),
inference(definition_unfolding,[],[f2948,f3211,f3211]) ).
fof(f4365,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ),
inference(definition_unfolding,[],[f2949,f3211,f3211]) ).
fof(f4366,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(definition_unfolding,[],[f2961,f3211]) ).
fof(f4370,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))) ),
inference(definition_unfolding,[],[f3064,f3211]) ).
fof(f4372,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f3078,f3211]) ).
fof(f4374,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2),X0) ),
inference(definition_unfolding,[],[f3080,f3211]) ).
fof(f4375,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0) ),
inference(definition_unfolding,[],[f3081,f3211,f3211]) ).
fof(f4382,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(definition_unfolding,[],[f3090,f3211]) ).
fof(f4383,plain,
! [X0,X1] :
( X0 != X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(definition_unfolding,[],[f3089,f3211]) ).
fof(f4385,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f3092,f3211]) ).
fof(f4386,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(definition_unfolding,[],[f3091,f3211]) ).
fof(f4387,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),c_Groups_Oone__class_Oone(X2)) ),
inference(definition_unfolding,[],[f3112,f3211]) ).
fof(f4390,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK8(X0,X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(definition_unfolding,[],[f3126,f3211,f3211]) ).
fof(f4391,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK8(X0,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(definition_unfolding,[],[f3125,f3211]) ).
fof(f4393,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(definition_unfolding,[],[f3129,f3211]) ).
fof(f4394,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) != X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(definition_unfolding,[],[f3132,f3211]) ).
fof(f4395,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(X0)) = X0 ),
inference(definition_unfolding,[],[f3131,f3211]) ).
fof(f4399,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f3137,f3211]) ).
fof(f4402,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(definition_unfolding,[],[f3141,f3211]) ).
fof(f4403,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0) ),
inference(definition_unfolding,[],[f3142,f3211]) ).
fof(f4406,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f3145,f3211]) ).
fof(f4408,plain,
! [X2,X0,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,X1,c_Groups_Oone__class_Oone(X2))
| c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),X1) ),
inference(definition_unfolding,[],[f3188,f3211]) ).
fof(f4409,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(definition_unfolding,[],[f3198,f3211,f3211,f3211]) ).
fof(f4416,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ),
inference(definition_unfolding,[],[f3242,f3211,f3211]) ).
fof(f4417,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ),
inference(definition_unfolding,[],[f3241,f3211,f3211,f3211]) ).
fof(f4418,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(definition_unfolding,[],[f3240,f3211]) ).
fof(f4419,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(definition_unfolding,[],[f3239,f3211,f3211]) ).
fof(f4427,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(definition_unfolding,[],[f3255,f3211]) ).
fof(f4428,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f3257,f3211]) ).
fof(f4429,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK12(X0,X1))) = X0 ),
inference(definition_unfolding,[],[f3256,f3211]) ).
fof(f4431,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Oorder(X2,X0,X1)))),X1)) ),
inference(definition_unfolding,[],[f3318,f3211]) ).
fof(f4433,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(definition_unfolding,[],[f3398,f3211,f3211,f3211,f3211]) ).
fof(f4434,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1 ),
inference(definition_unfolding,[],[f3397,f3211,f3211,f3211,f3211]) ).
fof(f4435,plain,
! [X2,X0,X1] :
( ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(definition_unfolding,[],[f3606,f3211]) ).
fof(f4436,plain,
! [X2,X0,X1] :
( ~ class_Groups_Omonoid__mult(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(definition_unfolding,[],[f3607,f3211]) ).
fof(f4438,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(definition_unfolding,[],[f3609,f3211]) ).
fof(f4439,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(definition_unfolding,[],[f3610,f3211]) ).
fof(f4441,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),X0)
| X0 = X1 ),
inference(definition_unfolding,[],[f3683,f3211,f3211]) ).
fof(f4445,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| 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,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),X0)) ),
inference(definition_unfolding,[],[f3727,f3211,f3211]) ).
fof(f4447,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(definition_unfolding,[],[f3728,f3211]) ).
fof(f4448,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),X0),
inference(definition_unfolding,[],[f3729,f3211]) ).
fof(f4450,plain,
! [X2,X0,X1] :
( ~ 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,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f3734,f3211,f3211]) ).
fof(f4451,plain,
! [X2,X3,X0,X1,X4] : hAPP(hAPP(X2,X1),hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),X0)) = hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(definition_unfolding,[],[f3742,f3211]) ).
fof(f4452,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(definition_unfolding,[],[f3743,f3211,f3211,f3211]) ).
fof(f4453,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(definition_unfolding,[],[f3744,f3211,f3211]) ).
fof(f4454,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(definition_unfolding,[],[f3745,f3211,f3211]) ).
fof(f4455,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(definition_unfolding,[],[f3748,f3211,f3211,f3211]) ).
fof(f4456,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(definition_unfolding,[],[f3747,f3211,f3211]) ).
fof(f4457,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
inference(definition_unfolding,[],[f3746,f3211,f3211]) ).
fof(f4460,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(X3,X1),X0) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X2,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(definition_unfolding,[],[f3898,f3211]) ).
fof(f4464,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),
inference(definition_unfolding,[],[f3931,f3211]) ).
fof(f4466,plain,
! [X0,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,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),X1) ),
inference(definition_unfolding,[],[f3967,f3211]) ).
fof(f4467,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(definition_unfolding,[],[f3980,f3211,f3211]) ).
fof(f4468,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(definition_unfolding,[],[f3981,f3211,f3211]) ).
fof(f4470,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0 ),
inference(definition_unfolding,[],[f3999,f3211]) ).
fof(f4471,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) ),
inference(definition_unfolding,[],[f4000,f3211]) ).
fof(f4472,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__ring__1(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
inference(definition_unfolding,[],[f4016,f3211,f3211,f3211,f3211]) ).
fof(f4473,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Omonoid__mult(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X2)) ),
inference(definition_unfolding,[],[f4019,f3211]) ).
fof(f4475,plain,
! [X2,X0] :
( ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X0) ),
inference(equality_resolution,[],[f2794]) ).
fof(f4476,plain,
! [X2,X1] :
( ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(equality_resolution,[],[f2792]) ).
fof(f4477,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sK6(X1,X2))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)))) ),
inference(equality_resolution,[],[f2798]) ).
fof(f4478,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),sK6(X1,X2))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)))) ),
inference(equality_resolution,[],[f2797]) ).
fof(f4479,plain,
! [X2,X0] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) ),
inference(equality_resolution,[],[f2801]) ).
fof(f4489,plain,
! [X1] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
inference(equality_resolution,[],[f2840]) ).
fof(f4501,plain,
! [X1] :
( ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(equality_resolution,[],[f2877]) ).
fof(f4503,plain,
! [X2,X3,X1] :
( ~ class_Fields_Ofield(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)))) ),
inference(equality_resolution,[],[f2896]) ).
fof(f4504,plain,
! [X2,X3,X1] :
( ~ class_Fields_Ofield(X3)
| c_Groups_Ozero__class_Ozero(X3) != X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)))) ),
inference(equality_resolution,[],[f2895]) ).
fof(f4505,plain,
! [X3,X1] :
( ~ class_Fields_Ofield(X3)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,c_Groups_Ozero__class_Ozero(X3),X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)))) ),
inference(equality_resolution,[],[f4504]) ).
fof(f4507,plain,
! [X3,X0,X1] :
( ~ class_Fields_Ofield(X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,c_Groups_Ozero__class_Ozero(X3),X1)),X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0 ),
inference(equality_resolution,[],[f2892]) ).
fof(f4515,plain,
! [X2,X0] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X0) ),
inference(equality_resolution,[],[f2936]) ).
fof(f4516,plain,
! [X2,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) ),
inference(equality_resolution,[],[f2935]) ).
fof(f4517,plain,
! [X2,X0] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X0)) ),
inference(equality_resolution,[],[f2951]) ).
fof(f4530,plain,
! [X2,X1] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X1) ),
inference(equality_resolution,[],[f3004]) ).
fof(f4536,plain,
! [X2,X1] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Oless(X2,X1,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X1) ),
inference(equality_resolution,[],[f3043]) ).
fof(f4538,plain,
! [X2,X1] :
( ~ class_Orderings_Oorder(X2)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X1) ),
inference(equality_resolution,[],[f3052]) ).
fof(f4542,plain,
! [X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),
inference(equality_resolution,[],[f4383]) ).
fof(f4543,plain,
! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_resolution,[],[f3093]) ).
fof(f4545,plain,
! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_resolution,[],[f3101]) ).
fof(f4551,plain,
! [X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),
inference(equality_resolution,[],[f4394]) ).
fof(f4553,plain,
! [X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f3151]) ).
fof(f4554,plain,
! [X2,X0] :
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X0) ),
inference(equality_resolution,[],[f3155]) ).
fof(f4555,plain,
! [X2,X0] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Omonom(X2,c_Groups_Ozero__class_Ozero(X2),X0) ),
inference(equality_resolution,[],[f3159]) ).
fof(f4562,plain,
! [X2,X1] :
( ~ class_Orderings_Opreorder(X2)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X1) ),
inference(equality_resolution,[],[f3180]) ).
fof(f4564,plain,
! [X2,X1] :
( ~ class_Orderings_Oorder(X2)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X1) ),
inference(equality_resolution,[],[f3181]) ).
fof(f4577,plain,
! [X2,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(equality_resolution,[],[f4428]) ).
fof(f4592,plain,
! [X2,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1)) = X1 ),
inference(equality_resolution,[],[f3331]) ).
fof(f4596,plain,
! [X1] :
( ~ 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_resolution,[],[f3345]) ).
fof(f4599,plain,
! [X2,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X1)) ),
inference(equality_resolution,[],[f3395]) ).
fof(f4601,plain,
! [X2,X0] :
( ~ class_Rings_Oidom(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(equality_resolution,[],[f4433]) ).
fof(f4602,plain,
! [X2,X1] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = X1 ),
inference(equality_resolution,[],[f3420]) ).
fof(f4603,plain,
! [X1] :
( ~ 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_resolution,[],[f3422]) ).
fof(f4604,plain,
! [X2,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(equality_resolution,[],[f3426]) ).
fof(f4605,plain,
! [X2,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))) ),
inference(equality_resolution,[],[f3429]) ).
fof(f4606,plain,
! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(equality_resolution,[],[f3436]) ).
fof(f4609,plain,
! [X3,X0,X1,X4] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
| c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)) ),
inference(equality_resolution,[],[f3468]) ).
fof(f4611,plain,
! [X1] : 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_resolution,[],[f3471]) ).
fof(f4613,plain,
! [X2,X0] :
( ~ class_Rings_Oidom(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X0)),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(equality_resolution,[],[f3482]) ).
fof(f4614,plain,
! [X2,X0] :
( ~ class_Rings_Oring__no__zero__divisors(X2)
| c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),X0) ),
inference(equality_resolution,[],[f3499]) ).
fof(f4615,plain,
! [X2,X1] :
( ~ class_Rings_Oring__no__zero__divisors(X2)
| c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ozero__class_Ozero(X2)) ),
inference(equality_resolution,[],[f3498]) ).
fof(f4616,plain,
! [X3,X0,X1] :
( ~ class_Rings_Odvd(X3)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))) ),
inference(equality_resolution,[],[f3513]) ).
fof(f4617,plain,
! [X2,X0] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)) ),
inference(equality_resolution,[],[f3587]) ).
fof(f4618,plain,
! [X2] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2))) ),
inference(equality_resolution,[],[f4617]) ).
fof(f4619,plain,
! [X3,X0,X1,X4,X5] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
| c_Groups_Ozero__class_Ozero(X5) = X4
| X0 = X1
| c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X1)) != c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X0)) ),
inference(equality_resolution,[],[f3588]) ).
fof(f4620,plain,
! [X3,X0,X1] :
( ~ class_Rings_Oidom(X3)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X0))) ),
inference(equality_resolution,[],[f3592]) ).
fof(f4621,plain,
! [X2,X3,X0] :
( ~ class_Rings_Oidom(X3)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ozero__class_Ozero(X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),c_Groups_Ozero__class_Ozero(X3)))) ),
inference(equality_resolution,[],[f3595]) ).
fof(f4622,plain,
! [X1] :
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)) ),
inference(equality_resolution,[],[f3605]) ).
fof(f4623,plain,
! [X1] :
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| c_Groups_Oone__class_Oone(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))) ),
inference(equality_resolution,[],[f3604]) ).
fof(f4624,plain,
! [X2,X0] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2)) ),
inference(equality_resolution,[],[f3634]) ).
fof(f4625,plain,
! [X2] :
( ~ class_Rings_Olinordered__ring__strict(X2)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2))),c_Groups_Ozero__class_Ozero(X2)) ),
inference(equality_resolution,[],[f4624]) ).
fof(f4626,plain,
! [X2,X0] :
( ~ class_Rings_Olinordered__ring__strict(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),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
| c_Groups_Ozero__class_Ozero(X2) != X0 ),
inference(equality_resolution,[],[f3636]) ).
fof(f4627,plain,
! [X2] :
( ~ class_Rings_Olinordered__ring__strict(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),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)))) ),
inference(equality_resolution,[],[f4626]) ).
fof(f4668,plain,
! [X2,X3,X0] :
( ~ class_Groups_Ozero(X3)
| hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X2) = X0 ),
inference(equality_resolution,[],[f3842]) ).
fof(f4672,plain,
! [X3,X0,X1,X4] :
( ~ class_Groups_Oab__group__add(X4)
| c_Groups_Ominus__class_Ominus(X4,X1,X0) != c_Groups_Ominus__class_Ominus(X4,X3,X3)
| X0 = X1 ),
inference(equality_resolution,[],[f3870]) ).
fof(f4674,plain,
! [X2,X1] :
( ~ class_Groups_Oab__group__add(X2)
| c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X1) ),
inference(equality_resolution,[],[f3894]) ).
fof(f4675,plain,
! [X2,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X1) ),
inference(equality_resolution,[],[f3897]) ).
fof(f4679,plain,
! [X3,X0,X1,X4,X5] :
( ~ class_Rings_Oring(X5)
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) ),
inference(equality_resolution,[],[f3944]) ).
fof(f4683,plain,
! [X2,X3,X0,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ),
inference(equality_resolution,[],[f3993]) ).
fof(f4685,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(equality_resolution,[],[f4001]) ).
fof(f4686,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(equality_resolution,[],[f4007]) ).
fof(f4687,plain,
! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f4009]) ).
fof(f4688,plain,
! [X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(equality_resolution,[],[f4012]) ).
fof(f4689,plain,
! [X2,X0] :
( ~ class_Power_Opower(X2)
| c_Groups_Oone__class_Oone(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(equality_resolution,[],[f4018]) ).
fof(f4690,plain,
! [X2,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X1) ),
inference(equality_resolution,[],[f4022]) ).
fof(f4691,plain,
! [X2,X3,X0,X6,X4,X5] :
( ~ class_Fields_Ofield(X6)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) = X4
| c_Polynomial_Opdivmod__rel(X6,c_Polynomial_OpCons(X6,X0,X5),X4,c_Polynomial_OpCons(X6,c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))),X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X0,X2),c_Polynomial_Osmult(X6,c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))),X4))) ),
inference(equality_resolution,[],[f4039]) ).
fof(f4694,plain,
! [X2,X3,X1] :
( ~ class_Rings_Odivision__ring(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),X2) = X1 ),
inference(equality_resolution,[],[f4058]) ).
fof(f4697,plain,
! [X2,X3,X1] :
( ~ class_Rings_Odivision__ring(X3)
| c_Groups_Ozero__class_Ozero(X3) = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Rings_Oinverse__class_Odivide(X3,X1,X2)),X2) = X1 ),
inference(equality_resolution,[],[f4060]) ).
fof(f4718,plain,
! [X1] : hBOOL(c_fequal(X1,X1)),
inference(equality_resolution,[],[f4319]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( hAPP(X0,sK2(X0,X1)) != hAPP(X1,sK2(X0,X1)) ) ),
inference(cnf_transformation,[],[f2767]) ).
tcf(c_50,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p,
inference(cnf_transformation,[],[f2768]) ).
tcf(c_51,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f2769]) ).
tcf(c_52,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
inference(cnf_transformation,[],[f4326]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____))))
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(cnf_transformation,[],[f4327]) ).
tcf(c_58,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK4) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(cnf_transformation,[],[f2779]) ).
tcf(c_59,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK4) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(cnf_transformation,[],[f2778]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Groups_Ozero__class_Ozero(X0)))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2786]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(c_Polynomial_Opoly(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),X1),X2)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(c_Polynomial_Opoly(X0,X1),X3)),X2) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2787]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ( hAPP(c_Polynomial_Opoly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2788]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3)))
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f2791]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ozero__class_Ozero(X0)),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Ozero__neq__one(X0)
| ~ class_Rings_Ono__zero__divisors(X0)
| ~ class_Rings_Omult__zero(X0)
| ~ class_Power_Opower(X0) ),
inference(cnf_transformation,[],[f4475]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Rings_Ozero__neq__one(X0)
| ~ class_Rings_Ono__zero__divisors(X0)
| ~ class_Rings_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f2793]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Ozero__neq__one(X0)
| ~ class_Rings_Ono__zero__divisors(X0)
| ~ class_Rings_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f4476]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Rings_Oring__1__no__zero__divisors(X0)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f2795]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),c_Groups_Ozero__class_Ozero(X0)),X1)) ),
inference(cnf_transformation,[],[f2796]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1))))
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),sK6(X0,X1)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(cnf_transformation,[],[f4477]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X0))))
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),sK6(X1,X0)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(cnf_transformation,[],[f4478]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( hAPP(c_Polynomial_Opoly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4479]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Oorder(X0,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Polynomial_Opoly(X0,X1),X2) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2800]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ~ class_Rings_Oidom(X0)
| ( c_Polynomial_Oorder(X0,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Polynomial_Opoly(X0,X1),X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f2799]) ).
tcf(c_81,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f4328]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(cnf_transformation,[],[f4331]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Osemiring__0(X0)
| ~ class_Power_Opower(X0) ),
inference(cnf_transformation,[],[f4332]) ).
tcf(c_86,plain,
! [X0: $i] :
( ( c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2807]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f2808]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X1))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2809]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ class_Rings_Oidom(X0)
| ~ class_Int_Oring__char__0(X0)
| ( c_Polynomial_Opoly(X0,X1) != c_Polynomial_Opoly(X0,X2) ) ),
inference(cnf_transformation,[],[f2810]) ).
tcf(c_90,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK7) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
inference(cnf_transformation,[],[f4333]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X0,X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X0,X1) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f4335]) ).
tcf(c_101,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f4343]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Osynthetic__div(X0,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__0(X0)
| ( c_Polynomial_Odegree(X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(cnf_transformation,[],[f2825]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Odegree(X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Rings_Ocomm__semiring__0(X0)
| ( c_Polynomial_Osynthetic__div(X0,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(cnf_transformation,[],[f2824]) ).
tcf(c_112,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f4489]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f2850]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f2851]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osynthetic__div(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2870]) ).
tcf(c_129,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != X0,
inference(cnf_transformation,[],[f4348]) ).
tcf(c_130,plain,
! [X0: $i] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f4501]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ~ class_Groups_Ozero(X0)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(cnf_transformation,[],[f2876]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f2880]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X2))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))) ),
inference(cnf_transformation,[],[f2879]) ).
tcf(c_135,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f2881]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Polynomial_Opoly__rec(X3,X1,X2,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2 )
| ~ class_Groups_Ozero(X1)
| ( hAPP(hAPP(hAPP(X0,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) != X2 ) ),
inference(cnf_transformation,[],[f2882]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(X0,X2,X1),c_Polynomial_Odegree(X0,X1))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2885]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Rings_Oidom(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),X2)) ),
inference(cnf_transformation,[],[f2886]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
inference(cnf_transformation,[],[f4350]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(cnf_transformation,[],[f2890]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X2))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1))) ),
inference(cnf_transformation,[],[f2889]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
| ~ class_Fields_Ofield(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))) ),
inference(cnf_transformation,[],[f4503]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4505]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,X3,X1)),X2))
| ( c_Groups_Ozero__class_Ozero(X0) = X3 )
| ~ class_Fields_Ofield(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),X2)) ),
inference(cnf_transformation,[],[f2894]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Fields_Ofield(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1)),X2)) ),
inference(cnf_transformation,[],[f4507]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X2),X3))
| ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Fields_Ofield(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,X1,X2)),X3)) ),
inference(cnf_transformation,[],[f2891]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f2899]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X3 )
| ~ class_Groups_Ozero(X0)
| ( c_Polynomial_OpCons(X0,X1,X2) != c_Polynomial_OpCons(X0,X3,X4) ) ),
inference(cnf_transformation,[],[f2904]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = X4 )
| ~ class_Groups_Ozero(X0)
| ( c_Polynomial_OpCons(X0,X1,X2) != c_Polynomial_OpCons(X0,X3,X4) ) ),
inference(cnf_transformation,[],[f2903]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Rings_Ocomm__semiring__0(X0)
| ( c_Polynomial_OpCons(X0,X1,X2) != c_Polynomial_Osmult(X0,X3,X2) ) ),
inference(cnf_transformation,[],[f2906]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X1,X2)),c_Polynomial_Odegree(X0,X2))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2907]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( hAPP(hAPP(hAPP(X1,X2),X3),c_If(X4,c_fequal(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X5,c_Polynomial_Opoly__rec(X4,X0,X5,X1,X3))) = c_Polynomial_Opoly__rec(X4,X0,X5,X1,c_Polynomial_OpCons(X0,X2,X3)) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2908]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_OpCons(X0,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X0,X2)))
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f4351]) ).
tcf(c_162,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f2910]) ).
tcf(c_164,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(cnf_transformation,[],[f2911]) ).
tcf(c_165,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X0),
inference(cnf_transformation,[],[f4352]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(cnf_transformation,[],[f4354]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f4357]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f4359]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osmult(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2924]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( hAPP(hAPP(hAPP(X0,X3),X4),c_Polynomial_Opoly__rec(X5,X1,X2,X0,X4)) = c_Polynomial_Opoly__rec(X5,X1,X2,X0,c_Polynomial_OpCons(X1,X3,X4)) )
| ~ class_Groups_Ozero(X1)
| ( hAPP(hAPP(hAPP(X0,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) != X2 ) ),
inference(cnf_transformation,[],[f2925]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,X1,X2)),X3)) ),
inference(cnf_transformation,[],[f2926]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),c_Polynomial_Osmult(X0,X3,X2)))
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),X2)) ),
inference(cnf_transformation,[],[f2927]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Groups_Ozero(X0)
| ( c_Polynomial_OpCons(X0,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(cnf_transformation,[],[f2929]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Groups_Ozero(X0)
| ( c_Polynomial_OpCons(X0,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(cnf_transformation,[],[f2928]) ).
tcf(c_183,plain,
! [X0: $i] :
( ( c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2931]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f2932]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f2933]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4515]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osmult(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4516]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Rings_Oidom(X0)
| ( c_Polynomial_Osmult(X0,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(cnf_transformation,[],[f2934]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2937]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X4)),X3))
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)),X3)) ),
inference(cnf_transformation,[],[f2938]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X4)))
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f2939]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)))
| ~ class_Rings_Ocomm__semiring__1(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f2940]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),X3))
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ~ class_Fields_Ofield(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),c_Polynomial_Osmult(X0,X2,X3))) ),
inference(cnf_transformation,[],[f2941]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),c_Polynomial_Osmult(X0,X3,X2)))
| ( c_Groups_Ozero__class_Ozero(X0) = X3 )
| ~ class_Fields_Ofield(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),X2)) ),
inference(cnf_transformation,[],[f2944]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Polynomial_OpCons(X0,hAPP(c_Polynomial_Opoly(X0,X1),X2),c_Polynomial_Osynthetic__div(X0,X1,X2)) = c_Polynomial_Osynthetic__div(X0,c_Polynomial_OpCons(X0,X3,X1),X2) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2945]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Odegree(X0,c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2946]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X0,X1)) = c_Polynomial_Odegree(X0,c_Polynomial_OpCons(X0,X2,X1)) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f4363]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) ) ),
inference(cnf_transformation,[],[f4364]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X3)
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2))) ),
inference(cnf_transformation,[],[f4365]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4517]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X1,X2)) = c_Polynomial_Odegree(X0,X2) )
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2950]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( hAPP(c_Polynomial_Opoly(X0,X1),X2) = X4 )
| ~ class_Rings_Ocomm__semiring__0(X0)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,c_Polynomial_Osmult(X0,X2,X3)) != c_Polynomial_OpCons(X0,X4,X3) ) ),
inference(cnf_transformation,[],[f2954]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Polynomial_Osynthetic__div(X0,X1,X2) = X3 )
| ~ class_Rings_Ocomm__semiring__0(X0)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,c_Polynomial_Osmult(X0,X2,X3)) != c_Polynomial_OpCons(X0,X4,X3) ) ),
inference(cnf_transformation,[],[f2953]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,c_Polynomial_Osmult(X0,X2,c_Polynomial_Osynthetic__div(X0,X1,X2))) = c_Polynomial_OpCons(X0,hAPP(c_Polynomial_Opoly(X0,X1),X2),c_Polynomial_Osynthetic__div(X0,X1,X2)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2955]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Odegree(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X0,X1,c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))),X2)) = X2 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2956]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X2) = c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2957]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Polynomial_Omonom(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2958]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2) ) ),
inference(cnf_transformation,[],[f2959]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Oone__class_Oone(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f2960]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Polynomial_Omonom(X0,X1,X2)) = c_Polynomial_Omonom(X0,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f4366]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)) ),
inference(cnf_transformation,[],[f2968]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1) ),
inference(cnf_transformation,[],[f2969]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Oplus__class_Oplus(X0,X1,X3))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f2970]) ).
tcf(c_223,plain,
! [X0: $i] :
( ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f2971]) ).
tcf(c_224,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f2972]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3) ) ),
inference(cnf_transformation,[],[f2973]) ).
tcf(c_226,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f2975]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oone__class_Oone(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f2976]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ class_Groups_Ozero(X0)
| ( c_Polynomial_Omonom(X0,X1,X2) != c_Polynomial_Omonom(X0,X3,X2) ) ),
inference(cnf_transformation,[],[f2977]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Omonom(X0,X1,X2),c_Polynomial_Omonom(X0,X3,X2)) = c_Polynomial_Omonom(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),X2) )
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2979]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X1)
| c_Orderings_Oord__class_Oless(X0,X1,X2)
| ( X1 = X2 )
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2980]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X3)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f2983]) ).
tcf(c_234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X3,X2)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X3,X1)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f2984]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f2989]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f2994]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X1)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f3002]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X1) ),
inference(cnf_transformation,[],[f4530]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X1)
| c_Orderings_Oord__class_Oless(X0,X1,X2)
| ( X1 = X2 )
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f3003]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X1) ),
inference(cnf_transformation,[],[f3006]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f3011]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X1,X2),c_Polynomial_OpCons(X0,X3,X4)) = c_Polynomial_OpCons(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X2,X4)) )
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f3023]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Odegree(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X2,X1)) = c_Polynomial_Odegree(X0,X2) )
| ~ class_Groups_Ocomm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2)) ),
inference(cnf_transformation,[],[f3024]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Odegree(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,X2)) = c_Polynomial_Odegree(X0,X2) )
| ~ class_Groups_Ocomm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2)) ),
inference(cnf_transformation,[],[f3025]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X3,X1)),X2)
| ~ class_Groups_Ocomm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X3),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),X2) ),
inference(cnf_transformation,[],[f3026]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(c_Polynomial_Opoly(X0,X1),X2),hAPP(c_Polynomial_Opoly(X0,X3),X2)) = hAPP(c_Polynomial_Opoly(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,X3)),X2) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3027]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),c_Polynomial_Osmult(X0,X3,X2)) = c_Polynomial_Osmult(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),X2) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3028]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X3,X2)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3029]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X3)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3030]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X3)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3031]) ).
tcf(c_274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X3,X2)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3032]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X1)
| c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f4536]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X2)
| ( X1 = X2 )
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3042]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(X0,X2,X1)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3051]) ).
tcf(c_292,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f3050]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3049]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X2)
| ( X1 = X2 )
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3054]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f3053]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X1) ),
inference(cnf_transformation,[],[f4538]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3059]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X1)
| c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f3058]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i] :
( ( hAPP(c_Polynomial_Opoly(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3060]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Oone__class_Oone(X0))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3061]) ).
tcf(c_304,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1) ),
inference(cnf_transformation,[],[f3062]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(c_Polynomial_Opoly(X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,X2)),X3) = hAPP(c_Polynomial_Opoly(X0,X1),c_Groups_Oplus__class_Oplus(X0,X2,X3)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3063]) ).
tcf(c_306,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1) ),
inference(cnf_transformation,[],[f4370]) ).
tcf(c_307,plain,
! [X0: $i] :
( ( c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3065]) ).
tcf(c_309,plain,
! [X0: $i] :
( ~ class_Rings_Ozero__neq__one(X0)
| ( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ) ),
inference(cnf_transformation,[],[f3067]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Groups_Oplus__class_Oplus(X0,X3,X2)))
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3068]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),c_Groups_Oone__class_Oone(X0)),X1))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3069]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Oone__class_Oone(X0)),X1) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Groups_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f3070]) ).
tcf(c_317,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(cnf_transformation,[],[f3074]) ).
tcf(c_318,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f3076]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(cnf_transformation,[],[f4372]) ).
tcf(c_322,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f4374]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X1 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f4375]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f4382]) ).
tcf(c_331,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(cnf_transformation,[],[f4542]) ).
tcf(c_333,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f4385]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f4386]) ).
tcf(c_337,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f4543]) ).
tcf(c_344,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f4545]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1 )
| ~ class_Groups_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f3103]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = X1 )
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f3104]) ).
tcf(c_347,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = X1 )
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f3105]) ).
tcf(c_349,plain,
! [X0: $i] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3106]) ).
tcf(c_350,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)),
inference(cnf_transformation,[],[f3108]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),c_Polynomial_Osmult(X0,X1,X3)) = c_Polynomial_Osmult(X0,X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X2,X3)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3109]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osmult(X0,c_Groups_Oone__class_Oone(X0),X1) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3110]) ).
tcf(c_353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,X1)),c_Polynomial_OpCons(X0,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,X1))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X3,X2),X1) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3111]) ).
tcf(c_354,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Oone__class_Oone(X0))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f4387]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1) ),
inference(cnf_transformation,[],[f3115]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)) ),
inference(cnf_transformation,[],[f3114]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X0)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f3117]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2))) ),
inference(cnf_transformation,[],[f3118]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3119]) ).
tcf(c_362,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f3120]) ).
tcf(c_363,plain,
! [X0: $i] :
( ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3121]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3122]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),X1) ),
inference(cnf_transformation,[],[f3123]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK8(X1,X0)) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f4390]) ).
tcf(c_370,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK8(X1,X0),X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f4391]) ).
tcf(c_372,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f4393]) ).
tcf(c_373,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(cnf_transformation,[],[f4551]) ).
tcf(c_374,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(X0)) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f4395]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f3133]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f3134]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f4399]) ).
tcf(c_383,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f4402]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f4403]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(cnf_transformation,[],[f4406]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X3,X1)),X2)
| ~ class_Groups_Ocomm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),X2) ),
inference(cnf_transformation,[],[f3146]) ).
tcf(c_390,plain,
! [X0: $i] :
( ( c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3148]) ).
tcf(c_391,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)) ),
inference(cnf_transformation,[],[f3149]) ).
tcf(c_393,plain,
! [X0: $i] : 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),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f4553]) ).
tcf(c_396,plain,
! [X0: $i,X1: $i] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f4554]) ).
tcf(c_397,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ~ class_Rings_Ocomm__semiring__0(X0)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(cnf_transformation,[],[f3154]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Odegree(X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,X2)) = c_Polynomial_Odegree(X0,X1) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3156]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Omonom(X0,c_Groups_Ozero__class_Ozero(X0),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f4555]) ).
tcf(c_401,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Groups_Ozero(X0)
| ( c_Polynomial_Omonom(X0,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(cnf_transformation,[],[f3158]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X1,X2)) = X2 )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f3160]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X1,X2)),X2)
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f3161]) ).
tcf(c_404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X3)
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X3)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2)) ),
inference(cnf_transformation,[],[f3162]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ozero__class_Ozero(X0)),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Osemiring__0(X0)
| ~ class_Power_Opower(X0) ),
inference(cnf_transformation,[],[f3163]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),X1) ),
inference(cnf_transformation,[],[f3165]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X3)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3169]) ).
tcf(c_413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X3,X2)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3171]) ).
tcf(c_417,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[],[f4562]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3183]) ).
tcf(c_420,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[],[f4564]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,X1)
| c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f3184]) ).
tcf(c_422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X0),X1,X2)
| ~ class_Orderings_Oord(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,hAPP(X1,sK10(X2,X1,X0)),hAPP(X2,sK10(X2,X1,X0))) ),
inference(cnf_transformation,[],[f3186]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4),hAPP(X3,X4))
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X3) ),
inference(cnf_transformation,[],[f3185]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Rings_Ocomm__semiring__0(X0)
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),c_Polynomial_OpCons(X0,X3,X2)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(cnf_transformation,[],[f3187]) ).
tcf(c_425,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),X1)
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Oone__class_Oone(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f4408]) ).
tcf(c_428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Oplus__class_Oplus(X0,X1,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3191]) ).
tcf(c_429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Oplus__class_Oplus(X0,X1,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3192]) ).
tcf(c_430,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X2,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3193]) ).
tcf(c_431,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3194]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i] :
( 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),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f3196]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ( 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),X0),X1)) ),
inference(cnf_transformation,[],[f3195]) ).
tcf(c_435,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(cnf_transformation,[],[f4409]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_fun(X0,X1),X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X3,X2)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X3) ),
inference(cnf_transformation,[],[f3201]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X3)
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X0,X1),X2,X3) ),
inference(cnf_transformation,[],[f3200]) ).
tcf(c_438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X0,X1),X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X3) ),
inference(cnf_transformation,[],[f3199]) ).
tcf(c_440,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f3203]) ).
tcf(c_442,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(cnf_transformation,[],[f3205]) ).
tcf(c_443,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(cnf_transformation,[],[f3204]) ).
tcf(c_444,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f3207]) ).
tcf(c_449,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(cnf_transformation,[],[f3213]) ).
tcf(c_450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) ) ),
inference(cnf_transformation,[],[f3214]) ).
tcf(c_451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3215]) ).
tcf(c_452,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3216]) ).
tcf(c_455,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3220]) ).
tcf(c_456,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) ),
inference(cnf_transformation,[],[f3219]) ).
tcf(c_457,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1),
inference(cnf_transformation,[],[f3221]) ).
tcf(c_458,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0),
inference(cnf_transformation,[],[f3222]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f3224]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3223]) ).
tcf(c_463,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(cnf_transformation,[],[f3227]) ).
tcf(c_464,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1),X2) ),
inference(cnf_transformation,[],[f3228]) ).
tcf(c_465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3229]) ).
tcf(c_466,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3230]) ).
tcf(c_469,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3234]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) ),
inference(cnf_transformation,[],[f3233]) ).
tcf(c_472,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK11(X1,X0)) = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3235]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(cnf_transformation,[],[f3238]) ).
tcf(c_477,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ) ),
inference(cnf_transformation,[],[f4416]) ).
tcf(c_478,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ) ),
inference(cnf_transformation,[],[f4417]) ).
tcf(c_479,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ) ),
inference(cnf_transformation,[],[f4418]) ).
tcf(c_480,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ) ),
inference(cnf_transformation,[],[f4419]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i] :
( 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),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(cnf_transformation,[],[f3251]) ).
tcf(c_491,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
inference(cnf_transformation,[],[f4427]) ).
tcf(c_492,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(cnf_transformation,[],[f4577]) ).
tcf(c_493,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK12(X1,X0))) = X1 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f4429]) ).
tcf(c_494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X3) = c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oplus__class_Oplus(X0,X2,X3)) )
| ~ class_Groups_Oab__semigroup__add(X0) ),
inference(cnf_transformation,[],[f3260]) ).
tcf(c_497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ~ class_Groups_Ocancel__semigroup__add(X0)
| ( c_Groups_Oplus__class_Oplus(X0,X1,X2) != c_Groups_Oplus__class_Oplus(X0,X1,X3) ) ),
inference(cnf_transformation,[],[f3265]) ).
tcf(c_498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ~ class_Groups_Ocancel__ab__semigroup__add(X0)
| ( c_Groups_Oplus__class_Oplus(X0,X1,X2) != c_Groups_Oplus__class_Oplus(X0,X1,X3) ) ),
inference(cnf_transformation,[],[f3266]) ).
tcf(c_499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ class_Groups_Ocancel__semigroup__add(X0)
| ( c_Groups_Oplus__class_Oplus(X0,X1,X2) != c_Groups_Oplus__class_Oplus(X0,X3,X2) ) ),
inference(cnf_transformation,[],[f3267]) ).
tcf(c_500,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 )
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f3270]) ).
tcf(c_501,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 )
| ~ class_Groups_Omonoid__add(X0) ),
inference(cnf_transformation,[],[f3271]) ).
tcf(c_504,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ozero__class_Ozero(X0),X1) = X1 )
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f3274]) ).
tcf(c_505,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ozero__class_Ozero(X0),X1) = X1 )
| ~ class_Groups_Omonoid__add(X0) ),
inference(cnf_transformation,[],[f3275]) ).
tcf(c_506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),c_Groups_Oplus__class_Oplus(X0,X2,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3277]) ).
tcf(c_508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,X3,X1),c_Groups_Oplus__class_Oplus(X0,X3,X2))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3279]) ).
tcf(c_510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),c_Groups_Oplus__class_Oplus(X0,X2,X3))
| ~ class_Groups_Oordered__ab__semigroup__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3280]) ).
tcf(c_511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,X3,X1),c_Groups_Oplus__class_Oplus(X0,X3,X2))
| ~ class_Groups_Oordered__ab__semigroup__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3281]) ).
tcf(c_512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,X3,X1),c_Groups_Oplus__class_Oplus(X0,X4,X2))
| ~ class_Groups_Oordered__ab__semigroup__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3282]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),c_Groups_Oplus__class_Oplus(X0,X3,X2)) ),
inference(cnf_transformation,[],[f3283]) ).
tcf(c_514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),c_Groups_Oplus__class_Oplus(X0,X1,X3)) ),
inference(cnf_transformation,[],[f3284]) ).
tcf(c_515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),c_Groups_Oplus__class_Oplus(X0,X2,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f3286]) ).
tcf(c_517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X3,X1),c_Groups_Oplus__class_Oplus(X0,X3,X2))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f3288]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),c_Groups_Oplus__class_Oplus(X0,X2,X3))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f3289]) ).
tcf(c_520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X3,X1),c_Groups_Oplus__class_Oplus(X0,X3,X2))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f3290]) ).
tcf(c_521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X3,X1),c_Groups_Oplus__class_Oplus(X0,X4,X2))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f3291]) ).
tcf(c_522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),c_Groups_Oplus__class_Oplus(X0,X3,X2)) ),
inference(cnf_transformation,[],[f3292]) ).
tcf(c_523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),c_Groups_Oplus__class_Oplus(X0,X1,X3)) ),
inference(cnf_transformation,[],[f3293]) ).
tcf(c_524,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,X2,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3294]) ).
tcf(c_525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Oplus__class_Oplus(X0,X3,X1))
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3295]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Oplus__class_Oplus(X0,X1,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3296]) ).
tcf(c_527,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f4724]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ( c_Groups_Oplus__class_Oplus(X0,X1,X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3298]) ).
tcf(c_529,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ( c_Groups_Oplus__class_Oplus(X0,X1,X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3297]) ).
tcf(c_531,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,X1,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3302]) ).
tcf(c_532,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,X1,X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3301]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,X1,X1))
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3304]) ).
tcf(c_534,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,X1,X1)) ),
inference(cnf_transformation,[],[f3303]) ).
tcf(c_535,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X2,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3305]) ).
tcf(c_536,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,X2,X1))
| ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3306]) ).
tcf(c_537,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3308]) ).
tcf(c_538,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3307]) ).
tcf(c_539,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,X1,X1))
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3310]) ).
tcf(c_540,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,X1,X1)) ),
inference(cnf_transformation,[],[f3309]) ).
tcf(c_541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),c_Groups_Oplus__class_Oplus(X0,X2,X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3311]) ).
tcf(c_542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X3,X1),c_Groups_Oplus__class_Oplus(X0,X4,X2))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3312]) ).
tcf(c_543,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3313]) ).
tcf(c_544,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3315]) ).
tcf(c_545,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3314]) ).
tcf(c_548,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Rings_Oidom(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Oorder(X0,X1,X2)))),X2)) ),
inference(cnf_transformation,[],[f4431]) ).
tcf(c_549,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3319]) ).
tcf(c_551,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),
inference(cnf_transformation,[],[f3321]) ).
tcf(c_552,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)),
inference(cnf_transformation,[],[f3322]) ).
tcf(c_553,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(cnf_transformation,[],[f3323]) ).
tcf(c_554,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) ) ),
inference(cnf_transformation,[],[f3324]) ).
tcf(c_555,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ) ),
inference(cnf_transformation,[],[f3326]) ).
tcf(c_560,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)) = X1 )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f4592]) ).
tcf(c_561,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ class_Groups_Ogroup__add(X0)
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) != c_Groups_Ouminus__class_Ouminus(X0,X2) ) ),
inference(cnf_transformation,[],[f3333]) ).
tcf(c_562,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2)) = c_Polynomial_Osmult(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2) )
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f3335]) ).
tcf(c_563,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_Polynomial_Opoly(X0,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1)),X2) = c_Groups_Ouminus__class_Ouminus(X0,hAPP(c_Polynomial_Opoly(X0,X1),X2)) )
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f3336]) ).
tcf(c_565,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_OpCons(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X2)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X1,X2)) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3338]) ).
tcf(c_566,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Polynomial_Omonom(X0,X1,X2)) = c_Polynomial_Omonom(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3339]) ).
tcf(c_571,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Olinordered__ab__group__add(X0) ),
inference(cnf_transformation,[],[f4596]) ).
tcf(c_572,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f3344]) ).
tcf(c_574,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Groups_Ogroup__add(X0)
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3346]) ).
tcf(c_575,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f3348]) ).
tcf(c_577,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2)) ),
inference(cnf_transformation,[],[f3349]) ).
tcf(c_579,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2) ),
inference(cnf_transformation,[],[f3351]) ).
tcf(c_581,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) ),
inference(cnf_transformation,[],[f3353]) ).
tcf(c_582,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3355]) ).
tcf(c_584,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2)) ),
inference(cnf_transformation,[],[f3356]) ).
tcf(c_586,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2) ),
inference(cnf_transformation,[],[f3358]) ).
tcf(c_587,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f3361]) ).
tcf(c_588,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) ),
inference(cnf_transformation,[],[f3360]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2)) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3362]) ).
tcf(c_590,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Oplus__class_Oplus(X0,X2,X1)) )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f3363]) ).
tcf(c_591,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oplus__class_Oplus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2)) = X2 )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f3364]) ).
tcf(c_592,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Oplus__class_Oplus(X0,X1,X2)) = X2 )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f3365]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Groups_Ouminus__class_Ouminus(X0,X2)))
| ~ class_Rings_Ocomm__ring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3367]) ).
tcf(c_594,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2))
| ~ class_Rings_Ocomm__ring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Groups_Ouminus__class_Ouminus(X0,X2))) ),
inference(cnf_transformation,[],[f3366]) ).
tcf(c_595,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),X2))
| ~ class_Rings_Ocomm__ring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3369]) ).
tcf(c_596,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2))
| ~ class_Rings_Ocomm__ring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),X2)) ),
inference(cnf_transformation,[],[f3368]) ).
tcf(c_597,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3370]) ).
tcf(c_598,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Odegree(X0,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1)) = c_Polynomial_Odegree(X0,X1) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3371]) ).
tcf(c_599,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Osmult(X0,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X2)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2)) )
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f3372]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3374]) ).
tcf(c_601,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(cnf_transformation,[],[f3373]) ).
tcf(c_602,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3376]) ).
tcf(c_603,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(cnf_transformation,[],[f3375]) ).
tcf(c_604,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3378]) ).
tcf(c_605,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3377]) ).
tcf(c_606,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3380]) ).
tcf(c_607,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1) ),
inference(cnf_transformation,[],[f3379]) ).
tcf(c_608,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3382]) ).
tcf(c_609,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(cnf_transformation,[],[f3381]) ).
tcf(c_610,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3384]) ).
tcf(c_611,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(cnf_transformation,[],[f3383]) ).
tcf(c_612,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3386]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3385]) ).
tcf(c_614,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3388]) ).
tcf(c_615,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1) ),
inference(cnf_transformation,[],[f3387]) ).
tcf(c_617,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,X2) = X1 )
| ~ class_Groups_Ogroup__add(X0)
| ( c_Groups_Oplus__class_Oplus(X0,X1,X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3391]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f3392]) ).
tcf(c_620,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3393]) ).
tcf(c_621,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f4599]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X2 )
| ~ class_Groups_Ogroup__add(X0)
| ( c_Groups_Oplus__class_Oplus(X0,X1,X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3396]) ).
tcf(c_624,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4601]) ).
tcf(c_625,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( c_Groups_Ouminus__class_Ouminus(X0,X2) = X1 )
| ~ class_Rings_Oidom(X0)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(cnf_transformation,[],[f4434]) ).
tcf(c_626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),c_Groups_Oplus__class_Oplus(X0,X3,X4)) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),c_Groups_Oplus__class_Oplus(X0,X2,X4)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3400]) ).
tcf(c_627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X3) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),X2) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3401]) ).
tcf(c_629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X3) = c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oplus__class_Oplus(X0,X2,X3)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3403]) ).
tcf(c_630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oplus__class_Oplus(X0,X2,X3)) = c_Groups_Oplus__class_Oplus(X0,X2,c_Groups_Oplus__class_Oplus(X0,X1,X3)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3404]) ).
tcf(c_631,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X2,X1) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3405]) ).
tcf(c_632,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3406]) ).
tcf(c_633,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3407]) ).
tcf(c_634,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3408]) ).
tcf(c_635,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3409]) ).
tcf(c_636,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ 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),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(cnf_transformation,[],[f3410]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(cnf_transformation,[],[f3411]) ).
tcf(c_638,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(cnf_transformation,[],[f3412]) ).
tcf(c_639,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_Polynomial_Opoly(X0,X2),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Oidom(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))),X2)) ),
inference(cnf_transformation,[],[f3414]) ).
tcf(c_640,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))),X1))
| ~ class_Rings_Oidom(X0)
| ( hAPP(c_Polynomial_Opoly(X0,X1),X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3413]) ).
tcf(c_641,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X0,X2,c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))),X1))
| ~ class_Rings_Oidom(X0)
| ( hAPP(c_Polynomial_Opoly(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3416]) ).
tcf(c_642,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_Polynomial_Opoly(X0,X2),c_Groups_Ouminus__class_Ouminus(X0,X1)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Oidom(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X0,X1,c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))),X2)) ),
inference(cnf_transformation,[],[f3415]) ).
tcf(c_643,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ozero__class_Ozero(X0),X1) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3417]) ).
tcf(c_644,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3418]) ).
tcf(c_645,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X0) ),
inference(cnf_transformation,[],[f4602]) ).
tcf(c_646,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X0)
| ( c_Groups_Oplus__class_Oplus(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f3419]) ).
tcf(c_647,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Olinordered__ab__group__add(X0) ),
inference(cnf_transformation,[],[f4603]) ).
tcf(c_648,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ( c_Groups_Oplus__class_Oplus(X0,X1,X1) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3421]) ).
tcf(c_649,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))),c_Polynomial_Oorder(X0,X1,X2))),X2))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f3423]) ).
tcf(c_650,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))),c_Polynomial_Osynthetic__div(X0,X2,X1)),c_Polynomial_OpCons(X0,hAPP(c_Polynomial_Opoly(X0,X2),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))) = X2 )
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f3424]) ).
tcf(c_651,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(cnf_transformation,[],[f4604]) ).
tcf(c_652,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK13(X1,X0)) = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3425]) ).
tcf(c_653,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Polynomial_Opos__poly(X0,c_Polynomial_OpCons(X0,X2,X1))
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X0,X1) ),
inference(cnf_transformation,[],[f3430]) ).
tcf(c_654,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opos__poly(X0,c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f4605]) ).
tcf(c_655,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Polynomial_Opos__poly(X0,X2)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X0,c_Polynomial_OpCons(X0,X1,X2)) ),
inference(cnf_transformation,[],[f3428]) ).
tcf(c_656,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Polynomial_Opos__poly(X0,X2)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X0,c_Polynomial_OpCons(X0,X1,X2)) ),
inference(cnf_transformation,[],[f3427]) ).
tcf(c_658,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3433]) ).
tcf(c_659,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,X1)
| ~ class_Lattices_Oboolean__algebra(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) ),
inference(cnf_transformation,[],[f3432]) ).
tcf(c_660,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f3434]) ).
tcf(c_661,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f3435]) ).
tcf(c_662,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ( X0 = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f3438]) ).
tcf(c_663,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f3437]) ).
tcf(c_664,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f4606]) ).
tcf(c_665,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f3440]) ).
tcf(c_666,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f3439]) ).
tcf(c_668,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) ),
inference(cnf_transformation,[],[f3441]) ).
tcf(c_669,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f3443]) ).
tcf(c_670,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f3444]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f3445]) ).
tcf(c_672,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f3446]) ).
tcf(c_673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f3447]) ).
tcf(c_674,plain,
! [X0: $i] :
( 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),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3448]) ).
tcf(c_675,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3450]) ).
tcf(c_676,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3449]) ).
tcf(c_677,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f3451]) ).
tcf(c_678,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f3452]) ).
tcf(c_679,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(cnf_transformation,[],[f3453]) ).
tcf(c_680,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[],[f3454]) ).
tcf(c_681,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f3455]) ).
tcf(c_682,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f3456]) ).
tcf(c_683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Polynomial_Omonom(X0,X1,X2)),c_Polynomial_Omonom(X0,X3,X4)) = c_Polynomial_Omonom(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3457]) ).
tcf(c_684,plain,
! [X0: $i] :
( 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),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3459]) ).
tcf(c_685,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,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),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3458]) ).
tcf(c_686,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f3460]) ).
tcf(c_690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oplus__class_Oplus(X0,X1,X3)),X2) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3465]) ).
tcf(c_691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) = c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X0) ),
inference(cnf_transformation,[],[f4609]) ).
tcf(c_692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = X4 )
| ( X1 = X3 )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X0)
| ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4)) != c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) ) ),
inference(cnf_transformation,[],[f3466]) ).
tcf(c_693,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Oplus__class_Oplus(X0,X2,X3)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3469]) ).
tcf(c_695,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f4611]) ).
tcf(c_697,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f3473]) ).
tcf(c_698,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Oone__class_Oone(X0)) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3474]) ).
tcf(c_699,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oone__class_Oone(X0)),X1) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3475]) ).
tcf(c_700,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(cnf_transformation,[],[f3476]) ).
tcf(c_701,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) = c_Groups_Ouminus__class_Ouminus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) )
| ~ class_Rings_Oring(X0) ),
inference(cnf_transformation,[],[f3477]) ).
tcf(c_702,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),X2) = c_Groups_Ouminus__class_Ouminus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) )
| ~ class_Rings_Oring(X0) ),
inference(cnf_transformation,[],[f3478]) ).
tcf(c_703,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) )
| ~ class_Rings_Oring(X0) ),
inference(cnf_transformation,[],[f3479]) ).
tcf(c_704,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),c_Groups_Ouminus__class_Ouminus(X0,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2) )
| ~ class_Rings_Oring(X0) ),
inference(cnf_transformation,[],[f3480]) ).
tcf(c_705,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),c_Groups_Ouminus__class_Ouminus(X0,X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1) )
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4613]) ).
tcf(c_706,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( c_Groups_Ouminus__class_Ouminus(X0,X2) = X1 )
| ~ class_Rings_Oidom(X0)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X2) ) ),
inference(cnf_transformation,[],[f3481]) ).
tcf(c_707,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X4)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3484]) ).
tcf(c_710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)),X2) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3487]) ).
tcf(c_712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3489]) ).
tcf(c_713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3490]) ).
tcf(c_714,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3491]) ).
tcf(c_715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)),X2) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3492]) ).
tcf(c_716,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3493]) ).
tcf(c_717,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3494]) ).
tcf(c_718,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Omult__zero(X0) ),
inference(cnf_transformation,[],[f3495]) ).
tcf(c_719,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Omult__zero(X0) ),
inference(cnf_transformation,[],[f3496]) ).
tcf(c_720,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Oring__no__zero__divisors(X0) ),
inference(cnf_transformation,[],[f4614]) ).
tcf(c_721,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Oring__no__zero__divisors(X0) ),
inference(cnf_transformation,[],[f4615]) ).
tcf(c_722,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Rings_Oring__no__zero__divisors(X0)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3497]) ).
tcf(c_724,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Rings_Ono__zero__divisors(X0)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3501]) ).
tcf(c_725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oplus__class_Oplus(X0,X1,X3)),X2) )
| ~ class_Rings_Ocomm__semiring(X0) ),
inference(cnf_transformation,[],[f3502]) ).
tcf(c_726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2),X4)) = c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oplus__class_Oplus(X0,X1,X3)),X2),X4) )
| ~ class_Rings_Osemiring(X0) ),
inference(cnf_transformation,[],[f3503]) ).
tcf(c_727,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oone__class_Oone(X0)),X1) = X1 )
| ~ class_Groups_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f3504]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oone__class_Oone(X0)),X1) = X1 )
| ~ class_Groups_Ocomm__monoid__mult(X0) ),
inference(cnf_transformation,[],[f3505]) ).
tcf(c_729,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Oone__class_Oone(X0)) = X1 )
| ~ class_Groups_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f3506]) ).
tcf(c_730,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Oone__class_Oone(X0)) = X1 )
| ~ class_Groups_Ocomm__monoid__mult(X0) ),
inference(cnf_transformation,[],[f3507]) ).
tcf(c_731,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3508]) ).
tcf(c_732,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1)))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3509]) ).
tcf(c_733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)))
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3510]) ).
tcf(c_734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)))
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3511]) ).
tcf(c_735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X2)))
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3512]) ).
tcf(c_736,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)))
| ~ class_Rings_Odvd(X0) ),
inference(cnf_transformation,[],[f4616]) ).
tcf(c_737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X3))
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)),X3)) ),
inference(cnf_transformation,[],[f3514]) ).
tcf(c_738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)),X3)) ),
inference(cnf_transformation,[],[f3515]) ).
tcf(c_739,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) )
| ~ class_Groups_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f3516]) ).
tcf(c_740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)),X2) )
| ~ class_Groups_Ocomm__monoid__mult(X0) ),
inference(cnf_transformation,[],[f3517]) ).
tcf(c_741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(c_Polynomial_Opoly(X0,X1),X2)),hAPP(c_Polynomial_Opoly(X0,X3),X2)) = hAPP(c_Polynomial_Opoly(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),X3)),X2) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3518]) ).
tcf(c_742,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Polynomial_Opos__poly(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X2),X1))
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X0,X2)
| ~ c_Polynomial_Opos__poly(X0,X1) ),
inference(cnf_transformation,[],[f3519]) ).
tcf(c_743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)) )
| ~ class_Groups_Oab__semigroup__mult(X0) ),
inference(cnf_transformation,[],[f3520]) ).
tcf(c_744,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3521]) ).
tcf(c_745,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3522]) ).
tcf(c_746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Polynomial_Osmult(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3) = c_Polynomial_Osmult(X0,X1,c_Polynomial_Osmult(X0,X2,X3)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3523]) ).
tcf(c_747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,X1,X2)),X3) = c_Polynomial_Osmult(X0,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X2),X3)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3524]) ).
tcf(c_748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),c_Polynomial_Osmult(X0,X2,X3)) = c_Polynomial_Osmult(X0,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),X3)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3525]) ).
tcf(c_749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,X3)),X2) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3526]) ).
tcf(c_750,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1))
| ~ class_Rings_Olinordered__ring(X0) ),
inference(cnf_transformation,[],[f3527]) ).
tcf(c_751,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3533]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3532]) ).
tcf(c_753,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3531]) ).
tcf(c_754,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3530]) ).
tcf(c_755,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3529]) ).
tcf(c_756,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3528]) ).
tcf(c_757,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3539]) ).
tcf(c_758,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3538]) ).
tcf(c_759,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3537]) ).
tcf(c_760,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3536]) ).
tcf(c_761,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3535]) ).
tcf(c_762,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3534]) ).
tcf(c_763,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1))
| ~ class_Rings_Oordered__cancel__semiring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3540]) ).
tcf(c_768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X1))
| ~ class_Rings_Oordered__semiring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3545]) ).
tcf(c_769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))
| ~ class_Rings_Oordered__semiring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3546]) ).
tcf(c_770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))
| ~ class_Rings_Oordered__comm__semiring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3547]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1))
| ~ class_Rings_Oordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3548]) ).
tcf(c_772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2))
| ~ class_Rings_Oordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3549]) ).
tcf(c_773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X3))
| ~ class_Rings_Oordered__semiring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3550]) ).
tcf(c_774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3))
| ~ class_Rings_Oordered__semiring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3551]) ).
tcf(c_775,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1))
| ~ class_Rings_Oordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3553]) ).
tcf(c_776,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1))
| ~ class_Rings_Oordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3552]) ).
tcf(c_777,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Oordered__cancel__semiring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3555]) ).
tcf(c_778,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Oordered__cancel__semiring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3554]) ).
tcf(c_781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))
| ~ class_Rings_Olinordered__comm__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3558]) ).
tcf(c_782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3559]) ).
tcf(c_783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X1))
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3560]) ).
tcf(c_784,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3561]) ).
tcf(c_787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X3,X2)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) ),
inference(cnf_transformation,[],[f3563]) ).
tcf(c_788,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3565]) ).
tcf(c_789,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3566]) ).
tcf(c_790,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3567]) ).
tcf(c_791,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3568]) ).
tcf(c_792,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1))
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3569]) ).
tcf(c_794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) ),
inference(cnf_transformation,[],[f3570]) ).
tcf(c_795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3577]) ).
tcf(c_796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3576]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) ),
inference(cnf_transformation,[],[f3575]) ).
tcf(c_798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X3,X2)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) ),
inference(cnf_transformation,[],[f3574]) ).
tcf(c_799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X3)
| c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) ),
inference(cnf_transformation,[],[f3573]) ).
tcf(c_800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X3,X2)
| c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) ),
inference(cnf_transformation,[],[f3572]) ).
tcf(c_801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X1))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3583]) ).
tcf(c_802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3582]) ).
tcf(c_803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) ),
inference(cnf_transformation,[],[f3581]) ).
tcf(c_804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X3,X1)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) ),
inference(cnf_transformation,[],[f3580]) ).
tcf(c_805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X3)
| c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) ),
inference(cnf_transformation,[],[f3579]) ).
tcf(c_806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X3,X1)
| c_Orderings_Oord__class_Oless(X0,X1,X3)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) ),
inference(cnf_transformation,[],[f3578]) ).
tcf(c_807,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Olinordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3584]) ).
tcf(c_808,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Ozero__class_Ozero(X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Ozero__class_Ozero(X0))) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Olinordered__ring__strict(X0) ),
inference(cnf_transformation,[],[f4618]) ).
tcf(c_809,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Rings_Olinordered__ring__strict(X0)
| ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X2)) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3586]) ).
tcf(c_810,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ~ class_Rings_Olinordered__ring__strict(X0)
| ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X2)) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3585]) ).
tcf(c_811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = X4 )
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X0)
| ( c_Groups_Oplus__class_Oplus(X0,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)) != c_Groups_Oplus__class_Oplus(X0,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X4)) ) ),
inference(cnf_transformation,[],[f4619]) ).
tcf(c_812,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X2)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1) ),
inference(cnf_transformation,[],[f3589]) ).
tcf(c_813,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),X2)))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4620]) ).
tcf(c_814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)))
| ~ class_Rings_Oidom(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3591]) ).
tcf(c_815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X2),X3))
| ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Rings_Oidom(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))) ),
inference(cnf_transformation,[],[f3590]) ).
tcf(c_816,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ozero__class_Ozero(X0))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),c_Groups_Ozero__class_Ozero(X0))))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4621]) ).
tcf(c_817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)))
| ~ class_Rings_Oidom(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3594]) ).
tcf(c_818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X3))
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ~ class_Rings_Oidom(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2))) ),
inference(cnf_transformation,[],[f3593]) ).
tcf(c_819,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))),X1) = c_Groups_Oplus__class_Oplus(X0,X1,X1) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3596]) ).
tcf(c_820,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oone__class_Oone(X0))),X2) = c_Groups_Oplus__class_Oplus(X0,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3597]) ).
tcf(c_821,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oone__class_Oone(X0))),X2) = c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X2) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3598]) ).
tcf(c_822,plain,
! [X0: $i] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(cnf_transformation,[],[f3599]) ).
tcf(c_823,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opos__poly(X0,X1)
| c_Polynomial_Opos__poly(X0,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f3600]) ).
tcf(c_824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(c_Polynomial_Opoly(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Polynomial_Omonom(X0,c_Groups_Oone__class_Oone(X0),X1)),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X1)),hAPP(c_Polynomial_Opoly(X0,X2),X3)) )
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f3601]) ).
tcf(c_825,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Oone__class_Oone(X0))),X1) = c_Groups_Ouminus__class_Ouminus(X0,X1) )
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f3602]) ).
tcf(c_826,plain,
! [X0: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Oone__class_Oone(X0)) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Rings_Oring__1__no__zero__divisors(X0) ),
inference(cnf_transformation,[],[f4622]) ).
tcf(c_827,plain,
! [X0: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Oone__class_Oone(X0))),c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Oone__class_Oone(X0))) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Rings_Oring__1__no__zero__divisors(X0) ),
inference(cnf_transformation,[],[f4623]) ).
tcf(c_828,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(X0) = X1 )
| ( c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Oone__class_Oone(X0)) = X1 )
| ~ class_Rings_Oring__1__no__zero__divisors(X0)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1) != c_Groups_Oone__class_Oone(X0) ) ),
inference(cnf_transformation,[],[f3603]) ).
tcf(c_829,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) )
| ~ class_Power_Opower(X0) ),
inference(cnf_transformation,[],[f4435]) ).
tcf(c_830,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) )
| ~ class_Groups_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f4436]) ).
tcf(c_832,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f4438]) ).
tcf(c_833,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f4439]) ).
tcf(c_834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) )
| ~ class_Groups_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f3611]) ).
tcf(c_835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3612]) ).
tcf(c_836,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Polynomial_Opos__poly(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X2,X1))
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X0,X2)
| ~ c_Polynomial_Opos__poly(X0,X1) ),
inference(cnf_transformation,[],[f3613]) ).
tcf(c_837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Polynomial_OpCons(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),c_Polynomial_Osmult(X0,X1,X3)) = c_Polynomial_Osmult(X0,X1,c_Polynomial_OpCons(X0,X2,X3)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3614]) ).
tcf(c_838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(c_Polynomial_Opoly(X0,X2),X3)) = hAPP(c_Polynomial_Opoly(X0,c_Polynomial_Osmult(X0,X1,X2)),X3) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3615]) ).
tcf(c_839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Polynomial_Omonom(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3) = c_Polynomial_Osmult(X0,X1,c_Polynomial_Omonom(X0,X2,X3)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3616]) ).
tcf(c_840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) ),
inference(cnf_transformation,[],[f3617]) ).
tcf(c_841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X3)
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) ),
inference(cnf_transformation,[],[f3618]) ).
tcf(c_842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) ),
inference(cnf_transformation,[],[f3619]) ).
tcf(c_843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X3)
| ~ class_Rings_Olinordered__semiring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) ),
inference(cnf_transformation,[],[f3620]) ).
tcf(c_844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X3)
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) ),
inference(cnf_transformation,[],[f3621]) ).
tcf(c_845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X3)
| ~ class_Rings_Olinordered__semiring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) ),
inference(cnf_transformation,[],[f3622]) ).
tcf(c_846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4))
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3623]) ).
tcf(c_847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X3))
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3624]) ).
tcf(c_848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X3))
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3625]) ).
tcf(c_849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X4,X2)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3626]) ).
tcf(c_850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3628]) ).
tcf(c_851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X3,X2)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) ),
inference(cnf_transformation,[],[f3627]) ).
tcf(c_852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3))
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3630]) ).
tcf(c_853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) ),
inference(cnf_transformation,[],[f3629]) ).
tcf(c_854,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X2)))
| ~ class_Rings_Olinordered__ring(X0) ),
inference(cnf_transformation,[],[f3631]) ).
tcf(c_855,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Ozero__class_Ozero(X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Ozero__class_Ozero(X0))),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__ring__strict(X0) ),
inference(cnf_transformation,[],[f4625]) ).
tcf(c_856,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X2)),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3633]) ).
tcf(c_857,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X2)),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3632]) ).
tcf(c_858,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Rings_Olinordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X2)),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3635]) ).
tcf(c_859,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X2)))
| ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Rings_Olinordered__ring__strict(X0) ),
inference(cnf_transformation,[],[f3638]) ).
tcf(c_860,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1)))
| ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Rings_Olinordered__ring__strict(X0) ),
inference(cnf_transformation,[],[f3637]) ).
tcf(c_861,plain,
! [X0: $i] :
( ~ class_Rings_Olinordered__ring__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Ozero__class_Ozero(X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Ozero__class_Ozero(X0)))) ),
inference(cnf_transformation,[],[f4627]) ).
tcf(c_862,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X2)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Oone__class_Oone(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3639]) ).
tcf(c_863,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X1),X2)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Oone__class_Oone(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3640]) ).
tcf(c_864,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1) ),
inference(cnf_transformation,[],[f3641]) ).
tcf(c_865,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),X1) ),
inference(cnf_transformation,[],[f3642]) ).
tcf(c_866,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Oone__class_Oone(X0))),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X1)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ouminus__class_Ouminus(X0,X2)),X1) )
| ~ class_Rings_Oring__1(X0) ),
inference(cnf_transformation,[],[f3643]) ).
tcf(c_867,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2)))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3644]) ).
tcf(c_868,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ( c_Polynomial_Odegree(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2)) )
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f3645]) ).
tcf(c_869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),hAPP(c_Polynomial_Opoly(X0,X3),X2))) = hAPP(c_Polynomial_Opoly(X0,c_Polynomial_OpCons(X0,X1,X3)),X2) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3646]) ).
tcf(c_870,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)) = X1 )
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f3647]) ).
tcf(c_871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,X0),X2),X3) = c_Groups_Ouminus__class_Ouminus(X0,hAPP(X2,X3)) )
| ~ class_Groups_Ouminus(X0) ),
inference(cnf_transformation,[],[f3648]) ).
tcf(c_872,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ class_Lattices_Oboolean__algebra(X0)
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) != c_Groups_Ouminus__class_Ouminus(X0,X2) ) ),
inference(cnf_transformation,[],[f3649]) ).
tcf(c_873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3)) = hAPP(c_Polynomial_Opoly(X0,c_Polynomial_Omonom(X0,X1,X3)),X2) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3651]) ).
tcf(c_874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),X4)
| ~ class_Rings_Olinordered__semiring__1(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X5,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ( c_Groups_Oplus__class_Oplus(X0,X1,X2) != c_Groups_Oone__class_Oone(X0) ) ),
inference(cnf_transformation,[],[f3652]) ).
tcf(c_875,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Oone__class_Oone(X0))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f3653]) ).
tcf(c_876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X3),X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X0,X1,X3)),X2) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3654]) ).
tcf(c_877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X2),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X2),c_Polynomial_OpCons(X0,X1,X3)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3655]) ).
tcf(c_878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),X4)
| ~ class_Rings_Olinordered__semiring__1__strict(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X5,X4)
| ~ c_Orderings_Oord__class_Oless(X0,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ( c_Groups_Oplus__class_Oplus(X0,X1,X2) != c_Groups_Oone__class_Oone(X0) ) ),
inference(cnf_transformation,[],[f3656]) ).
tcf(c_879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),sK14(X1,X3,X0))))
| ~ class_Rings_Odvd(X0)
| ~ class_Rings_Osemiring__0(X0)
| ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Groups_Oplus__class_Oplus(X0,X2,c_Groups_Ozero__class_Ozero(X0)))) ),
inference(cnf_transformation,[],[f3659]) ).
tcf(c_880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Groups_Oplus__class_Oplus(X1,sK15(X2,X0,X1),c_Groups_Ozero__class_Ozero(X1))))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1)
| ~ hBOOL(hAPP(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))) ),
inference(cnf_transformation,[],[f3658]) ).
tcf(c_881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X0,sK15(X2,X0,X1)))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1)
| ~ hBOOL(hAPP(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))) ),
inference(cnf_transformation,[],[f3657]) ).
tcf(c_882,plain,
! [X0: $i,X1: $i] :
( 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),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3660]) ).
tcf(c_883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X2),c_Polynomial_Opcompose(X0,X3,X2))) = c_Polynomial_Opcompose(X0,c_Polynomial_OpCons(X0,X1,X3),X2) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3661]) ).
tcf(c_884,plain,
! [X0: $i] :
( ( c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0)) = c_Power_Opower__class_Opower(X0) )
| ~ class_Power_Opower(X0) ),
inference(cnf_transformation,[],[f3662]) ).
tcf(c_885,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)),X1),
inference(cnf_transformation,[],[f3663]) ).
tcf(c_886,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(cnf_transformation,[],[f3664]) ).
tcf(c_887,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f3665]) ).
tcf(c_888,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(cnf_transformation,[],[f3666]) ).
tcf(c_889,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)),
inference(cnf_transformation,[],[f3667]) ).
tcf(c_890,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),X1) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)),
inference(cnf_transformation,[],[f3668]) ).
tcf(c_891,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
inference(cnf_transformation,[],[f3669]) ).
tcf(c_892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3670]) ).
tcf(c_894,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ) ),
inference(cnf_transformation,[],[f3671]) ).
tcf(c_899,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(cnf_transformation,[],[f3677]) ).
tcf(c_900,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f3680]) ).
tcf(c_902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) )
| ~ class_Groups_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f3682]) ).
tcf(c_903,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),X2) ) ),
inference(cnf_transformation,[],[f4441]) ).
tcf(c_904,plain,
! [X0: $i,X1: $i] :
( 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),X0))
| ~ 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),X0) ),
inference(cnf_transformation,[],[f3685]) ).
tcf(c_905,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)),X1),
inference(cnf_transformation,[],[f3686]) ).
tcf(c_906,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(cnf_transformation,[],[f3687]) ).
tcf(c_907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3688]) ).
tcf(c_910,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))),
inference(cnf_transformation,[],[f3691]) ).
tcf(c_911,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f3692]) ).
tcf(c_912,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f3693]) ).
tcf(c_916,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f3697]) ).
tcf(c_918,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(cnf_transformation,[],[f3699]) ).
tcf(c_919,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(cnf_transformation,[],[f3698]) ).
tcf(c_920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4))) ),
inference(cnf_transformation,[],[f3702]) ).
tcf(c_921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3)),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))) ),
inference(cnf_transformation,[],[f3701]) ).
tcf(c_922,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(cnf_transformation,[],[f3704]) ).
tcf(c_923,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)))) ),
inference(cnf_transformation,[],[f3703]) ).
tcf(c_924,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X1)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(cnf_transformation,[],[f3705]) ).
tcf(c_925,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0),
inference(cnf_transformation,[],[f3706]) ).
tcf(c_926,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)),
inference(cnf_transformation,[],[f3707]) ).
tcf(c_927,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(cnf_transformation,[],[f3708]) ).
tcf(c_929,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)))
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(cnf_transformation,[],[f3709]) ).
tcf(c_930,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Opcompose(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X0,X1)),c_Polynomial_Odegree(X0,X2)))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3711]) ).
tcf(c_936,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| ~ 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),X0) ),
inference(cnf_transformation,[],[f3719]) ).
tcf(c_937,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
inference(cnf_transformation,[],[f3718]) ).
tcf(c_938,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
inference(cnf_transformation,[],[f3717]) ).
tcf(c_940,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) ),
inference(cnf_transformation,[],[f3721]) ).
tcf(c_941,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) ),
inference(cnf_transformation,[],[f3720]) ).
tcf(c_942,plain,
! [X0: $i,X1: $i] :
( 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),X0))
| ~ 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),X0) ),
inference(cnf_transformation,[],[f3725]) ).
tcf(c_943,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ 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),X0),X1)) ),
inference(cnf_transformation,[],[f3724]) ).
tcf(c_944,plain,
! [X0: $i,X1: $i] :
( 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),X0),X1)) ),
inference(cnf_transformation,[],[f3723]) ).
tcf(c_945,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f4445]) ).
tcf(c_947,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),
inference(cnf_transformation,[],[f4447]) ).
tcf(c_948,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),
inference(cnf_transformation,[],[f4448]) ).
tcf(c_949,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),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),X0) ),
inference(cnf_transformation,[],[f3730]) ).
tcf(c_951,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(cnf_transformation,[],[f3732]) ).
tcf(c_952,plain,
! [X0: $i,X1: $i] :
( ( 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),X0)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(cnf_transformation,[],[f3731]) ).
tcf(c_954,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ 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,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),X2)) ),
inference(cnf_transformation,[],[f4450]) ).
tcf(c_955,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != X0 ) ),
inference(cnf_transformation,[],[f3736]) ).
tcf(c_956,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2))) ),
inference(cnf_transformation,[],[f3737]) ).
tcf(c_957,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(cnf_transformation,[],[f3738]) ).
tcf(c_958,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Opcompose(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3739]) ).
tcf(c_959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(c_Polynomial_Opoly(X0,X1),hAPP(c_Polynomial_Opoly(X0,X2),X3)) = hAPP(c_Polynomial_Opoly(X0,c_Polynomial_Opcompose(X0,X1,X2)),X3) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3740]) ).
tcf(c_960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP(hAPP(c_Power_Opower_Opower(X0,X1,X2),X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(cnf_transformation,[],[f3741]) ).
tcf(c_961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP(hAPP(X0,X1),hAPP(hAPP(c_Power_Opower_Opower(X2,X3,X0),X1),X4)) = hAPP(hAPP(c_Power_Opower_Opower(X2,X3,X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X4)),
inference(cnf_transformation,[],[f4451]) ).
tcf(c_962,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
inference(cnf_transformation,[],[f4452]) ).
tcf(c_963,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
inference(cnf_transformation,[],[f4453]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
inference(cnf_transformation,[],[f4454]) ).
tcf(c_965,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
inference(cnf_transformation,[],[f4455]) ).
tcf(c_966,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f4456]) ).
tcf(c_967,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f4457]) ).
tcf(c_969,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3752]) ).
tcf(c_970,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
inference(cnf_transformation,[],[f3751]) ).
tcf(c_971,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ 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),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
inference(cnf_transformation,[],[f3750]) ).
tcf(c_972,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3755]) ).
tcf(c_973,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) ),
inference(cnf_transformation,[],[f3754]) ).
tcf(c_975,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X0,X1)),X2))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f3756]) ).
tcf(c_976,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))) ),
inference(cnf_transformation,[],[f3758]) ).
tcf(c_977,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(cnf_transformation,[],[f3757]) ).
tcf(c_978,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),X1)) ),
inference(cnf_transformation,[],[f3760]) ).
tcf(c_979,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(cnf_transformation,[],[f3759]) ).
tcf(c_981,plain,
! [X0: $i,X1: $i] :
( ( 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),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X0)) ),
inference(cnf_transformation,[],[f3761]) ).
tcf(c_983,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X1)) ),
inference(cnf_transformation,[],[f3763]) ).
tcf(c_985,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(cnf_transformation,[],[f3766]) ).
tcf(c_987,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) != X1 ) ),
inference(cnf_transformation,[],[f3768]) ).
tcf(c_988,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) != X1 ) ),
inference(cnf_transformation,[],[f3769]) ).
tcf(c_989,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ 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),X0),X1),X2)) ),
inference(cnf_transformation,[],[f3770]) ).
tcf(c_990,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
inference(cnf_transformation,[],[f3771]) ).
tcf(c_991,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0),
inference(cnf_transformation,[],[f3772]) ).
tcf(c_992,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(cnf_transformation,[],[f3773]) ).
tcf(c_993,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0),
inference(cnf_transformation,[],[f3774]) ).
tcf(c_994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ 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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),X2),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),X0),X1),X2) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4),X5) ) ),
inference(cnf_transformation,[],[f3775]) ).
tcf(c_995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,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),X0),X1),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4)) ),
inference(cnf_transformation,[],[f3776]) ).
tcf(c_996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
| ~ 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),X0),X1),X2))
| ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),X2) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4),X5) ) ),
inference(cnf_transformation,[],[f3777]) ).
tcf(c_997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X0)
| ~ 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_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4)) ),
inference(cnf_transformation,[],[f3778]) ).
tcf(c_998,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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),X0)
| ~ 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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3779]) ).
tcf(c_1000,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) ),
inference(cnf_transformation,[],[f3780]) ).
tcf(c_1002,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2))) ),
inference(cnf_transformation,[],[f3782]) ).
tcf(c_1004,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) ) ),
inference(cnf_transformation,[],[f3784]) ).
tcf(c_1005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X3)) = 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,X0,X2)),X1),X3),
inference(cnf_transformation,[],[f3787]) ).
tcf(c_1006,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),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),X0) ),
inference(cnf_transformation,[],[f3789]) ).
tcf(c_1008,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) ) ),
inference(cnf_transformation,[],[f3790]) ).
tcf(c_1010,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f3793]) ).
tcf(c_1011,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2))) ),
inference(cnf_transformation,[],[f3792]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Polynomial_Opdivmod__rel(X4,X0,X2,X3,X1)
| ~ sP1(X4,X3,X2,X1,X0)
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3796]) ).
tcf(c_1013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP0(X1,X4,X2,X3,X0)
| ~ sP1(X0,X3,X2,X4,X1)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3795]) ).
tcf(c_1022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP1(X0,X1,X2,X3,X4)
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f3806]) ).
tcf(c_1025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Fields_Ofield(X0)
| ~ c_Polynomial_Opdivmod__rel(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X2,X3) ),
inference(cnf_transformation,[],[f3809]) ).
tcf(c_1026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X3 )
| ~ class_Fields_Ofield(X0)
| ~ c_Polynomial_Opdivmod__rel(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X2,X3) ),
inference(cnf_transformation,[],[f3808]) ).
tcf(c_1028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Fields_Ofield(X0)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,X3) ),
inference(cnf_transformation,[],[f3812]) ).
tcf(c_1029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ class_Fields_Ofield(X0)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,X3) ),
inference(cnf_transformation,[],[f3811]) ).
tcf(c_1030,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f3814]) ).
tcf(c_1031,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1)
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f3815]) ).
tcf(c_1032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Polynomial_Osmult(X0,X5,X1),X2,c_Polynomial_Osmult(X0,X5,X3),c_Polynomial_Osmult(X0,X5,X4))
| ~ class_Fields_Ofield(X0)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3816]) ).
tcf(c_1033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X3 = X5 )
| ~ class_Fields_Ofield(X0)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X5,X6)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3818]) ).
tcf(c_1034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X4 = X6 )
| ~ class_Fields_Ofield(X0)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X5,X6)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3817]) ).
tcf(c_1037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( c_Polynomial_Opdivmod__rel(X0,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X6),X2),X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X6),X4),X7))
| ~ class_Fields_Ofield(X0)
| ~ c_Polynomial_Opdivmod__rel(X0,X5,X6,X1,X7)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3821]) ).
tcf(c_1039,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3823]) ).
tcf(c_1041,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3825]) ).
tcf(c_1045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Oplus__class_Oplus(X0,X2,X3)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3829]) ).
tcf(c_1047,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),X2) = c_Groups_Ouminus__class_Ouminus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3831]) ).
tcf(c_1048,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) = c_Groups_Ouminus__class_Ouminus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3832]) ).
tcf(c_1049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1))))
| ~ hBOOL(hAPP(X0,X3))
| ~ 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)
| ~ hBOOL(hAPP(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK16(X0,X1),X1))) ),
inference(cnf_transformation,[],[f3834]) ).
tcf(c_1050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X2,sK16(X2,X1)))
| hBOOL(hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1))))
| ~ hBOOL(hAPP(X2,X3))
| ~ 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),X0) ),
inference(cnf_transformation,[],[f3833]) ).
tcf(c_1051,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK17(X1,X0),X1)
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f3837]) ).
tcf(c_1052,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK17(X1,X2)) ),
inference(cnf_transformation,[],[f3836]) ).
tcf(c_1053,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK17(X1,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f3835]) ).
tcf(c_1054,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),X2)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ~ class_Groups_Ozero(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),X2)
| ( hAPP(c_Polynomial_Ocoeff(X0,X1),X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3838]) ).
tcf(c_1055,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X0) )
| ~ class_Groups_Omonoid__mult(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f3839]) ).
tcf(c_1056,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ class_Rings_Oidom(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),X2))
| ( hAPP(c_Polynomial_Ocoeff(X0,X1),c_Polynomial_Odegree(X0,X1)) != hAPP(c_Polynomial_Ocoeff(X0,X2),c_Polynomial_Odegree(X0,X2)) ) ),
inference(cnf_transformation,[],[f3840]) ).
tcf(c_1057,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_Polynomial_Ocoeff(X0,c_Polynomial_Omonom(X0,X1,X2)),X2) = X1 )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f4668]) ).
tcf(c_1058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( hAPP(c_Polynomial_Ocoeff(X0,c_Polynomial_Omonom(X0,X1,X2)),X3) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f3841]) ).
tcf(c_1059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(c_Polynomial_Ocoeff(X0,X1),X2),hAPP(c_Polynomial_Ocoeff(X0,X3),X2)) = hAPP(c_Polynomial_Ocoeff(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,X3)),X2) )
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f3843]) ).
tcf(c_1060,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)) = c_Groups_Ominus__class_Ominus(X0,X2,X1) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3844]) ).
tcf(c_1061,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X2) = X1 )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f3845]) ).
tcf(c_1062,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2),X2) = X1 )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f3846]) ).
tcf(c_1063,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),
inference(cnf_transformation,[],[f3847]) ).
tcf(c_1064,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
inference(cnf_transformation,[],[f3848]) ).
tcf(c_1065,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(cnf_transformation,[],[f3849]) ).
tcf(c_1066,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0) = X1,
inference(cnf_transformation,[],[f3850]) ).
tcf(c_1067,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1) = X0,
inference(cnf_transformation,[],[f3851]) ).
tcf(c_1068,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3853]) ).
tcf(c_1069,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f3852]) ).
tcf(c_1070,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X2)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2),c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3855]) ).
tcf(c_1071,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f3854]) ).
tcf(c_1072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Groups_Ominus__class_Ominus(X0,X3,X2)))
| ~ class_Rings_Ocomm__ring__1(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3856]) ).
tcf(c_1075,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f3859]) ).
tcf(c_1076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),c_Polynomial_Omonom(X0,X1,X2),c_Polynomial_Omonom(X0,X3,X2)) = c_Polynomial_Omonom(X0,c_Groups_Ominus__class_Ominus(X0,X1,X3),X2) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3860]) ).
tcf(c_1077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Polynomial_OpCons(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X3,X4)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X1,X3),c_Polynomial_OpCons(X0,X2,X4)) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3861]) ).
tcf(c_1078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,hAPP(c_Polynomial_Opoly(X0,X1),X2),hAPP(c_Polynomial_Opoly(X0,X3),X2)) = hAPP(c_Polynomial_Opoly(X0,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X1,X3)),X2) )
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f3862]) ).
tcf(c_1079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),c_Polynomial_Osmult(X0,X3,X2)) = c_Polynomial_Osmult(X0,c_Groups_Ominus__class_Ominus(X0,X1,X3),X2) )
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f3863]) ).
tcf(c_1080,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1),
inference(cnf_transformation,[],[f3864]) ).
tcf(c_1081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,hAPP(c_Polynomial_Ocoeff(X0,X1),X2),hAPP(c_Polynomial_Ocoeff(X0,X3),X2)) = hAPP(c_Polynomial_Ocoeff(X0,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X1,X3)),X2) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3865]) ).
tcf(c_1082,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ class_Groups_Ozero(X0)
| ( c_Polynomial_Ocoeff(X0,X1) != c_Polynomial_Ocoeff(X0,X2) ) ),
inference(cnf_transformation,[],[f3866]) ).
tcf(c_1083,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ class_Groups_Ozero(X0)
| ( hAPP(c_Polynomial_Ocoeff(X0,X1),sK18(X1,X2,X0)) != hAPP(c_Polynomial_Ocoeff(X0,X2),sK18(X1,X2,X0)) ) ),
inference(cnf_transformation,[],[f3869]) ).
tcf(c_1085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ~ class_Groups_Oab__group__add(X0)
| ( c_Groups_Ominus__class_Ominus(X0,X1,X1) != c_Groups_Ominus__class_Ominus(X0,X2,X3) ) ),
inference(cnf_transformation,[],[f4672]) ).
tcf(c_1086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,X0),X2,X3),X4) = c_Groups_Ominus__class_Ominus(X0,hAPP(X2,X4),hAPP(X3,X4)) )
| ~ class_Groups_Ominus(X0) ),
inference(cnf_transformation,[],[f3872]) ).
tcf(c_1088,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(cnf_transformation,[],[f3873]) ).
tcf(c_1089,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3875]) ).
tcf(c_1091,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) ) ),
inference(cnf_transformation,[],[f3876]) ).
tcf(c_1092,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3878]) ).
tcf(c_1093,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3879]) ).
tcf(c_1094,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3880]) ).
tcf(c_1095,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0),
inference(cnf_transformation,[],[f3881]) ).
tcf(c_1096,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3882]) ).
tcf(c_1097,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3883]) ).
tcf(c_1098,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f3884]) ).
tcf(c_1099,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f3885]) ).
tcf(c_1100,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f3886]) ).
tcf(c_1102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X2)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X3,X4)
| ( c_Groups_Ominus__class_Ominus(X0,X1,X2) != c_Groups_Ominus__class_Ominus(X0,X3,X4) ) ),
inference(cnf_transformation,[],[f3889]) ).
tcf(c_1103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(X0,X3,X4)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2)
| ( c_Groups_Ominus__class_Ominus(X0,X1,X2) != c_Groups_Ominus__class_Ominus(X0,X3,X4) ) ),
inference(cnf_transformation,[],[f3888]) ).
tcf(c_1104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X3,X4)
| ( c_Groups_Ominus__class_Ominus(X0,X1,X2) != c_Groups_Ominus__class_Ominus(X0,X3,X4) ) ),
inference(cnf_transformation,[],[f3891]) ).
tcf(c_1105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X3,X4)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ( c_Groups_Ominus__class_Ominus(X0,X1,X2) != c_Groups_Ominus__class_Ominus(X0,X3,X4) ) ),
inference(cnf_transformation,[],[f3890]) ).
tcf(c_1106,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f3892]) ).
tcf(c_1108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ class_Groups_Oab__group__add(X0)
| ( c_Groups_Ominus__class_Ominus(X0,X1,X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3895]) ).
tcf(c_1109,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,X1,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f4674]) ).
tcf(c_1110,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,X1,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f4675]) ).
tcf(c_1111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ class_Groups_Ogroup__add(X0)
| ( c_Groups_Ominus__class_Ominus(X0,X1,X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3896]) ).
tcf(c_1112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(c_Polynomial_Ocoeff(X0,c_Polynomial_OpCons(X0,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)) = hAPP(c_Polynomial_Ocoeff(X0,X2),X3) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f4460]) ).
tcf(c_1113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(c_Polynomial_Ocoeff(X0,X2),X3)) = hAPP(c_Polynomial_Ocoeff(X0,c_Polynomial_Osmult(X0,X1,X2)),X3) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3899]) ).
tcf(c_1114,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_Polynomial_Ocoeff(X0,c_Polynomial_OpCons(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f3900]) ).
tcf(c_1117,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3903]) ).
tcf(c_1118,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(cnf_transformation,[],[f3905]) ).
tcf(c_1119,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) ),
inference(cnf_transformation,[],[f3904]) ).
tcf(c_1120,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3906]) ).
tcf(c_1123,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ 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,X0,X1),X2) ),
inference(cnf_transformation,[],[f3910]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(cnf_transformation,[],[f3909]) ).
tcf(c_1128,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3914]) ).
tcf(c_1130,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3916]) ).
tcf(c_1131,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(cnf_transformation,[],[f3917]) ).
tcf(c_1132,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(cnf_transformation,[],[f3918]) ).
tcf(c_1134,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(cnf_transformation,[],[f3919]) ).
tcf(c_1135,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3921]) ).
tcf(c_1136,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ) ),
inference(cnf_transformation,[],[f3922]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(cnf_transformation,[],[f3924]) ).
tcf(c_1138,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(cnf_transformation,[],[f3923]) ).
tcf(c_1139,plain,
! [X0: $i,X1: $i] :
( ( hAPP(c_Polynomial_Ocoeff(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f3925]) ).
tcf(c_1142,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(cnf_transformation,[],[f3927]) ).
tcf(c_1143,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3929]) ).
tcf(c_1144,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f3930]) ).
tcf(c_1145,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(cnf_transformation,[],[f4464]) ).
tcf(c_1146,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0)
| ~ 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),X0) ),
inference(cnf_transformation,[],[f3932]) ).
tcf(c_1147,plain,
! [X0: $i,X1: $i] :
( 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,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3934]) ).
tcf(c_1148,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(cnf_transformation,[],[f3933]) ).
tcf(c_1149,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2)) = c_Groups_Oplus__class_Oplus(X0,X1,X2) )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f3935]) ).
tcf(c_1150,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2)) = c_Groups_Ominus__class_Ominus(X0,X1,X2) )
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f3936]) ).
tcf(c_1151,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2)) = c_Groups_Ominus__class_Ominus(X0,X1,X2) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3937]) ).
tcf(c_1152,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2)) = c_Groups_Ominus__class_Ominus(X0,X1,X2) )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f3938]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,c_Groups_Ozero__class_Ozero(X0),X1) = c_Groups_Ouminus__class_Ouminus(X0,X1) )
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f3939]) ).
tcf(c_1154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ominus__class_Ominus(X0,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X4)),X3)) = c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X3)) )
| ~ class_Rings_Oring(X0) ),
inference(cnf_transformation,[],[f3940]) ).
tcf(c_1156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X4)),X2),X3) = X5 )
| ~ class_Rings_Oring(X0)
| ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3) != c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X2),X5) ) ),
inference(cnf_transformation,[],[f3941]) ).
tcf(c_1157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X3,X1)),X2),X4)) = c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2),X4) )
| ~ class_Rings_Oring(X0) ),
inference(cnf_transformation,[],[f4679]) ).
tcf(c_1158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X4,X1)),X2),X5) = X3 )
| ~ class_Rings_Oring(X0)
| ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3) != c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X2),X5) ) ),
inference(cnf_transformation,[],[f3943]) ).
tcf(c_1159,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),
inference(cnf_transformation,[],[f3945]) ).
tcf(c_1160,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)),X1),
inference(cnf_transformation,[],[f3946]) ).
tcf(c_1161,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_Polynomial_Ocoeff(X0,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1)),X2) = c_Groups_Ouminus__class_Ouminus(X0,hAPP(c_Polynomial_Ocoeff(X0,X1),X2)) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3947]) ).
tcf(c_1162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X2)),c_Groups_Ominus__class_Ominus(X0,X3,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X2)),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),c_Groups_Ominus__class_Ominus(X0,X3,X4))) = c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X4)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3948]) ).
tcf(c_1164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ominus__class_Ominus(X0,X2,X3)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3950]) ).
tcf(c_1166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X3)),X2) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3952]) ).
tcf(c_1167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4),X1),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X4),X5))
| ~ class_Rings_Oordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X2,X3)),X4),X5)) ),
inference(cnf_transformation,[],[f3954]) ).
tcf(c_1168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X3,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X4,X1)),X2),X5))
| ~ class_Rings_Oordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X2),X5)) ),
inference(cnf_transformation,[],[f3953]) ).
tcf(c_1169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3),X4),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3),X5))
| ~ class_Rings_Oordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X2)),X3),X4),X5) ),
inference(cnf_transformation,[],[f3956]) ).
tcf(c_1170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X4)),X2),X3),X5)
| ~ class_Rings_Oordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X2),X5)) ),
inference(cnf_transformation,[],[f3955]) ).
tcf(c_1171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3),X4),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3),X5))
| ~ class_Rings_Oordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X2)),X3),X4),X5) ),
inference(cnf_transformation,[],[f3958]) ).
tcf(c_1172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X4)),X2),X3),X5)
| ~ class_Rings_Oordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X2),X5)) ),
inference(cnf_transformation,[],[f3957]) ).
tcf(c_1173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4),X1),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X4),X5))
| ~ class_Rings_Oordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X2,X3)),X4),X5)) ),
inference(cnf_transformation,[],[f3960]) ).
tcf(c_1174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Orderings_Oord__class_Oless(X0,X3,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X4,X1)),X2),X5))
| ~ class_Rings_Oordered__ring(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3),c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X2),X5)) ),
inference(cnf_transformation,[],[f3959]) ).
tcf(c_1175,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oone__class_Oone(X0))),c_Groups_Ominus__class_Ominus(X0,X1,c_Groups_Oone__class_Oone(X0))) = c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1),c_Groups_Oone__class_Oone(X0)) )
| ~ class_Rings_Oring__1(X0) ),
inference(cnf_transformation,[],[f3961]) ).
tcf(c_1178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Groups_Oplus__class_Oplus(X0,X2,X5)))
| ~ class_Rings_Odvd(X0)
| ~ class_Rings_Ocomm__ring(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Groups_Oplus__class_Oplus(X0,c_Groups_Ominus__class_Ominus(X0,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4)),X5))) ),
inference(cnf_transformation,[],[f3965]) ).
tcf(c_1179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Groups_Oplus__class_Oplus(X0,c_Groups_Ominus__class_Ominus(X0,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X5),X4)),X3)))
| ~ class_Rings_Odvd(X0)
| ~ class_Rings_Ocomm__ring(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Groups_Oplus__class_Oplus(X0,X2,X3))) ),
inference(cnf_transformation,[],[f3964]) ).
tcf(c_1181,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f4466]) ).
tcf(c_1182,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK19(X0,X1,X2)) = X1 ) ),
inference(cnf_transformation,[],[f3973]) ).
tcf(c_1183,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| hBOOL(hAPP(X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(X0,sK19(X1,X2,X0))) ),
inference(cnf_transformation,[],[f3972]) ).
tcf(c_1184,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK19(X1,X2,X0)) = X2 )
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3971]) ).
tcf(c_1185,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X0,sK19(X1,X2,X0))) ),
inference(cnf_transformation,[],[f3970]) ).
tcf(c_1188,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X0,sK20(X1,X2,X0))) ),
inference(cnf_transformation,[],[f3979]) ).
tcf(c_1189,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK20(X1,X2,X0)) = X2 )
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3978]) ).
tcf(c_1190,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| hBOOL(hAPP(X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(X0,sK20(X1,X2,X0))) ),
inference(cnf_transformation,[],[f3977]) ).
tcf(c_1191,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK20(X0,X1,X2)) = X1 ) ),
inference(cnf_transformation,[],[f3976]) ).
tcf(c_1192,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(cnf_transformation,[],[f3975]) ).
tcf(c_1194,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f4467]) ).
tcf(c_1195,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f4468]) ).
tcf(c_1196,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_Polynomial_Ocoeff(X0,X1),X2) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Ozero(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),X2) ),
inference(cnf_transformation,[],[f3982]) ).
tcf(c_1197,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Polynomial_Odegree(X0,X1))
| ( hAPP(c_Polynomial_Ocoeff(X0,X1),X2) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f3983]) ).
tcf(c_1198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X2),X3),X4) ),
inference(cnf_transformation,[],[f3985]) ).
tcf(c_1199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3)),X1),X2),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),X4)) ),
inference(cnf_transformation,[],[f3984]) ).
tcf(c_1200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X2),X3),X4) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3986]) ).
tcf(c_1202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3)),X1),X2) = X4 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),X4) ) ),
inference(cnf_transformation,[],[f3987]) ).
tcf(c_1203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4)) ),
inference(cnf_transformation,[],[f3990]) ).
tcf(c_1204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X0)),X1),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),X4)) ),
inference(cnf_transformation,[],[f3989]) ).
tcf(c_1205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X2),X4)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3991]) ).
tcf(c_1206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X2),X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f4683]) ).
tcf(c_1207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X0)),X1),X4) = X2 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X3)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),X4) ) ),
inference(cnf_transformation,[],[f3992]) ).
tcf(c_1210,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ~ class_Groups_Ozero(X0)
| ( hAPP(c_Polynomial_Ocoeff(X0,X1),c_Polynomial_Odegree(X0,X1)) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f3995]) ).
tcf(c_1211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Polynomial_Odegree(X0,c_Polynomial_Osynthetic__div(X0,X1,X2)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3997]) ).
tcf(c_1213,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f4470]) ).
tcf(c_1214,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f4685]) ).
tcf(c_1215,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ) ),
inference(cnf_transformation,[],[f4471]) ).
tcf(c_1216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( 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),X0),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X2),X3),X4) ),
inference(cnf_transformation,[],[f4003]) ).
tcf(c_1217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3)),X1),X2),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X0)
| ~ 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),X0),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),X4)) ),
inference(cnf_transformation,[],[f4002]) ).
tcf(c_1218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( 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),X2),X3),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4)) ),
inference(cnf_transformation,[],[f4005]) ).
tcf(c_1219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X0)),X1),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X3)
| ~ 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),X0),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),X4)) ),
inference(cnf_transformation,[],[f4004]) ).
tcf(c_1220,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f4686]) ).
tcf(c_1221,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
inference(cnf_transformation,[],[f4006]) ).
tcf(c_1222,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f4687]) ).
tcf(c_1223,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) ) ),
inference(cnf_transformation,[],[f4008]) ).
tcf(c_1224,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(c_Polynomial_Ocoeff(X0,X1),c_Polynomial_Odegree(X0,X1))),hAPP(c_Polynomial_Ocoeff(X0,X2),c_Polynomial_Odegree(X0,X2))) = hAPP(c_Polynomial_Ocoeff(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2))) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f4010]) ).
tcf(c_1225,plain,
! [X0: $i] :
( ( hAPP(c_Polynomial_Ocoeff(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f4688]) ).
tcf(c_1226,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(c_Polynomial_Ocoeff(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f4011]) ).
tcf(c_1227,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opos__poly(X0,X1)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(c_Polynomial_Ocoeff(X0,X1),c_Polynomial_Odegree(X0,X1))) ),
inference(cnf_transformation,[],[f4014]) ).
tcf(c_1228,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(c_Polynomial_Ocoeff(X0,X1),c_Polynomial_Odegree(X0,X1)))
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X0,X1) ),
inference(cnf_transformation,[],[f4013]) ).
tcf(c_1229,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_Polynomial_Ocoeff(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X0,X1,c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))),X2)),X2) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f4015]) ).
tcf(c_1230,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X2)),c_Groups_Oplus__class_Oplus(X0,X1,X2)) )
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f4472]) ).
tcf(c_1231,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Power_Opower(X0) ),
inference(cnf_transformation,[],[f4689]) ).
tcf(c_1232,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2) )
| ~ class_Power_Opower(X0) ),
inference(cnf_transformation,[],[f4017]) ).
tcf(c_1233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0)) )
| ~ class_Groups_Omonoid__mult(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f4473]) ).
tcf(c_1234,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X0),X1,X1)
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4690]) ).
tcf(c_1235,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X0),X2,X1)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X0,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X1,X2)) ),
inference(cnf_transformation,[],[f4021]) ).
tcf(c_1236,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Polynomial_Opos__poly(X0,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X2,X1))
| ( X1 = X2 )
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X0),X1,X2) ),
inference(cnf_transformation,[],[f4020]) ).
tcf(c_1237,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X0),X2,X1)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X0,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X1,X2)) ),
inference(cnf_transformation,[],[f4024]) ).
tcf(c_1238,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Polynomial_Opos__poly(X0,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X2,X1))
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X0),X1,X2) ),
inference(cnf_transformation,[],[f4023]) ).
tcf(c_1239,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),c_Polynomial_Osmult(X0,X1,X3)) = c_Polynomial_Osmult(X0,X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X2,X3)) )
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f4025]) ).
tcf(c_1240,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))) ),
inference(cnf_transformation,[],[f4026]) ).
tcf(c_1241,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = X1 )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f4027]) ).
tcf(c_1242,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),
inference(cnf_transformation,[],[f4028]) ).
tcf(c_1243,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),
inference(cnf_transformation,[],[f4029]) ).
tcf(c_1244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X3,X1)),X2)
| ~ class_Groups_Oab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),X2) ),
inference(cnf_transformation,[],[f4030]) ).
tcf(c_1245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X3,X1)),X2)
| ~ class_Groups_Oab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X3),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),X2) ),
inference(cnf_transformation,[],[f4031]) ).
tcf(c_1246,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f4033]) ).
tcf(c_1247,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f4032]) ).
tcf(c_1248,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
inference(cnf_transformation,[],[f4034]) ).
tcf(c_1249,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X2)),X1),
inference(cnf_transformation,[],[f4035]) ).
tcf(c_1250,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f4036]) ).
tcf(c_1251,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f4038]) ).
tcf(c_1252,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f4037]) ).
tcf(c_1253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Polynomial_OpCons(X0,X5,X1),X2,c_Polynomial_OpCons(X0,c_Rings_Oinverse__class_Odivide(X0,hAPP(c_Polynomial_Ocoeff(X0,c_Polynomial_OpCons(X0,X5,X4)),c_Polynomial_Odegree(X0,X2)),hAPP(c_Polynomial_Ocoeff(X0,X2),c_Polynomial_Odegree(X0,X2))),X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X5,X4),c_Polynomial_Osmult(X0,c_Rings_Oinverse__class_Odivide(X0,hAPP(c_Polynomial_Ocoeff(X0,c_Polynomial_OpCons(X0,X5,X4)),c_Polynomial_Odegree(X0,X2)),hAPP(c_Polynomial_Ocoeff(X0,X2),c_Polynomial_Odegree(X0,X2))),X2)))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Fields_Ofield(X0)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f4691]) ).
tcf(c_1254,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2)) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f4040]) ).
tcf(c_1256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2),c_Rings_Oinverse__class_Odivide(X0,X3,X2)) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,X1,X3),X2) )
| ~ class_RealVector_Oreal__normed__field(X0) ),
inference(cnf_transformation,[],[f4042]) ).
tcf(c_1258,plain,
! [X0: $i,X1: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,X1,c_Groups_Oone__class_Oone(X0)) = X1 )
| ~ class_Rings_Odivision__ring(X0) ),
inference(cnf_transformation,[],[f4044]) ).
tcf(c_1261,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Rings_Oinverse__class_Odivide(X0,X1,X1) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Rings_Odivision__ring__inverse__zero(X0) ),
inference(cnf_transformation,[],[f4046]) ).
tcf(c_1264,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ~ class_Rings_Odivision__ring(X0)
| ( c_Rings_Oinverse__class_Odivide(X0,X1,X2) != c_Groups_Oone__class_Oone(X0) ) ),
inference(cnf_transformation,[],[f4049]) ).
tcf(c_1265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Rings_Oinverse__class_Odivide(X0,X1,X3)),X2) )
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(cnf_transformation,[],[f4051]) ).
tcf(c_1266,plain,
! [X0: $i,X1: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Odivision__ring__inverse__zero(X0) ),
inference(cnf_transformation,[],[f4052]) ).
tcf(c_1268,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),X1)),X2) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) )
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(cnf_transformation,[],[f4054]) ).
tcf(c_1272,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X2) = X1 )
| ~ class_Rings_Odivision__ring(X0) ),
inference(cnf_transformation,[],[f4694]) ).
tcf(c_1275,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Rings_Oinverse__class_Odivide(X0,X1,X2)),X2) = X1 )
| ~ class_Rings_Odivision__ring(X0) ),
inference(cnf_transformation,[],[f4697]) ).
tcf(c_1278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Rings_Oinverse__class_Odivide(X0,X2,X3)) = c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3) )
| ~ class_Rings_Odivision__ring(X0) ),
inference(cnf_transformation,[],[f4064]) ).
tcf(c_1279,plain,
! [X0: $i,X1: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ozero__class_Ozero(X0),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_RealVector_Oreal__normed__field(X0) ),
inference(cnf_transformation,[],[f4065]) ).
tcf(c_1280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2),c_Rings_Oinverse__class_Odivide(X0,X3,X2)) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),X2) )
| ~ class_RealVector_Oreal__normed__field(X0) ),
inference(cnf_transformation,[],[f4066]) ).
tcf(c_1281,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2)) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2) )
| ~ class_RealVector_Oreal__normed__field(X0) ),
inference(cnf_transformation,[],[f4067]) ).
tcf(c_1282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X2) = X3 )
| ( c_Rings_Oinverse__class_Odivide(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) )
| ~ class_Fields_Ofield(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f4068]) ).
tcf(c_1283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Rings_Oinverse__class_Odivide(X0,X1,X3)),c_Rings_Oinverse__class_Odivide(X0,X2,X4)) )
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(cnf_transformation,[],[f4069]) ).
tcf(c_1284,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2)) = c_Rings_Oinverse__class_Odivide(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2)) )
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(cnf_transformation,[],[f4070]) ).
tcf(c_1286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X4 )
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Rings_Oinverse__class_Odivide(X0,X1,X4) = c_Rings_Oinverse__class_Odivide(X0,X3,X2) )
| ~ class_Fields_Ofield(X0)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4) ) ),
inference(cnf_transformation,[],[f4073]) ).
tcf(c_1287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X4 )
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2) )
| ~ class_Fields_Ofield(X0)
| ( c_Rings_Oinverse__class_Odivide(X0,X1,X2) != c_Rings_Oinverse__class_Odivide(X0,X3,X4) ) ),
inference(cnf_transformation,[],[f4072]) ).
tcf(c_1288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) = c_Rings_Oinverse__class_Odivide(X0,X2,X3) )
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(cnf_transformation,[],[f4074]) ).
tcf(c_1300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X3 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),X3) = c_Groups_Oplus__class_Oplus(X0,X2,c_Rings_Oinverse__class_Odivide(X0,X1,X3)) )
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(cnf_transformation,[],[f4088]) ).
tcf(c_1301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3),X1) = c_Groups_Oplus__class_Oplus(X0,X2,c_Rings_Oinverse__class_Odivide(X0,X3,X1)) )
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4089]) ).
tcf(c_1302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X3 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),X3) = c_Groups_Oplus__class_Oplus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X3),X2) )
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(cnf_transformation,[],[f4090]) ).
tcf(c_1303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),X2) = c_Groups_Oplus__class_Oplus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2),X3) )
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4091]) ).
tcf(c_1304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X4 )
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X2)) = c_Groups_Oplus__class_Oplus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X4),c_Rings_Oinverse__class_Odivide(X0,X3,X2)) )
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4092]) ).
tcf(c_1305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X4 )
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X2)) = c_Groups_Ominus__class_Ominus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X4),c_Rings_Oinverse__class_Odivide(X0,X3,X2)) )
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4093]) ).
tcf(c_1306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),X2) = c_Groups_Ominus__class_Ominus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2),X3) )
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4094]) ).
tcf(c_1307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3),X1) = c_Groups_Ominus__class_Ominus(X0,X2,c_Rings_Oinverse__class_Odivide(X0,X3,X1)) )
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4095]) ).
tcf(c_1308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,X2,X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,X1,X5),X4)),X3)) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X5),X3)),X4) )
| ~ class_RealVector_Oreal__field(X0) ),
inference(cnf_transformation,[],[f4096]) ).
tcf(c_1309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X3 )
| ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X2,X3)),c_Polynomial_Osmult(X0,c_Rings_Oinverse__class_Odivide(X0,hAPP(c_Polynomial_Ocoeff(X0,c_Polynomial_OpCons(X0,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X2,X3))),c_Polynomial_Odegree(X0,X3)),hAPP(c_Polynomial_Ocoeff(X0,X3),c_Polynomial_Odegree(X0,X3))),X3)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X1,X2),X3) )
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4097]) ).
tcf(c_1310,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,X2) )
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4098]) ).
tcf(c_1311,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1),X2) )
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4099]) ).
tcf(c_1312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Polynomial_Osmult(X0,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X2,X3)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),X3) )
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4100]) ).
tcf(c_1313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,c_Polynomial_Osmult(X0,X2,X3)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,X3) )
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4101]) ).
tcf(c_1314,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,c_Groups_Ozero__class_Ozero(X0),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Divides_Osemiring__div(X0) ),
inference(cnf_transformation,[],[f4102]) ).
tcf(c_1315,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 )
| ~ class_Divides_Osemiring__div(X0) ),
inference(cnf_transformation,[],[f4103]) ).
tcf(c_1316,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X1,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Divides_Osemiring__div(X0) ),
inference(cnf_transformation,[],[f4104]) ).
tcf(c_1317,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X2,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Divides_Osemiring__div(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2)) ),
inference(cnf_transformation,[],[f4105]) ).
tcf(c_1318,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X2),X1))
| ~ class_Divides_Osemiring__div(X0)
| ( c_Divides_Odiv__class_Omod(X0,X1,X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(cnf_transformation,[],[f4107]) ).
tcf(c_1320,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(X0,c_Divides_Odiv__class_Omod(X0,X1,X2),X2) = c_Divides_Odiv__class_Omod(X0,X1,X2) )
| ~ class_Divides_Osemiring__div(X0) ),
inference(cnf_transformation,[],[f4108]) ).
tcf(c_1321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2))
| ~ class_Divides_Osemiring__div(X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Divides_Odiv__class_Omod(X0,X2,X3))) ),
inference(cnf_transformation,[],[f4109]) ).
tcf(c_1322,plain,
! [X0: $i] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f4110]) ).
tcf(c_1323,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4111]) ).
tcf(c_1324,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f4112]) ).
tcf(c_1325,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f4113]) ).
tcf(c_1326,plain,
! [X0: $i,X1: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(X1,X0))
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f4114]) ).
tcf(c_1327,plain,
! [X0: $i,X1: $i] :
( class_Orderings_Opreorder(tc_fun(X1,X0))
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[],[f4115]) ).
tcf(c_1328,plain,
! [X0: $i,X1: $i] :
( class_Orderings_Oorder(tc_fun(X1,X0))
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[],[f4116]) ).
tcf(c_1329,plain,
! [X0: $i,X1: $i] :
( class_Orderings_Oord(tc_fun(X1,X0))
| ~ class_Orderings_Oord(X0) ),
inference(cnf_transformation,[],[f4117]) ).
tcf(c_1330,plain,
! [X0: $i,X1: $i] :
( class_Groups_Ouminus(tc_fun(X1,X0))
| ~ class_Groups_Ouminus(X0) ),
inference(cnf_transformation,[],[f4118]) ).
tcf(c_1331,plain,
! [X0: $i,X1: $i] :
( class_Groups_Ominus(tc_fun(X1,X0))
| ~ class_Groups_Ominus(X0) ),
inference(cnf_transformation,[],[f4119]) ).
tcf(c_1332,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[],[f4120]) ).
tcf(c_1333,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f4121]) ).
tcf(c_1334,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f4122]) ).
tcf(c_1336,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f4124]) ).
tcf(c_1337,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f4125]) ).
tcf(c_1338,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f4126]) ).
tcf(c_1339,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f4127]) ).
tcf(c_1340,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f4128]) ).
tcf(c_1341,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f4129]) ).
tcf(c_1342,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f4130]) ).
tcf(c_1343,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f4131]) ).
tcf(c_1344,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f4132]) ).
tcf(c_1345,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f4133]) ).
tcf(c_1346,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f4134]) ).
tcf(c_1347,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f4135]) ).
tcf(c_1348,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f4136]) ).
tcf(c_1349,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f4137]) ).
tcf(c_1350,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f4138]) ).
tcf(c_1351,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f4139]) ).
tcf(c_1352,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f4140]) ).
tcf(c_1353,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f4141]) ).
tcf(c_1354,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f4142]) ).
tcf(c_1355,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f4143]) ).
tcf(c_1356,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f4144]) ).
tcf(c_1357,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f4145]) ).
tcf(c_1358,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f4146]) ).
tcf(c_1359,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f4147]) ).
tcf(c_1360,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f4148]) ).
tcf(c_1361,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f4149]) ).
tcf(c_1362,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f4150]) ).
tcf(c_1364,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f4152]) ).
tcf(c_1365,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f4153]) ).
tcf(c_1366,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f4154]) ).
tcf(c_1367,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[],[f4155]) ).
tcf(c_1368,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f4156]) ).
tcf(c_1369,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f4157]) ).
tcf(c_1370,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f4158]) ).
tcf(c_1372,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f4160]) ).
tcf(c_1373,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f4161]) ).
tcf(c_1374,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f4162]) ).
tcf(c_1375,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f4163]) ).
tcf(c_1376,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[],[f4164]) ).
tcf(c_1377,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f4165]) ).
tcf(c_1378,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f4166]) ).
tcf(c_1379,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f4167]) ).
tcf(c_1380,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(cnf_transformation,[],[f4168]) ).
tcf(c_1381,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f4169]) ).
tcf(c_1382,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(cnf_transformation,[],[f4170]) ).
tcf(c_1383,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f4171]) ).
tcf(c_1384,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f4172]) ).
tcf(c_1385,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f4173]) ).
tcf(c_1386,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f4174]) ).
tcf(c_1388,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(cnf_transformation,[],[f4176]) ).
tcf(c_1389,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f4177]) ).
tcf(c_1390,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f4178]) ).
tcf(c_1391,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f4179]) ).
tcf(c_1393,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f4181]) ).
tcf(c_1394,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f4182]) ).
tcf(c_1395,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f4183]) ).
tcf(c_1396,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f4184]) ).
tcf(c_1397,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f4185]) ).
tcf(c_1398,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f4186]) ).
tcf(c_1399,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f4187]) ).
tcf(c_1400,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f4188]) ).
tcf(c_1401,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f4189]) ).
tcf(c_1402,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f4190]) ).
tcf(c_1403,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f4191]) ).
tcf(c_1404,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f4192]) ).
tcf(c_1405,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f4193]) ).
tcf(c_1406,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f4194]) ).
tcf(c_1407,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f4195]) ).
tcf(c_1408,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f4196]) ).
tcf(c_1409,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f4197]) ).
tcf(c_1410,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f4198]) ).
tcf(c_1412,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f4200]) ).
tcf(c_1413,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f4201]) ).
tcf(c_1414,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f4202]) ).
tcf(c_1415,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f4203]) ).
tcf(c_1417,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f4205]) ).
tcf(c_1418,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f4206]) ).
tcf(c_1419,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f4207]) ).
tcf(c_1420,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f4208]) ).
tcf(c_1421,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f4209]) ).
tcf(c_1422,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f4210]) ).
tcf(c_1423,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f4211]) ).
tcf(c_1424,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f4212]) ).
tcf(c_1426,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(cnf_transformation,[],[f4214]) ).
tcf(c_1427,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(cnf_transformation,[],[f4215]) ).
tcf(c_1428,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f4216]) ).
tcf(c_1429,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f4217]) ).
tcf(c_1430,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f4218]) ).
tcf(c_1431,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(cnf_transformation,[],[f4219]) ).
tcf(c_1432,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f4220]) ).
tcf(c_1433,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4221]) ).
tcf(c_1434,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4222]) ).
tcf(c_1435,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4223]) ).
tcf(c_1436,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4224]) ).
tcf(c_1437,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4225]) ).
tcf(c_1438,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4226]) ).
tcf(c_1439,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4227]) ).
tcf(c_1440,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4228]) ).
tcf(c_1441,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4229]) ).
tcf(c_1442,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4230]) ).
tcf(c_1443,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4231]) ).
tcf(c_1444,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4232]) ).
tcf(c_1445,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4233]) ).
tcf(c_1446,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4234]) ).
tcf(c_1447,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4235]) ).
tcf(c_1448,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4236]) ).
tcf(c_1449,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4237]) ).
tcf(c_1450,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4238]) ).
tcf(c_1451,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4239]) ).
tcf(c_1452,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4240]) ).
tcf(c_1453,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4241]) ).
tcf(c_1454,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4242]) ).
tcf(c_1455,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4243]) ).
tcf(c_1456,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4244]) ).
tcf(c_1457,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4245]) ).
tcf(c_1458,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4246]) ).
tcf(c_1459,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4247]) ).
tcf(c_1460,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4248]) ).
tcf(c_1461,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4249]) ).
tcf(c_1462,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4250]) ).
tcf(c_1463,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4251]) ).
tcf(c_1464,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4252]) ).
tcf(c_1465,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4253]) ).
tcf(c_1466,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4254]) ).
tcf(c_1467,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4255]) ).
tcf(c_1468,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4256]) ).
tcf(c_1469,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4257]) ).
tcf(c_1470,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4258]) ).
tcf(c_1472,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4260]) ).
tcf(c_1473,plain,
! [X0: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4261]) ).
tcf(c_1474,plain,
! [X0: $i] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4262]) ).
tcf(c_1475,plain,
! [X0: $i] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4263]) ).
tcf(c_1476,plain,
! [X0: $i] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4264]) ).
tcf(c_1477,plain,
! [X0: $i] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4265]) ).
tcf(c_1478,plain,
! [X0: $i] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4266]) ).
tcf(c_1479,plain,
! [X0: $i] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4267]) ).
tcf(c_1480,plain,
! [X0: $i] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4268]) ).
tcf(c_1481,plain,
! [X0: $i] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4269]) ).
tcf(c_1482,plain,
! [X0: $i] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f4270]) ).
tcf(c_1483,plain,
! [X0: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4271]) ).
tcf(c_1484,plain,
! [X0: $i] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4272]) ).
tcf(c_1485,plain,
! [X0: $i] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4273]) ).
tcf(c_1486,plain,
! [X0: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4274]) ).
tcf(c_1487,plain,
! [X0: $i] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4275]) ).
tcf(c_1488,plain,
! [X0: $i] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4276]) ).
tcf(c_1489,plain,
! [X0: $i] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4277]) ).
tcf(c_1490,plain,
! [X0: $i] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f4278]) ).
tcf(c_1491,plain,
! [X0: $i] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4279]) ).
tcf(c_1492,plain,
! [X0: $i] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4280]) ).
tcf(c_1493,plain,
! [X0: $i] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f4281]) ).
tcf(c_1494,plain,
! [X0: $i] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f4282]) ).
tcf(c_1495,plain,
! [X0: $i] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f4283]) ).
tcf(c_1496,plain,
! [X0: $i] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4284]) ).
tcf(c_1497,plain,
! [X0: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4285]) ).
tcf(c_1498,plain,
! [X0: $i] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f4286]) ).
tcf(c_1499,plain,
! [X0: $i] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4287]) ).
tcf(c_1500,plain,
! [X0: $i] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4288]) ).
tcf(c_1501,plain,
! [X0: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f4289]) ).
tcf(c_1502,plain,
! [X0: $i] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f4290]) ).
tcf(c_1503,plain,
! [X0: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f4291]) ).
tcf(c_1505,plain,
! [X0: $i] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f4293]) ).
tcf(c_1506,plain,
! [X0: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f4294]) ).
tcf(c_1507,plain,
! [X0: $i] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4295]) ).
tcf(c_1508,plain,
! [X0: $i] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4296]) ).
tcf(c_1509,plain,
! [X0: $i] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4297]) ).
tcf(c_1510,plain,
! [X0: $i] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f4298]) ).
tcf(c_1511,plain,
! [X0: $i] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f4299]) ).
tcf(c_1513,plain,
! [X0: $i] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f4301]) ).
tcf(c_1514,plain,
! [X0: $i] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f4302]) ).
tcf(c_1515,plain,
! [X0: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f4303]) ).
tcf(c_1516,plain,
! [X0: $i] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f4304]) ).
tcf(c_1517,plain,
! [X0: $i] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4305]) ).
tcf(c_1518,plain,
! [X0: $i] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4306]) ).
tcf(c_1519,plain,
! [X0: $i] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f4307]) ).
tcf(c_1520,plain,
! [X0: $i] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f4308]) ).
tcf(c_1521,plain,
! [X0: $i] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f4309]) ).
tcf(c_1522,plain,
! [X0: $i] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f4310]) ).
tcf(c_1523,plain,
! [X0: $i] :
( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f4311]) ).
tcf(c_1524,plain,
! [X0: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f4312]) ).
tcf(c_1525,plain,
! [X0: $i] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f4313]) ).
tcf(c_1526,plain,
! [X0: $i] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f4314]) ).
tcf(c_1527,plain,
! [X0: $i] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f4315]) ).
tcf(c_1529,plain,
! [X0: $i] :
( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f4317]) ).
tcf(c_1530,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ hBOOL(c_fequal(X0,X1)) ),
inference(cnf_transformation,[],[f4318]) ).
tcf(c_1531,plain,
! [X0: $i] : hBOOL(c_fequal(X0,X0)),
inference(cnf_transformation,[],[f4718]) ).
tcf(c_1532,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK21) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(cnf_transformation,[],[f4325]) ).
tcf(c_1533,negated_conjecture,
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK21) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(cnf_transformation,[],[f4324]) ).
tcf(c_1536,negated_conjecture,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(cnf_transformation,[],[f4321]) ).
tcf(c_1537,negated_conjecture,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(cnf_transformation,[],[f4320]) ).
tcf(c_2272,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Oless__eq(X0,X1,X1) ),
inference(global_subsumption_just,[status(thm)],[c_284,c_249,c_284]) ).
tcf(c_2273,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) ),
inference(renaming,[status(thm)],[c_2272]) ).
tcf(c_2286,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(global_subsumption_just,[status(thm)],[c_1123,c_464,c_1123]) ).
tcf(c_2329,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(global_subsumption_just,[status(thm)],[c_1537,c_50,c_1536]) ).
tcf(c_2330,negated_conjecture,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(renaming,[status(thm)],[c_2329]) ).
tcf(c_2332,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(global_subsumption_just,[status(thm)],[c_1536,c_2330]) ).
tcf(c_2333,negated_conjecture,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(renaming,[status(thm)],[c_2332]) ).
tcf(c_2340,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_383,c_333]) ).
tcf(c_2341,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(renaming,[status(thm)],[c_2340]) ).
tcf(c_2342,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380]) ).
tcf(c_2343,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(renaming,[status(thm)],[c_2342]) ).
tcf(c_2346,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_167,c_387]) ).
tcf(c_2347,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(renaming,[status(thm)],[c_2346]) ).
tcf(c_2352,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_383,c_333,c_172]) ).
tcf(c_2353,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(renaming,[status(thm)],[c_2352]) ).
tcf(c_2362,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334]) ).
tcf(c_2363,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(renaming,[status(thm)],[c_2362]) ).
tcf(c_2380,plain,
! [X0: $i] :
( ~ 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),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(prop_impl_just,[status(thm)],[c_685]) ).
tcf(c_2381,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,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),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(renaming,[status(thm)],[c_2380]) ).
tcf(c_2382,plain,
! [X0: $i] :
( 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),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(prop_impl_just,[status(thm)],[c_684]) ).
tcf(c_2396,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_1142,c_383,c_333]) ).
tcf(c_2397,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(renaming,[status(thm)],[c_2396]) ).
tcf(c_2398,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_1143,c_380]) ).
tcf(c_2399,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(renaming,[status(thm)],[c_2398]) ).
tcf(c_2516,plain,
! [X0: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_1506]) ).
tcf(c_2620,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )
| ~ class_Rings_Oidom(X0) ),
inference(prop_impl_just,[status(thm)],[c_624]) ).
tcf(c_2650,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) )
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(prop_impl_just,[status(thm)],[c_309]) ).
tcf(c_2651,plain,
! [X0: $i] :
( ~ class_Rings_Ozero__neq__one(X0)
| ( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ) ),
inference(renaming,[status(thm)],[c_2650]) ).
tcf(c_2694,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(prop_impl_just,[status(thm)],[c_967]) ).
tcf(c_2695,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(renaming,[status(thm)],[c_2694]) ).
tcf(c_2696,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
inference(prop_impl_just,[status(thm)],[c_141]) ).
tcf(c_2698,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
inference(prop_impl_just,[status(thm)],[c_966]) ).
tcf(c_2699,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(renaming,[status(thm)],[c_2698]) ).
tcf(c_2700,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
| ~ class_Fields_Ofield(X0) ),
inference(prop_impl_just,[status(thm)],[c_146]) ).
tcf(c_2702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP1(X0,X1,X2,X3,X4)
| ~ class_Fields_Ofield(X0) ),
inference(prop_impl_just,[status(thm)],[c_1022]) ).
tcf(c_2704,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Fields_Ofield(X0) ),
inference(prop_impl_just,[status(thm)],[c_1030]) ).
tcf(c_2706,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1)
| ~ class_Fields_Ofield(X0) ),
inference(prop_impl_just,[status(thm)],[c_1031]) ).
tcf(c_2708,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,X2) )
| ~ class_Fields_Ofield(X0) ),
inference(prop_impl_just,[status(thm)],[c_1310]) ).
tcf(c_2710,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1),X2) )
| ~ class_Fields_Ofield(X0) ),
inference(prop_impl_just,[status(thm)],[c_1311]) ).
tcf(c_2712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Polynomial_Osmult(X0,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X2,X3)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),X3) )
| ~ class_Fields_Ofield(X0) ),
inference(prop_impl_just,[status(thm)],[c_1312]) ).
tcf(c_2714,plain,
! [X0: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(prop_impl_just,[status(thm)],[c_1503]) ).
tcf(c_2744,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_330,c_333]) ).
tcf(c_2745,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(renaming,[status(thm)],[c_2744]) ).
tcf(c_2748,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_466]) ).
tcf(c_2749,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(renaming,[status(thm)],[c_2748]) ).
tcf(c_2750,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_635,c_334,c_380]) ).
tcf(c_2751,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(renaming,[status(thm)],[c_2750]) ).
tcf(c_2752,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_634,c_334,c_380]) ).
tcf(c_2753,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(renaming,[status(thm)],[c_2752]) ).
tcf(c_2754,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_469]) ).
tcf(c_2755,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) ),
inference(renaming,[status(thm)],[c_2754]) ).
tcf(c_2756,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK11(X1,X0)) = X1 )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_472]) ).
tcf(c_2757,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK11(X1,X0)) = X1 ) ),
inference(renaming,[status(thm)],[c_2756]) ).
tcf(c_2758,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK13(X1,X0)) = X1 )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_652]) ).
tcf(c_2759,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK13(X1,X0)) = X1 ) ),
inference(renaming,[status(thm)],[c_2758]) ).
tcf(c_2760,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_972]) ).
tcf(c_2761,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) ),
inference(renaming,[status(thm)],[c_2760]) ).
tcf(c_2762,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_969]) ).
tcf(c_2763,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
inference(renaming,[status(thm)],[c_2762]) ).
tcf(c_2766,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_1093]) ).
tcf(c_2767,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(renaming,[status(thm)],[c_2766]) ).
tcf(c_2768,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X0 )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_1092]) ).
tcf(c_2769,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1 ) ),
inference(renaming,[status(thm)],[c_2768]) ).
tcf(c_2770,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_1094]) ).
tcf(c_2771,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ),
inference(renaming,[status(thm)],[c_2770]) ).
tcf(c_2772,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_1117]) ).
tcf(c_2773,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ) ),
inference(renaming,[status(thm)],[c_2772]) ).
tcf(c_2774,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_1120]) ).
tcf(c_2775,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2)) ),
inference(renaming,[status(thm)],[c_2774]) ).
tcf(c_2778,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_1128]) ).
tcf(c_2779,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ) ),
inference(renaming,[status(thm)],[c_2778]) ).
tcf(c_2782,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_1130]) ).
tcf(c_2783,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ) ),
inference(renaming,[status(thm)],[c_2782]) ).
tcf(c_2788,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_1194]) ).
tcf(c_2789,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))) ) ),
inference(renaming,[status(thm)],[c_2788]) ).
tcf(c_2790,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_1195]) ).
tcf(c_2791,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ) ),
inference(renaming,[status(thm)],[c_2790]) ).
tcf(c_2792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X2),X3),X4) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_1200]) ).
tcf(c_2793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X3)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3)),X1),X2),X4) ) ),
inference(renaming,[status(thm)],[c_2792]) ).
tcf(c_2794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X2),X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_1206]) ).
tcf(c_2795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0)),X1),X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X3) ) ),
inference(renaming,[status(thm)],[c_2794]) ).
tcf(c_2796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X2),X4)) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_334,c_380,c_1205]) ).
tcf(c_2797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X0)),X1),X4)) ) ),
inference(renaming,[status(thm)],[c_2796]) ).
tcf(c_2848,plain,
! [X0: $i] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(prop_impl_just,[status(thm)],[c_1476]) ).
tcf(c_2966,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(prop_impl_just,[status(thm)],[c_372]) ).
tcf(c_3000,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 )
| ~ class_Groups_Omonoid__add(X0) ),
inference(prop_impl_just,[status(thm)],[c_501]) ).
tcf(c_3002,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ozero__class_Ozero(X0),X1) = X1 )
| ~ class_Groups_Omonoid__add(X0) ),
inference(prop_impl_just,[status(thm)],[c_505]) ).
tcf(c_3104,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X2)),c_Groups_Oplus__class_Oplus(X0,X1,X2)) )
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_1230]) ).
tcf(c_3150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oplus__class_Oplus(X0,X1,X3)),X2) )
| ~ class_Rings_Ocomm__semiring(X0) ),
inference(prop_impl_just,[status(thm)],[c_725]) ).
tcf(c_3246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Oplus__class_Oplus(X0,X2,X3)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(prop_impl_just,[status(thm)],[c_1045]) ).
tcf(c_3248,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) = c_Groups_Ouminus__class_Ouminus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(prop_impl_just,[status(thm)],[c_1048]) ).
tcf(c_3250,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),X2) = c_Groups_Ouminus__class_Ouminus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(prop_impl_just,[status(thm)],[c_1047]) ).
tcf(c_3252,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(prop_impl_just,[status(thm)],[c_1041]) ).
tcf(c_3254,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(prop_impl_just,[status(thm)],[c_1039]) ).
tcf(c_3256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X2)),c_Groups_Ominus__class_Ominus(X0,X3,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X2)),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),c_Groups_Ominus__class_Ominus(X0,X3,X4))) = c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X4)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(prop_impl_just,[status(thm)],[c_1162]) ).
tcf(c_3258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ominus__class_Ominus(X0,X2,X3)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(prop_impl_just,[status(thm)],[c_1164]) ).
tcf(c_3260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X3)),X2) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(prop_impl_just,[status(thm)],[c_1166]) ).
tcf(c_3288,plain,
! [X0: $i,X1: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,X1,c_Groups_Oone__class_Oone(X0)) = X1 )
| ~ class_Rings_Odivision__ring(X0) ),
inference(prop_impl_just,[status(thm)],[c_1258]) ).
tcf(c_3294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Rings_Oinverse__class_Odivide(X0,X2,X3)) = c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3) )
| ~ class_Rings_Odivision__ring(X0) ),
inference(prop_impl_just,[status(thm)],[c_1278]) ).
tcf(c_3296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2),c_Rings_Oinverse__class_Odivide(X0,X3,X2)) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,X1,X3),X2) )
| ~ class_RealVector_Oreal__normed__field(X0) ),
inference(prop_impl_just,[status(thm)],[c_1256]) ).
tcf(c_3298,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2)) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2) )
| ~ class_RealVector_Oreal__normed__field(X0) ),
inference(prop_impl_just,[status(thm)],[c_1281]) ).
tcf(c_3300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2),c_Rings_Oinverse__class_Odivide(X0,X3,X2)) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),X2) )
| ~ class_RealVector_Oreal__normed__field(X0) ),
inference(prop_impl_just,[status(thm)],[c_1280]) ).
tcf(c_3302,plain,
! [X0: $i,X1: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ozero__class_Ozero(X0),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_RealVector_Oreal__normed__field(X0) ),
inference(prop_impl_just,[status(thm)],[c_1279]) ).
tcf(c_3306,plain,
! [X0: $i,X1: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Odivision__ring__inverse__zero(X0) ),
inference(prop_impl_just,[status(thm)],[c_1266]) ).
tcf(c_3308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Rings_Oinverse__class_Odivide(X0,X1,X3)),X2) )
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(prop_impl_just,[status(thm)],[c_1265]) ).
tcf(c_3312,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),X1)),X2) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) )
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(prop_impl_just,[status(thm)],[c_1268]) ).
tcf(c_3314,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2)) = c_Rings_Oinverse__class_Odivide(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2)) )
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(prop_impl_just,[status(thm)],[c_1284]) ).
tcf(c_3318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Rings_Oinverse__class_Odivide(X0,X1,X3)),c_Rings_Oinverse__class_Odivide(X0,X2,X4)) )
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(prop_impl_just,[status(thm)],[c_1283]) ).
tcf(c_3322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,X2,X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,X1,X5),X4)),X3)) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X5),X3)),X4) )
| ~ class_RealVector_Oreal__field(X0) ),
inference(prop_impl_just,[status(thm)],[c_1308]) ).
tcf(c_3324,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,c_Groups_Ozero__class_Ozero(X0),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Divides_Osemiring__div(X0) ),
inference(prop_impl_just,[status(thm)],[c_1314]) ).
tcf(c_3326,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 )
| ~ class_Divides_Osemiring__div(X0) ),
inference(prop_impl_just,[status(thm)],[c_1315]) ).
tcf(c_3328,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X1,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Divides_Osemiring__div(X0) ),
inference(prop_impl_just,[status(thm)],[c_1316]) ).
tcf(c_3330,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(X0,c_Divides_Odiv__class_Omod(X0,X1,X2),X2) = c_Divides_Odiv__class_Omod(X0,X1,X2) )
| ~ class_Divides_Osemiring__div(X0) ),
inference(prop_impl_just,[status(thm)],[c_1320]) ).
tcf(c_5536,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_152,c_2343]) ).
tcf(c_5537,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(bin_hyper_res,[status(thm)],[c_170,c_2341]) ).
tcf(c_5538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(bin_hyper_res,[status(thm)],[c_192,c_2343]) ).
tcf(c_5541,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK8(X0,X1)) = X1 ) ),
inference(bin_hyper_res,[status(thm)],[c_369,c_2363]) ).
tcf(c_5542,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK8(X1,X0),X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(bin_hyper_res,[status(thm)],[c_370,c_2363]) ).
tcf(c_5545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_465,c_2343]) ).
tcf(c_5547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_907,c_2343]) ).
tcf(c_5548,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(bin_hyper_res,[status(thm)],[c_1088,c_2347]) ).
tcf(c_5549,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_1089,c_2343]) ).
tcf(c_5550,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ( X0 = X2 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) ) ),
inference(bin_hyper_res,[status(thm)],[c_1091,c_2347]) ).
tcf(c_5553,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(bin_hyper_res,[status(thm)],[c_1134,c_2347]) ).
tcf(c_5554,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_1135,c_2343]) ).
tcf(c_5555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X2),X3),X4) ),
inference(bin_hyper_res,[status(thm)],[c_1198,c_2347]) ).
tcf(c_5556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| 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),X0),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X2),X3),X4) ),
inference(bin_hyper_res,[status(thm)],[c_1216,c_2347]) ).
tcf(c_5557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2),X3)) )
| ~ class_Groups_Omonoid__mult(X0) ),
inference(bin_hyper_res,[status(thm)],[c_1233,c_2343]) ).
tcf(c_5558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) )
| ~ class_Fields_Ofield(X0) ),
inference(bin_hyper_res,[status(thm)],[c_1282,c_2343]) ).
tcf(c_11584,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(demodulation,[status(thm)],[c_682,c_925]) ).
tcf(c_11601,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK7,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
inference(demodulation,[status(thm)],[c_90,c_551]) ).
tcf(c_11606,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
inference(demodulation,[status(thm)],[c_52,c_551]) ).
tcf(c_11697,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(light_normalisation,[status(thm)],[c_393,c_1222]) ).
tcf(c_11748,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(demodulation,[status(thm)],[c_11584,c_1242]) ).
tcf(c_11908,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(demodulation,[status(thm)],[c_678,c_925]) ).
tcf(c_12387,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(demodulation,[status(thm)],[c_2966,c_440]) ).
tcf(c_12503,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(demodulation,[status(thm)],[c_1080,c_1065]) ).
tcf(c_12534,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),
inference(demodulation,[status(thm)],[c_889,c_1242]) ).
tcf(c_13039,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,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_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(demodulation,[status(thm)],[c_2381,c_927]) ).
tcf(c_13046,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(demodulation,[status(thm)],[c_2382,c_927]) ).
tcf(c_13440,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(demodulation,[status(thm)],[c_81,c_440]) ).
tcf(c_13513,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK17(X1,X0))))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(demodulation,[status(thm)],[c_1053,c_551]) ).
tcf(c_14149,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(demodulation,[status(thm)],[c_479,c_440]) ).
tcf(c_14258,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(demodulation,[status(thm)],[c_2695,c_440]) ).
tcf(c_14265,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(demodulation,[status(thm)],[c_2699,c_440]) ).
tcf(c_14422,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(demodulation,[status(thm)],[c_2696,c_440]) ).
tcf(c_14445,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(demodulation,[status(thm)],[c_5549,c_551,c_12503]) ).
tcf(c_14951,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(demodulation,[status(thm)],[c_480,c_440]) ).
tcf(c_14961,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(demodulation,[status(thm)],[c_477,c_440]) ).
tcf(c_15291,plain,
! [X0: $i] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(demodulation,[status(thm)],[c_435,c_440]) ).
tcf(c_15523,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ 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_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(demodulation,[status(thm)],[c_964,c_440]) ).
tcf(c_15533,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ 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_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(demodulation,[status(thm)],[c_963,c_440]) ).
tcf(c_15583,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(demodulation,[status(thm)],[c_84,c_440]) ).
tcf(c_15749,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(demodulation,[status(thm)],[c_478,c_440]) ).
tcf(c_15887,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(demodulation,[status(thm)],[c_965,c_440]) ).
tcf(c_15897,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ 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_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(demodulation,[status(thm)],[c_962,c_440]) ).
tcf(c_15967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( 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,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))),X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) ) ),
inference(demodulation,[status(thm)],[c_2795,c_1005]) ).
tcf(c_16040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3),X2))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))) ),
inference(demodulation,[status(thm)],[c_921,c_927]) ).
tcf(c_16050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4)))) ),
inference(demodulation,[status(thm)],[c_920,c_927]) ).
tcf(c_16064,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) )
| ~ class_Rings_Oidom(X0) ),
inference(demodulation,[status(thm)],[c_2620,c_440]) ).
tcf(c_16091,plain,
! [X0: $i] :
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(demodulation,[status(thm)],[c_57,c_551,c_11606]) ).
tcf(c_16095,plain,
! [X0: $i] :
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16091,c_2333]) ).
tcf(c_16166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1))))
| ~ hBOOL(hAPP(X0,X3))
| ~ 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)
| ~ hBOOL(hAPP(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,sK16(X0,X1)))) ),
inference(demodulation,[status(thm)],[c_1049,c_925]) ).
tcf(c_16430,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( c_Groups_Ouminus__class_Ouminus(X0,X2) = X1 )
| ~ class_Rings_Oidom(X0)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(demodulation,[status(thm)],[c_625,c_440]) ).
tcf(c_16463,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X2)),c_Groups_Oplus__class_Oplus(X0,X1,X2)) )
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(demodulation,[status(thm)],[c_3104,c_440]) ).
tcf(c_16672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,X2,X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,X1,X5),X4)),X3)) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X5),X3)),X4) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3322,c_1449]) ).
tcf(c_16673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X4),X3)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),X3),
inference(unflattening,[status(thm)],[c_16672]) ).
tcf(c_16679,plain,
! [X0: $i,X1: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3306,c_1434]) ).
tcf(c_16680,plain,
! [X0: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unflattening,[status(thm)],[c_16679]) ).
tcf(c_16685,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Rings_Oinverse__class_Odivide(X0,X1,X1) = c_Groups_Oone__class_Oone(X0) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1261,c_1434]) ).
tcf(c_16686,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(unflattening,[status(thm)],[c_16685]) ).
tcf(c_16697,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2)) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3298,c_1438]) ).
tcf(c_16698,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),
inference(unflattening,[status(thm)],[c_16697]) ).
tcf(c_16703,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2),c_Rings_Oinverse__class_Odivide(X0,X3,X2)) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),X2) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3300,c_1438]) ).
tcf(c_16704,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2),X1),
inference(unflattening,[status(thm)],[c_16703]) ).
tcf(c_16709,plain,
! [X0: $i,X1: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ozero__class_Ozero(X0),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3302,c_1438]) ).
tcf(c_16710,plain,
! [X0: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unflattening,[status(thm)],[c_16709]) ).
tcf(c_16715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2),c_Rings_Oinverse__class_Odivide(X0,X3,X2)) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,X1,X3),X2) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3296,c_1438]) ).
tcf(c_16716,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),X1),
inference(unflattening,[status(thm)],[c_16715]) ).
tcf(c_16751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Oplus__class_Oplus(X0,X1,X3)),X2) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3150,c_1451]) ).
tcf(c_16752,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2)),X1),
inference(unflattening,[status(thm)],[c_16751]) ).
tcf(c_16809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( c_Polynomial_Opdivmod__rel(X8,X0,X4,X6,X2)
| ~ class_Fields_Ofield(X9)
| ~ sP0(X0,X2,X4,X6,X8)
| ( X8 != X9 )
| ( X6 != X7 )
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1012,c_2702]) ).
tcf(c_16810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Polynomial_Opdivmod__rel(X4,X0,X2,X3,X1)
| ~ class_Fields_Ofield(X4)
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(unflattening,[status(thm)],[c_16809]) ).
tcf(c_16821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( sP0(X2,X8,X4,X6,X0)
| ~ class_Fields_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X0,X2,X4,X6,X8)
| ( X8 != X9 )
| ( X6 != X7 )
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1013,c_2702]) ).
tcf(c_16822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP0(X1,X4,X2,X3,X0)
| ~ class_Fields_Ofield(X0)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4) ),
inference(unflattening,[status(thm)],[c_16821]) ).
tcf(c_16928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X3)),X2) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3260,c_1435]) ).
tcf(c_16929,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2)),X1),
inference(unflattening,[status(thm)],[c_16928]) ).
tcf(c_16934,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ominus__class_Ominus(X0,X2,X3)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3258,c_1435]) ).
tcf(c_16935,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),
inference(unflattening,[status(thm)],[c_16934]) ).
tcf(c_16940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X2)),c_Groups_Ominus__class_Ominus(X0,X3,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X2)),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),c_Groups_Ominus__class_Ominus(X0,X3,X4))) = c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X4)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3256,c_1435]) ).
tcf(c_16941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),
inference(unflattening,[status(thm)],[c_16940]) ).
tcf(c_16946,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),X2) = c_Groups_Ouminus__class_Ouminus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3250,c_1435]) ).
tcf(c_16947,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(unflattening,[status(thm)],[c_16946]) ).
tcf(c_16952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Oplus__class_Oplus(X0,X2,X3)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3246,c_1435]) ).
tcf(c_16953,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),
inference(unflattening,[status(thm)],[c_16952]) ).
tcf(c_16960,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3252,c_1435]) ).
tcf(c_16961,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unflattening,[status(thm)],[c_16960]) ).
tcf(c_16966,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3254,c_1435]) ).
tcf(c_16967,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unflattening,[status(thm)],[c_16966]) ).
tcf(c_16972,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) = c_Groups_Ouminus__class_Ouminus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3248,c_1435]) ).
tcf(c_16973,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(unflattening,[status(thm)],[c_16972]) ).
tcf(c_17041,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ozero__class_Ozero(X0),X1) = X1 )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3002,c_1456]) ).
tcf(c_17042,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = X0,
inference(unflattening,[status(thm)],[c_17041]) ).
tcf(c_17047,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3000,c_1456]) ).
tcf(c_17048,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0,
inference(unflattening,[status(thm)],[c_17047]) ).
tcf(c_17110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( 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__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ( tc_Polynomial_Opoly(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_781,c_2848]) ).
tcf(c_17111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),X3))
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X0),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) ),
inference(unflattening,[status(thm)],[c_17110]) ).
tcf(c_17553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Rings_Oinverse__class_Odivide(X0,X2,X3)) = c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3294,c_1450]) ).
tcf(c_17554,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),
inference(unflattening,[status(thm)],[c_17553]) ).
tcf(c_17559,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Rings_Oinverse__class_Odivide(X0,X1,X2)),X2) = X1 )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1275,c_1450]) ).
tcf(c_17560,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X1) = X0 ) ),
inference(unflattening,[status(thm)],[c_17559]) ).
tcf(c_17568,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X2) = X1 )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1272,c_1450]) ).
tcf(c_17569,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X1) = X0 ) ),
inference(unflattening,[status(thm)],[c_17568]) ).
tcf(c_17597,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( X0 != tc_Complex_Ocomplex )
| ( c_Rings_Oinverse__class_Odivide(X0,X1,X2) != c_Groups_Oone__class_Oone(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_1264,c_1450]) ).
tcf(c_17598,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(unflattening,[status(thm)],[c_17597]) ).
tcf(c_17613,plain,
! [X0: $i,X1: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,X1,c_Groups_Oone__class_Oone(X0)) = X1 )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3288,c_1450]) ).
tcf(c_17614,plain,
! [X0: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = X0,
inference(unflattening,[status(thm)],[c_17613]) ).
tcf(c_17636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X3 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),X3) = c_Groups_Oplus__class_Oplus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X3),X2) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1302,c_1441]) ).
tcf(c_17637,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X2 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),X1) ) ),
inference(unflattening,[status(thm)],[c_17636]) ).
tcf(c_17645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X3 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),X3) = c_Groups_Oplus__class_Oplus(X0,X2,c_Rings_Oinverse__class_Odivide(X0,X1,X3)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1300,c_1441]) ).
tcf(c_17646,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X2 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)) ) ),
inference(unflattening,[status(thm)],[c_17645]) ).
tcf(c_17675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X3)) = c_Rings_Oinverse__class_Odivide(X0,X2,X3) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1288,c_1441]) ).
tcf(c_17676,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2) ) ),
inference(unflattening,[status(thm)],[c_17675]) ).
tcf(c_17689,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2)) = c_Rings_Oinverse__class_Odivide(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3314,c_1441]) ).
tcf(c_17690,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(unflattening,[status(thm)],[c_17689]) ).
tcf(c_17695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Rings_Oinverse__class_Odivide(X0,X1,X3)),c_Rings_Oinverse__class_Odivide(X0,X2,X4)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3318,c_1441]) ).
tcf(c_17696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3)),
inference(unflattening,[status(thm)],[c_17695]) ).
tcf(c_17701,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),X1)),X2) = c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3312,c_1441]) ).
tcf(c_17702,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1)),
inference(unflattening,[status(thm)],[c_17701]) ).
tcf(c_17707,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Rings_Oinverse__class_Odivide(X0,X1,X3)),X2) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_3308,c_1441]) ).
tcf(c_17708,plain,
! [X0: $i,X1: $i,X2: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),X1)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),X1),
inference(unflattening,[status(thm)],[c_17707]) ).
tcf(c_17928,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( X0 != tc_Int_Oint )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_74,c_1342]) ).
tcf(c_17929,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(unflattening,[status(thm)],[c_17928]) ).
tcf(c_17959,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( X0 != tc_Complex_Ocomplex )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_74,c_1437]) ).
tcf(c_17960,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(unflattening,[status(thm)],[c_17959]) ).
tcf(c_18381,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X2),X1))
| ( X0 != tc_Int_Oint )
| ( c_Divides_Odiv__class_Omod(X0,X1,X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_1318,c_1362]) ).
tcf(c_18382,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(unflattening,[status(thm)],[c_18381]) ).
tcf(c_18390,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X2,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2))
| ( X0 != tc_Int_Oint ) ),
inference(resolution_lifted,[status(thm)],[c_1317,c_1362]) ).
tcf(c_18391,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(unflattening,[status(thm)],[c_18390]) ).
tcf(c_18434,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X2),X1))
| ( X0 != tc_Nat_Onat )
| ( c_Divides_Odiv__class_Omod(X0,X1,X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_1318,c_1410]) ).
tcf(c_18435,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(unflattening,[status(thm)],[c_18434]) ).
tcf(c_18442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X2,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2))
| ( X0 != tc_Nat_Onat ) ),
inference(resolution_lifted,[status(thm)],[c_1317,c_1410]) ).
tcf(c_18443,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(unflattening,[status(thm)],[c_18442]) ).
tcf(c_19876,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Ono__zero__divisors(X0)
| ~ class_Rings_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ( X0 != tc_Int_Oint )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_1365]) ).
tcf(c_19877,plain,
! [X0: $i] :
( ~ class_Rings_Ono__zero__divisors(tc_Int_Oint)
| ~ class_Rings_Omult__zero(tc_Int_Oint)
| ~ class_Power_Opower(tc_Int_Oint)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(unflattening,[status(thm)],[c_19876]) ).
tcf(c_19879,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(global_subsumption_just,[status(thm)],[c_19877,c_1383,c_1374,c_1356,c_19877]) ).
tcf(c_19895,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ozero__class_Ozero(X0)),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Ono__zero__divisors(X0)
| ~ class_Rings_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ( X0 != tc_Int_Oint ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_1365]) ).
tcf(c_19896,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ class_Rings_Ono__zero__divisors(tc_Int_Oint)
| ~ class_Rings_Omult__zero(tc_Int_Oint)
| ~ class_Power_Opower(tc_Int_Oint) ),
inference(unflattening,[status(thm)],[c_19895]) ).
tcf(c_19898,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(global_subsumption_just,[status(thm)],[c_19896,c_1383,c_1374,c_1356,c_19896]) ).
tcf(c_19907,plain,
! [X0: $i] :
( ( X0 != tc_Nat_Onat )
| ( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_2651,c_1412]) ).
tcf(c_19908,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(unflattening,[status(thm)],[c_19907]) ).
tcf(c_19921,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Rings_Ono__zero__divisors(X0)
| ~ class_Rings_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ( X0 != tc_Nat_Onat )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_1412]) ).
tcf(c_19922,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ class_Rings_Ono__zero__divisors(tc_Nat_Onat)
| ~ class_Rings_Omult__zero(tc_Nat_Onat)
| ~ class_Power_Opower(tc_Nat_Onat)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(unflattening,[status(thm)],[c_19921]) ).
tcf(c_19924,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(global_subsumption_just,[status(thm)],[c_19922,c_1423,c_1418,c_1406,c_19922]) ).
tcf(c_19933,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ozero__class_Ozero(X0)),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Ono__zero__divisors(X0)
| ~ class_Rings_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ( X0 != tc_Nat_Onat ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_1412]) ).
tcf(c_19934,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Rings_Ono__zero__divisors(tc_Nat_Onat)
| ~ class_Rings_Omult__zero(tc_Nat_Onat)
| ~ class_Power_Opower(tc_Nat_Onat) ),
inference(unflattening,[status(thm)],[c_19933]) ).
tcf(c_19936,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(global_subsumption_just,[status(thm)],[c_19934,c_1423,c_1418,c_1406,c_19934]) ).
tcf(c_19945,plain,
! [X0: $i] :
( ( X0 != tc_Complex_Ocomplex )
| ( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_2651,c_1453]) ).
tcf(c_19946,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(unflattening,[status(thm)],[c_19945]) ).
tcf(c_19950,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Ono__zero__divisors(X0)
| ~ class_Rings_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ( X0 != tc_Complex_Ocomplex )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_1453]) ).
tcf(c_19951,plain,
! [X0: $i] :
( ~ class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)
| ~ class_Rings_Omult__zero(tc_Complex_Ocomplex)
| ~ class_Power_Opower(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(unflattening,[status(thm)],[c_19950]) ).
tcf(c_19953,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(global_subsumption_just,[status(thm)],[c_19951,c_1467,c_1459,c_1445,c_19951]) ).
tcf(c_19969,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ozero__class_Ozero(X0)),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Ono__zero__divisors(X0)
| ~ class_Rings_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_1453]) ).
tcf(c_19970,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)
| ~ class_Rings_Omult__zero(tc_Complex_Ocomplex)
| ~ class_Power_Opower(tc_Complex_Ocomplex) ),
inference(unflattening,[status(thm)],[c_19969]) ).
tcf(c_19972,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(global_subsumption_just,[status(thm)],[c_19970,c_1467,c_1459,c_1445,c_19970]) ).
tcf(c_19981,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| ( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) )
| ( tc_Polynomial_Opoly(X1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_2651,c_2516]) ).
tcf(c_19982,plain,
! [X0: $i] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) ) ),
inference(unflattening,[status(thm)],[c_19981]) ).
tcf(c_19990,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Rings_Ono__zero__divisors(X0)
| ~ class_Rings_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Rings_Ocomm__semiring__1(X2)
| ( tc_Polynomial_Opoly(X2) != X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_2516]) ).
tcf(c_19991,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Power_Opower(tc_Polynomial_Opoly(X0))
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(unflattening,[status(thm)],[c_19990]) ).
tcf(c_19993,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_19991,c_1524,c_19991]) ).
tcf(c_20008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ class_Rings_Ono__zero__divisors(X0)
| ~ class_Rings_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Rings_Ocomm__semiring__1(X3)
| ( tc_Polynomial_Opoly(X3) != X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_2516]) ).
tcf(c_20009,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Power_Opower(tc_Polynomial_Opoly(X0))
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(unflattening,[status(thm)],[c_20008]) ).
tcf(c_20011,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_20009,c_1524,c_20009]) ).
tcf(c_20029,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) )
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Rings_Ocomm__semiring__1(X0)
| ( tc_Polynomial_Opoly(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_2516]) ).
tcf(c_20030,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Power_Opower(tc_Polynomial_Opoly(X0)) ),
inference(unflattening,[status(thm)],[c_20029]) ).
tcf(c_20032,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__1(X0)
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_20030,c_1524,c_20030]) ).
tcf(c_22479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Rings_Oinverse__class_Odivide(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_5558,c_1466]) ).
tcf(c_22480,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ) ),
inference(unflattening,[status(thm)],[c_22479]) ).
tcf(c_22491,plain,
! [X0: $i] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2714,c_1466]) ).
tcf(c_22492,plain,
class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unflattening,[status(thm)],[c_22491]) ).
tcf(c_22496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,c_Polynomial_Osmult(X0,X2,X3)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,X3) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1313,c_1466]) ).
tcf(c_22497,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X2) ) ),
inference(unflattening,[status(thm)],[c_22496]) ).
tcf(c_22505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Polynomial_Osmult(X0,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X2,X3)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),X3) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2712,c_1466]) ).
tcf(c_22506,plain,
! [X0: $i,X1: $i,X2: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1),X2),
inference(unflattening,[status(thm)],[c_22505]) ).
tcf(c_22511,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1),X2) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2710,c_1466]) ).
tcf(c_22512,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X1)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0),X1),
inference(unflattening,[status(thm)],[c_22511]) ).
tcf(c_22517,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X1,X2) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2708,c_1466]) ).
tcf(c_22518,plain,
! [X0: $i,X1: $i] : c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X1),
inference(unflattening,[status(thm)],[c_22517]) ).
tcf(c_22523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X3 )
| ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X2,X3)),c_Polynomial_Osmult(X0,c_Rings_Oinverse__class_Odivide(X0,hAPP(c_Polynomial_Ocoeff(X0,c_Polynomial_OpCons(X0,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),X2,X3))),c_Polynomial_Odegree(X0,X3)),hAPP(c_Polynomial_Ocoeff(X0,X3),c_Polynomial_Odegree(X0,X3))),X3)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X1,X2),X3) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1309,c_1466]) ).
tcf(c_22524,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X2 )
| ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,X2)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,X2))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,X2),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))),X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),X2) ) ),
inference(unflattening,[status(thm)],[c_22523]) ).
tcf(c_22532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3),X1) = c_Groups_Ominus__class_Ominus(X0,X2,c_Rings_Oinverse__class_Odivide(X0,X3,X1)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1307,c_1466]) ).
tcf(c_22533,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)) ) ),
inference(unflattening,[status(thm)],[c_22532]) ).
tcf(c_22541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),X2) = c_Groups_Ominus__class_Ominus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2),X3) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1306,c_1466]) ).
tcf(c_22542,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) ) ),
inference(unflattening,[status(thm)],[c_22541]) ).
tcf(c_22550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X4 )
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X2)) = c_Groups_Ominus__class_Ominus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X4),c_Rings_Oinverse__class_Odivide(X0,X3,X2)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1305,c_1466]) ).
tcf(c_22551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X3 )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(unflattening,[status(thm)],[c_22550]) ).
tcf(c_22562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X4 )
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X4),X2)) = c_Groups_Oplus__class_Oplus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X4),c_Rings_Oinverse__class_Odivide(X0,X3,X2)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1304,c_1466]) ).
tcf(c_22563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X3 )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(unflattening,[status(thm)],[c_22562]) ).
tcf(c_22574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),X2) = c_Groups_Oplus__class_Oplus(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2),X3) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1303,c_1466]) ).
tcf(c_22575,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) ) ),
inference(unflattening,[status(thm)],[c_22574]) ).
tcf(c_22582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ( c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oplus__class_Oplus(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),X3),X1) = c_Groups_Oplus__class_Oplus(X0,X2,c_Rings_Oinverse__class_Odivide(X0,X3,X1)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1301,c_1466]) ).
tcf(c_22583,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)) ) ),
inference(unflattening,[status(thm)],[c_22582]) ).
tcf(c_22591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X4 )
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X2) )
| ( X0 != tc_Complex_Ocomplex )
| ( c_Rings_Oinverse__class_Odivide(X0,X1,X2) != c_Rings_Oinverse__class_Odivide(X0,X3,X4) ) ),
inference(resolution_lifted,[status(thm)],[c_1287,c_1466]) ).
tcf(c_22592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X3 )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1) )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3) ) ),
inference(unflattening,[status(thm)],[c_22591]) ).
tcf(c_22606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ozero__class_Ozero(X0) = X4 )
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ( c_Rings_Oinverse__class_Odivide(X0,X1,X4) = c_Rings_Oinverse__class_Odivide(X0,X3,X2) )
| ( X0 != tc_Complex_Ocomplex )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X3),X4) ) ),
inference(resolution_lifted,[status(thm)],[c_1286,c_1466]) ).
tcf(c_22607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X3 )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3) ) ),
inference(unflattening,[status(thm)],[c_22606]) ).
tcf(c_22623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Polynomial_OpCons(X0,X5,X1),X2,c_Polynomial_OpCons(X0,c_Rings_Oinverse__class_Odivide(X0,hAPP(c_Polynomial_Ocoeff(X0,c_Polynomial_OpCons(X0,X5,X4)),c_Polynomial_Odegree(X0,X2)),hAPP(c_Polynomial_Ocoeff(X0,X2),c_Polynomial_Odegree(X0,X2))),X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(X0,X5,X4),c_Polynomial_Osmult(X0,c_Rings_Oinverse__class_Odivide(X0,hAPP(c_Polynomial_Ocoeff(X0,c_Polynomial_OpCons(X0,X5,X4)),c_Polynomial_Odegree(X0,X2)),hAPP(c_Polynomial_Ocoeff(X0,X2),c_Polynomial_Odegree(X0,X2))),X2)))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1253,c_1466]) ).
tcf(c_22624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X4,X0),X1,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X4,X3)),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1))),X2),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,X4,X3),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X4,X3)),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1))),X1)))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,X1,X2,X3) ),
inference(unflattening,[status(thm)],[c_22623]) ).
tcf(c_22635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( c_Polynomial_Opdivmod__rel(X0,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X6),X2),X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X6),X4),X7))
| ~ c_Polynomial_Opdivmod__rel(X0,X5,X6,X1,X7)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1037,c_1466]) ).
tcf(c_22636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X5),X1),X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X5),X3),X6))
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X4,X5,X0,X6)
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,X1,X2,X3) ),
inference(unflattening,[status(thm)],[c_22635]) ).
tcf(c_22647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X4 = X6 )
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X5,X6)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1034,c_1466]) ).
tcf(c_22648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X3 = X5 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,X1,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,X1,X2,X3) ),
inference(unflattening,[status(thm)],[c_22647]) ).
tcf(c_22659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X3 = X5 )
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X5,X6)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1033,c_1466]) ).
tcf(c_22660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X2 = X4 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,X1,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,X1,X2,X3) ),
inference(unflattening,[status(thm)],[c_22659]) ).
tcf(c_22670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Polynomial_Osmult(X0,X5,X1),X2,c_Polynomial_Osmult(X0,X5,X3),c_Polynomial_Osmult(X0,X5,X4))
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1032,c_1466]) ).
tcf(c_22671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X4,X0),X1,c_Polynomial_Osmult(tc_Complex_Ocomplex,X4,X2),c_Polynomial_Osmult(tc_Complex_Ocomplex,X4,X3))
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,X1,X2,X3) ),
inference(unflattening,[status(thm)],[c_22670]) ).
tcf(c_22679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ c_Polynomial_Opdivmod__rel(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,X3)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1029,c_1466]) ).
tcf(c_22680,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,X2) ),
inference(unflattening,[status(thm)],[c_22679]) ).
tcf(c_22688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ c_Polynomial_Opdivmod__rel(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,X3)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1028,c_1466]) ).
tcf(c_22689,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,X2) ),
inference(unflattening,[status(thm)],[c_22688]) ).
tcf(c_22697,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2706,c_1466]) ).
tcf(c_22698,plain,
! [X0: $i] : c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),
inference(unflattening,[status(thm)],[c_22697]) ).
tcf(c_22703,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X3 )
| ~ c_Polynomial_Opdivmod__rel(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X2,X3)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1026,c_1466]) ).
tcf(c_22704,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X2 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_22703]) ).
tcf(c_22712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ c_Polynomial_Opdivmod__rel(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X2,X3)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_1025,c_1466]) ).
tcf(c_22713,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_22712]) ).
tcf(c_22720,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2704,c_1466]) ).
tcf(c_22721,plain,
! [X0: $i] : c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(unflattening,[status(thm)],[c_22720]) ).
tcf(c_22726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),c_Polynomial_Osmult(X0,X3,X2)))
| ( c_Groups_Ozero__class_Ozero(X0) = X3 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),X2))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_195,c_1466]) ).
tcf(c_22727,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X1)))
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X2 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)) ),
inference(unflattening,[status(thm)],[c_22726]) ).
tcf(c_22738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),X3))
| ( c_Groups_Ozero__class_Ozero(X0) = X2 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),c_Polynomial_Osmult(X0,X2,X3)))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_193,c_1466]) ).
tcf(c_22739,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X2))
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2))) ),
inference(unflattening,[status(thm)],[c_22738]) ).
tcf(c_22750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X2),X3))
| ( c_Groups_Ozero__class_Ozero(X0) = X1 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,X1,X2)),X3))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_149,c_1466]) ).
tcf(c_22751,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X2))
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1)),X2)) ),
inference(unflattening,[status(thm)],[c_22750]) ).
tcf(c_22762,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1)),X2))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_148,c_1466]) ).
tcf(c_22763,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)),X1)) ),
inference(unflattening,[status(thm)],[c_22762]) ).
tcf(c_22771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,X3,X1)),X2))
| ( c_Groups_Ozero__class_Ozero(X0) = X3 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),X2))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_147,c_1466]) ).
tcf(c_22772,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X0)),X1))
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X2 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)) ),
inference(unflattening,[status(thm)],[c_22771]) ).
tcf(c_22783,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2700,c_1466]) ).
tcf(c_22784,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(unflattening,[status(thm)],[c_22783]) ).
tcf(c_22789,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),c_Polynomial_Osmult(X0,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0)),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_145,c_1466]) ).
tcf(c_22790,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) ),
inference(unflattening,[status(thm)],[c_22789]) ).
tcf(c_22887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Divides_Odiv__class_Omod(X0,X2,X3)))
| ( X0 != tc_Int_Oint ) ),
inference(resolution_lifted,[status(thm)],[c_1321,c_1362]) ).
tcf(c_22888,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))) ),
inference(unflattening,[status(thm)],[c_22887]) ).
tcf(c_22898,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(X0,c_Divides_Odiv__class_Omod(X0,X1,X2),X2) = c_Divides_Odiv__class_Omod(X0,X1,X2) )
| ( X0 != tc_Int_Oint ) ),
inference(resolution_lifted,[status(thm)],[c_3330,c_1362]) ).
tcf(c_22899,plain,
! [X0: $i,X1: $i] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),X1) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),
inference(unflattening,[status(thm)],[c_22898]) ).
tcf(c_22919,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X1,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ( X0 != tc_Int_Oint ) ),
inference(resolution_lifted,[status(thm)],[c_3328,c_1362]) ).
tcf(c_22920,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(unflattening,[status(thm)],[c_22919]) ).
tcf(c_22924,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 )
| ( X0 != tc_Int_Oint ) ),
inference(resolution_lifted,[status(thm)],[c_3326,c_1362]) ).
tcf(c_22925,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(unflattening,[status(thm)],[c_22924]) ).
tcf(c_22929,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,c_Groups_Ozero__class_Ozero(X0),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ( X0 != tc_Int_Oint ) ),
inference(resolution_lifted,[status(thm)],[c_3324,c_1362]) ).
tcf(c_22930,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(unflattening,[status(thm)],[c_22929]) ).
tcf(c_22934,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Divides_Odiv__class_Omod(X0,X2,X3)))
| ( X0 != tc_Nat_Onat ) ),
inference(resolution_lifted,[status(thm)],[c_1321,c_1410]) ).
tcf(c_22935,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))) ),
inference(unflattening,[status(thm)],[c_22934]) ).
tcf(c_22945,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(X0,c_Divides_Odiv__class_Omod(X0,X1,X2),X2) = c_Divides_Odiv__class_Omod(X0,X1,X2) )
| ( X0 != tc_Nat_Onat ) ),
inference(resolution_lifted,[status(thm)],[c_3330,c_1410]) ).
tcf(c_22946,plain,
! [X0: $i,X1: $i] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),X1) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),
inference(unflattening,[status(thm)],[c_22945]) ).
tcf(c_22966,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X1,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ( X0 != tc_Nat_Onat ) ),
inference(resolution_lifted,[status(thm)],[c_3328,c_1410]) ).
tcf(c_22967,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(unflattening,[status(thm)],[c_22966]) ).
tcf(c_22971,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 )
| ( X0 != tc_Nat_Onat ) ),
inference(resolution_lifted,[status(thm)],[c_3326,c_1410]) ).
tcf(c_22972,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(unflattening,[status(thm)],[c_22971]) ).
tcf(c_22976,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,c_Groups_Ozero__class_Ozero(X0),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ( X0 != tc_Nat_Onat ) ),
inference(resolution_lifted,[status(thm)],[c_3324,c_1410]) ).
tcf(c_22977,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(unflattening,[status(thm)],[c_22976]) ).
tcf(c_22981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),c_Divides_Odiv__class_Omod(X0,X2,X3)))
| ( tc_Polynomial_Opoly(tc_Complex_Ocomplex) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_1321,c_22492]) ).
tcf(c_22982,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,X2))) ),
inference(unflattening,[status(thm)],[c_22981]) ).
tcf(c_22992,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(X0,c_Divides_Odiv__class_Omod(X0,X1,X2),X2) = c_Divides_Odiv__class_Omod(X0,X1,X2) )
| ( tc_Polynomial_Opoly(tc_Complex_Ocomplex) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_3330,c_22492]) ).
tcf(c_22993,plain,
! [X0: $i,X1: $i] : c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X1),X1) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X1),
inference(unflattening,[status(thm)],[c_22992]) ).
tcf(c_22998,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X2),X1))
| ( tc_Polynomial_Opoly(tc_Complex_Ocomplex) != X0 )
| ( c_Divides_Odiv__class_Omod(X0,X1,X2) != c_Groups_Ozero__class_Ozero(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_1318,c_22492]) ).
tcf(c_22999,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0))
| ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(unflattening,[status(thm)],[c_22998]) ).
tcf(c_23007,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X2,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X0),X1),X2))
| ( tc_Polynomial_Opoly(tc_Complex_Ocomplex) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_1317,c_22492]) ).
tcf(c_23008,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)) ),
inference(unflattening,[status(thm)],[c_23007]) ).
tcf(c_23016,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X1,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ( tc_Polynomial_Opoly(tc_Complex_Ocomplex) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_3328,c_22492]) ).
tcf(c_23017,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unflattening,[status(thm)],[c_23016]) ).
tcf(c_23022,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,X1,c_Groups_Ozero__class_Ozero(X0)) = X1 )
| ( tc_Polynomial_Opoly(tc_Complex_Ocomplex) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_3326,c_22492]) ).
tcf(c_23023,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0,
inference(unflattening,[status(thm)],[c_23022]) ).
tcf(c_23028,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(X0,c_Groups_Ozero__class_Ozero(X0),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ( tc_Polynomial_Opoly(tc_Complex_Ocomplex) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_3324,c_22492]) ).
tcf(c_23029,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unflattening,[status(thm)],[c_23028]) ).
tcf(c_23603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Oplus__class_Oplus(X0,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ( X0 != tc_Int_Oint ) ),
inference(resolution_lifted,[status(thm)],[c_526,c_1339]) ).
tcf(c_23604,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(unflattening,[status(thm)],[c_23603]) ).
tcf(c_27693,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_2343]) ).
tcf(c_27694,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(renaming,[status(thm)],[c_27693]) ).
tcf(c_28281,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)) = X1 )
| ~ class_Groups_Ogroup__add(X0) ),
inference(prop_impl_just,[status(thm)],[c_560]) ).
tcf(c_29201,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2) )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_17676]) ).
tcf(c_29202,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2) ) ),
inference(renaming,[status(thm)],[c_29201]) ).
tcf(c_29211,plain,
! [X0: $i,X1: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X1) = X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_17569]) ).
tcf(c_29212,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X1) = X0 ) ),
inference(renaming,[status(thm)],[c_29211]) ).
tcf(c_30666,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_5536,c_27694]) ).
tcf(c_30667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(bin_hyper_res,[status(thm)],[c_5545,c_27694]) ).
tcf(c_30668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) ),
inference(bin_hyper_res,[status(thm)],[c_5547,c_27694]) ).
tcf(c_30670,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) ) ),
inference(bin_hyper_res,[status(thm)],[c_14445,c_27694]) ).
tcf(c_37700,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(light_normalisation,[status(thm)],[c_16947,c_16973]) ).
tcf(c_38189,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1)) = X0 ) ),
inference(demodulation,[status(thm)],[c_29212,c_17554]) ).
tcf(c_39092,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2) ) ),
inference(demodulation,[status(thm)],[c_29202,c_17554]) ).
tcf(c_39652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3)),
inference(demodulation,[status(thm)],[c_17696,c_17554]) ).
tcf(c_39653,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2) ) ),
inference(demodulation,[status(thm)],[c_39092,c_39652]) ).
tcf(c_40877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),
inference(demodulation,[status(thm)],[c_16941,c_16953]) ).
tcf(c_45741,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)) = X1 )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_28281,c_1458]) ).
tcf(c_45742,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = X0,
inference(unflattening,[status(thm)],[c_45741]) ).
tcf(c_49958,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_2341]) ).
tcf(c_49959,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(renaming,[status(thm)],[c_49958]) ).
tcf(c_49960,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_2343]) ).
tcf(c_49961,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(renaming,[status(thm)],[c_49960]) ).
tcf(c_49998,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_2397]) ).
tcf(c_49999,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(renaming,[status(thm)],[c_49998]) ).
tcf(c_50000,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_2399]) ).
tcf(c_50001,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(renaming,[status(thm)],[c_50000]) ).
tcf(c_50010,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(prop_impl_just,[status(thm)],[c_13039]) ).
tcf(c_50011,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,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_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(renaming,[status(thm)],[c_50010]) ).
tcf(c_50012,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(prop_impl_just,[status(thm)],[c_13046]) ).
tcf(c_50016,plain,
! [X0: $i] :
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(prop_impl_just,[status(thm)],[c_16095]) ).
tcf(c_50022,plain,
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK4) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(prop_impl_just,[status(thm)],[c_51,c_58]) ).
tcf(c_50023,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK4) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(renaming,[status(thm)],[c_50022]) ).
tcf(c_50024,plain,
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK4) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(prop_impl_just,[status(thm)],[c_51,c_59]) ).
tcf(c_50025,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK4) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(renaming,[status(thm)],[c_50024]) ).
tcf(c_50124,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_19982]) ).
tcf(c_50125,plain,
! [X0: $i] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) ) ),
inference(renaming,[status(thm)],[c_50124]) ).
tcf(c_50236,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) )
| ~ class_Rings_Oidom(X0) ),
inference(prop_impl_just,[status(thm)],[c_16064]) ).
tcf(c_50282,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
inference(prop_impl_just,[status(thm)],[c_18435]) ).
tcf(c_50283,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(renaming,[status(thm)],[c_50282]) ).
tcf(c_50286,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ),
inference(prop_impl_just,[status(thm)],[c_18443]) ).
tcf(c_50288,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(prop_impl_just,[status(thm)],[c_18382]) ).
tcf(c_50289,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(renaming,[status(thm)],[c_50288]) ).
tcf(c_50290,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ),
inference(prop_impl_just,[status(thm)],[c_18391]) ).
tcf(c_50294,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(prop_impl_just,[status(thm)],[c_2353]) ).
tcf(c_50322,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_2745]) ).
tcf(c_50323,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(renaming,[status(thm)],[c_50322]) ).
tcf(c_50324,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_2753]) ).
tcf(c_50325,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(renaming,[status(thm)],[c_50324]) ).
tcf(c_50326,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK11(X1,X0)) = X1 )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_2757]) ).
tcf(c_50327,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK11(X1,X0)) = X1 ) ),
inference(renaming,[status(thm)],[c_50326]) ).
tcf(c_50328,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK13(X1,X0)) = X1 )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_2759]) ).
tcf(c_50329,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK13(X1,X0)) = X1 ) ),
inference(renaming,[status(thm)],[c_50328]) ).
tcf(c_50334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))),X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_15967]) ).
tcf(c_50335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( 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,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))),X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) ) ),
inference(renaming,[status(thm)],[c_50334]) ).
tcf(c_50356,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1 )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2769]) ).
tcf(c_50357,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1 ) ),
inference(renaming,[status(thm)],[c_50356]) ).
tcf(c_50358,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2783]) ).
tcf(c_50359,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ) ),
inference(renaming,[status(thm)],[c_50358]) ).
tcf(c_50360,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2791]) ).
tcf(c_50361,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ) ),
inference(renaming,[status(thm)],[c_50360]) ).
tcf(c_50432,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) ),
inference(prop_impl_just,[status(thm)],[c_2273]) ).
tcf(c_50488,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
inference(prop_impl_just,[status(thm)],[c_2751]) ).
tcf(c_50489,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(renaming,[status(thm)],[c_50488]) ).
tcf(c_50490,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
inference(prop_impl_just,[status(thm)],[c_2763]) ).
tcf(c_50491,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
inference(renaming,[status(thm)],[c_50490]) ).
tcf(c_50492,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
inference(prop_impl_just,[status(thm)],[c_2767]) ).
tcf(c_50493,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(renaming,[status(thm)],[c_50492]) ).
tcf(c_50494,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
inference(prop_impl_just,[status(thm)],[c_2749]) ).
tcf(c_50495,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(renaming,[status(thm)],[c_50494]) ).
tcf(c_50500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X0)),X1),X4)) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0) ),
inference(prop_impl_just,[status(thm)],[c_2797]) ).
tcf(c_50501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X0)),X1),X4)) ) ),
inference(renaming,[status(thm)],[c_50500]) ).
tcf(c_50516,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(prop_impl_just,[status(thm)],[c_2755]) ).
tcf(c_50517,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) ),
inference(renaming,[status(thm)],[c_50516]) ).
tcf(c_50518,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(prop_impl_just,[status(thm)],[c_2761]) ).
tcf(c_50519,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) ),
inference(renaming,[status(thm)],[c_50518]) ).
tcf(c_50520,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(prop_impl_just,[status(thm)],[c_2773]) ).
tcf(c_50521,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ) ),
inference(renaming,[status(thm)],[c_50520]) ).
tcf(c_50522,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(prop_impl_just,[status(thm)],[c_2789]) ).
tcf(c_50523,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))) ) ),
inference(renaming,[status(thm)],[c_50522]) ).
tcf(c_50530,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(prop_impl_just,[status(thm)],[c_2286]) ).
tcf(c_50644,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ominus__class_Ominus(X0,X1,X2)),c_Groups_Oplus__class_Oplus(X0,X1,X2)) )
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_16463]) ).
tcf(c_50738,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_2771]) ).
tcf(c_50739,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ),
inference(renaming,[status(thm)],[c_50738]) ).
tcf(c_50740,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_2775]) ).
tcf(c_50741,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2)) ),
inference(renaming,[status(thm)],[c_50740]) ).
tcf(c_50742,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_2779]) ).
tcf(c_50743,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ) ),
inference(renaming,[status(thm)],[c_50742]) ).
tcf(c_50940,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_12387]) ).
tcf(c_50941,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(renaming,[status(thm)],[c_50940]) ).
tcf(c_50942,plain,
! [X0: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_19898]) ).
tcf(c_50943,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(renaming,[status(thm)],[c_50942]) ).
tcf(c_50944,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_19924]) ).
tcf(c_50945,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(renaming,[status(thm)],[c_50944]) ).
tcf(c_50946,plain,
! [X0: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_19936]) ).
tcf(c_50947,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(renaming,[status(thm)],[c_50946]) ).
tcf(c_50948,plain,
! [X0: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_19972]) ).
tcf(c_50949,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(renaming,[status(thm)],[c_50948]) ).
tcf(c_51156,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,X2)
| ( X0 = X2 ) ),
inference(prop_impl_just,[status(thm)],[c_22680]) ).
tcf(c_51157,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,X2) ),
inference(renaming,[status(thm)],[c_51156]) ).
tcf(c_51232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3)),X1),X2),X4) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X3) ),
inference(prop_impl_just,[status(thm)],[c_2793]) ).
tcf(c_51233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X3)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3)),X1),X2),X4) ) ),
inference(renaming,[status(thm)],[c_51232]) ).
tcf(c_51374,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_17929]) ).
tcf(c_51375,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(renaming,[status(thm)],[c_51374]) ).
tcf(c_51446,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(prop_impl_just,[status(thm)],[c_14258]) ).
tcf(c_51448,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(prop_impl_just,[status(thm)],[c_14265]) ).
tcf(c_51452,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(prop_impl_just,[status(thm)],[c_14422]) ).
tcf(c_51464,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(prop_impl_just,[status(thm)],[c_16686]) ).
tcf(c_51468,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_17960]) ).
tcf(c_51469,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(renaming,[status(thm)],[c_51468]) ).
tcf(c_51470,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)) )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_22533]) ).
tcf(c_51471,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)) ) ),
inference(renaming,[status(thm)],[c_51470]) ).
tcf(c_51472,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)) )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_22583]) ).
tcf(c_51473,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)) ) ),
inference(renaming,[status(thm)],[c_51472]) ).
tcf(c_51474,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2) )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_39653]) ).
tcf(c_51475,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2) ) ),
inference(renaming,[status(thm)],[c_51474]) ).
tcf(c_51476,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X1) = X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_17560]) ).
tcf(c_51477,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X1) = X0 ) ),
inference(renaming,[status(thm)],[c_51476]) ).
tcf(c_51478,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X2) )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_22497]) ).
tcf(c_51479,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X2) ) ),
inference(renaming,[status(thm)],[c_51478]) ).
tcf(c_51480,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_22542]) ).
tcf(c_51481,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) ) ),
inference(renaming,[status(thm)],[c_51480]) ).
tcf(c_51482,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_22575]) ).
tcf(c_51483,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) ) ),
inference(renaming,[status(thm)],[c_51482]) ).
tcf(c_51484,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1)) = X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_38189]) ).
tcf(c_51485,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X1 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1)) = X0 ) ),
inference(renaming,[status(thm)],[c_51484]) ).
tcf(c_51488,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X2 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),X1) ) ),
inference(prop_impl_just,[status(thm)],[c_17637]) ).
tcf(c_51492,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)) )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X2 ) ),
inference(prop_impl_just,[status(thm)],[c_17646]) ).
tcf(c_51493,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X2 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)) ) ),
inference(renaming,[status(thm)],[c_51492]) ).
tcf(c_51520,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,X2)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_22689]) ).
tcf(c_51521,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,X2) ),
inference(renaming,[status(thm)],[c_51520]) ).
tcf(c_51522,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,X1,X2)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_22713]) ).
tcf(c_51523,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,X1,X2) ),
inference(renaming,[status(thm)],[c_51522]) ).
tcf(c_51524,plain,
! [X0: $i,X1: $i] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)),X1))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_22763]) ).
tcf(c_51525,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)),X1)) ),
inference(renaming,[status(thm)],[c_51524]) ).
tcf(c_51534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X4,X0),X1,c_Polynomial_Osmult(tc_Complex_Ocomplex,X4,X2),c_Polynomial_Osmult(tc_Complex_Ocomplex,X4,X3))
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_22671]) ).
tcf(c_51540,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X2 )
| ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,X2)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,X2))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,X2),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))),X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),X2) ) ),
inference(prop_impl_just,[status(thm)],[c_22524]) ).
tcf(c_51544,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,X1,X2)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X2 ) ),
inference(prop_impl_just,[status(thm)],[c_22704]) ).
tcf(c_51545,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X2 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,X1,X2) ),
inference(renaming,[status(thm)],[c_51544]) ).
tcf(c_51564,plain,
! [X0: $i,X1: $i] :
( ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)) ),
inference(prop_impl_just,[status(thm)],[c_23008]) ).
tcf(c_51568,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) ),
inference(prop_impl_just,[status(thm)],[c_22790]) ).
tcf(c_51572,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0))
| ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(prop_impl_just,[status(thm)],[c_22999]) ).
tcf(c_52924,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_30666,c_49959]) ).
tcf(c_72166,definition,
iPr_def_10 = tc_Polynomial_Opoly(tc_Complex_Ocomplex),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_72167,definition,
iPr_def_11 = c_Rings_Odvd__class_Odvd(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_72168,definition,
iPr_def_12 = hAPP(iPr_def_11,v_p),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_72169,definition,
iPr_def_13 = c_Power_Opower__class_Opower(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_72170,definition,
iPr_def_14 = hAPP(iPr_def_13,v_q),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_72171,definition,
iPr_def_15 = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_72172,definition,
iPr_def_16 = hAPP(iPr_def_14,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_72173,definition,
iPr_def_17 = hAPP(iPr_def_12,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_72174,definition,
iPr_def_18 = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_72175,definition,
iPr_def_19 = hAPP(iPr_def_18,sK21),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_72176,definition,
iPr_def_20 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_72177,definition,
iPr_def_21 = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_72178,definition,
iPr_def_22 = hAPP(iPr_def_21,sK21),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_72179,negated_conjecture,
( ( iPr_def_19 = iPr_def_20 )
| ~ hBOOL(iPr_def_17) ),
inference(demodulation,[status(thm)],[c_1533,c_72176,c_72174,c_72175,c_72171,c_72169,c_72170,c_72172,c_72166,c_72167,c_72168,c_72173]) ).
tcf(c_72180,negated_conjecture,
( ~ hBOOL(iPr_def_17)
| ( iPr_def_22 != iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1532,c_72177,c_72178]) ).
tcf(c_90482,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK7,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_11601,c_72171]) ).
tcf(c_90483,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_11606,c_72171]) ).
tcf(c_90491,plain,
! [X0: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,iPr_def_20) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_16680,c_72176]) ).
tcf(c_90492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),iPr_def_20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),iPr_def_20)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),iPr_def_20),
inference(superposition,[status(thm)],[c_90491,c_16673]) ).
tcf(c_90493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),iPr_def_20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2)),iPr_def_20),
inference(superposition,[status(thm)],[c_90491,c_16673]) ).
tcf(c_90496,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,iPr_def_20)) = iPr_def_20,
inference(superposition,[status(thm)],[c_90491,c_16698]) ).
tcf(c_90498,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_90496,c_90491]) ).
tcf(c_90499,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X2),X1),
inference(superposition,[status(thm)],[c_16698,c_16704]) ).
tcf(c_90500,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,iPr_def_20)),
inference(superposition,[status(thm)],[c_90491,c_16704]) ).
tcf(c_90501,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),X1),
inference(superposition,[status(thm)],[c_16698,c_16704]) ).
tcf(c_90502,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,iPr_def_20),iPr_def_20),
inference(superposition,[status(thm)],[c_90491,c_16704]) ).
tcf(c_90503,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_90502,c_90491]) ).
tcf(c_90508,plain,
! [X0: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X0) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_16710,c_72176]) ).
tcf(c_90509,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,X0),X1),
inference(superposition,[status(thm)],[c_90508,c_16704]) ).
tcf(c_90510,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),iPr_def_20) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,iPr_def_20),X1),
inference(superposition,[status(thm)],[c_90508,c_16704]) ).
tcf(c_90517,plain,
( class_Groups_Ocancel__comm__monoid__add(iPr_def_10)
| ~ class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1322]) ).
tcf(c_90518,plain,
class_Groups_Ocancel__comm__monoid__add(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90517,c_1323]) ).
tcf(c_90523,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(iPr_def_10)
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1473]) ).
tcf(c_90524,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90523,c_1470]) ).
tcf(c_90529,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1474]) ).
tcf(c_90536,plain,
( class_Groups_Oordered__ab__semigroup__add__imp__le(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1475]) ).
tcf(c_90551,plain,
( class_Rings_Olinordered__semiring__1__strict(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1477]) ).
tcf(c_90562,plain,
( class_Rings_Olinordered__semiring__strict(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1478]) ).
tcf(c_90573,plain,
( class_Groups_Oordered__ab__semigroup__add(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1479]) ).
tcf(c_90584,plain,
( class_Groups_Oordered__comm__monoid__add(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1480]) ).
tcf(c_90591,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X2),X1),
inference(superposition,[status(thm)],[c_16698,c_16716]) ).
tcf(c_90592,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),iPr_def_20) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,iPr_def_20)),
inference(superposition,[status(thm)],[c_90491,c_16716]) ).
tcf(c_90593,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,X0),X1),
inference(superposition,[status(thm)],[c_90508,c_16716]) ).
tcf(c_90594,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),X1),
inference(superposition,[status(thm)],[c_16698,c_16716]) ).
tcf(c_90595,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),iPr_def_20) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,iPr_def_20),iPr_def_20),
inference(superposition,[status(thm)],[c_90491,c_16716]) ).
tcf(c_90596,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),iPr_def_20) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,iPr_def_20),X1),
inference(superposition,[status(thm)],[c_90508,c_16716]) ).
tcf(c_90597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X5),X4)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X5),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))),X4),
inference(superposition,[status(thm)],[c_16716,c_16673]) ).
tcf(c_90598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X5),X1),X4)),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X5,X1)),X3)),X4),
inference(superposition,[status(thm)],[c_16716,c_16673]) ).
tcf(c_90599,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),iPr_def_20) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_90595,c_90491]) ).
tcf(c_90612,plain,
( class_Groups_Olinordered__ab__group__add(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1481]) ).
tcf(c_90619,plain,
( class_Groups_Ocancel__ab__semigroup__add(iPr_def_10)
| ~ class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1482]) ).
tcf(c_90620,plain,
class_Groups_Ocancel__ab__semigroup__add(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90619,c_1323]) ).
tcf(c_90625,plain,
( class_Rings_Oring__1__no__zero__divisors(iPr_def_10)
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1483]) ).
tcf(c_90626,plain,
class_Rings_Oring__1__no__zero__divisors(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90625,c_1470]) ).
tcf(c_90631,plain,
( class_Rings_Oordered__cancel__semiring(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1484]) ).
tcf(c_90646,plain,
( class_Rings_Olinordered__ring__strict(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1485]) ).
tcf(c_90657,plain,
( class_Rings_Oring__no__zero__divisors(iPr_def_10)
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1486]) ).
tcf(c_90658,plain,
class_Rings_Oring__no__zero__divisors(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90657,c_1470]) ).
tcf(c_90663,plain,
( class_Rings_Oordered__comm__semiring(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1487]) ).
tcf(c_90674,plain,
( class_Rings_Olinordered__semiring__1(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1488]) ).
tcf(c_90685,plain,
( class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1489]) ).
tcf(c_90692,plain,
( class_Groups_Ocancel__semigroup__add(iPr_def_10)
| ~ class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1490]) ).
tcf(c_90693,plain,
class_Groups_Ocancel__semigroup__add(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90692,c_1323]) ).
tcf(c_90698,plain,
( class_Rings_Olinordered__semiring(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1491]) ).
tcf(c_90705,plain,
( class_Rings_Olinordered__semidom(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1492]) ).
tcf(c_90724,plain,
( class_Groups_Oab__semigroup__mult(iPr_def_10)
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1493]) ).
tcf(c_90725,plain,
class_Groups_Oab__semigroup__mult(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90724,c_1448]) ).
tcf(c_90730,plain,
( class_Groups_Ocomm__monoid__mult(iPr_def_10)
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1494]) ).
tcf(c_90731,plain,
class_Groups_Ocomm__monoid__mult(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90730,c_1447]) ).
tcf(c_90736,plain,
( class_Groups_Oab__semigroup__add(iPr_def_10)
| ~ class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1495]) ).
tcf(c_90737,plain,
class_Groups_Oab__semigroup__add(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90736,c_1446]) ).
tcf(c_90742,plain,
( class_Rings_Oordered__semiring(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1496]) ).
tcf(c_90749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X5),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X4),
inference(superposition,[status(thm)],[c_16929,c_16673]) ).
tcf(c_90750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X5)),X1),X4)),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X5),X1)),X3)),X4),
inference(superposition,[status(thm)],[c_16929,c_16673]) ).
tcf(c_90757,plain,
( class_Rings_Ono__zero__divisors(iPr_def_10)
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1497]) ).
tcf(c_90758,plain,
class_Rings_Ono__zero__divisors(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90757,c_1470]) ).
tcf(c_90763,plain,
( class_Groups_Ocomm__monoid__add(iPr_def_10)
| ~ class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1498]) ).
tcf(c_90764,plain,
class_Groups_Ocomm__monoid__add(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90763,c_1446]) ).
tcf(c_90769,plain,
( class_Rings_Olinordered__ring(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1499]) ).
tcf(c_90776,plain,
( class_Rings_Olinordered__idom(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1500]) ).
tcf(c_90791,plain,
( class_Rings_Ocomm__semiring__1(iPr_def_10)
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1501]) ).
tcf(c_90792,plain,
class_Rings_Ocomm__semiring__1(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90791,c_1447]) ).
tcf(c_90797,plain,
( class_Rings_Ocomm__semiring__0(iPr_def_10)
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1502]) ).
tcf(c_90798,plain,
class_Rings_Ocomm__semiring__0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90797,c_1448]) ).
tcf(c_90803,plain,
( class_Groups_Oab__group__add(iPr_def_10)
| ~ class_Groups_Oab__group__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1505]) ).
tcf(c_90804,plain,
class_Groups_Oab__group__add(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90803,c_1452]) ).
tcf(c_90809,plain,
( class_Rings_Oordered__ring(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1507]) ).
tcf(c_90817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3)),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X5),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3))),X4),
inference(superposition,[status(thm)],[c_16935,c_16673]) ).
tcf(c_90818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X5)),X4)),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X5)),X3)),X4),
inference(superposition,[status(thm)],[c_16935,c_16673]) ).
tcf(c_90819,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X1)),
inference(superposition,[status(thm)],[c_16935,c_16929]) ).
tcf(c_90827,plain,
( class_Orderings_Opreorder(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1508]) ).
tcf(c_90834,plain,
( class_Orderings_Olinorder(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1509]) ).
tcf(c_90841,plain,
( class_Groups_Omonoid__mult(iPr_def_10)
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1510]) ).
tcf(c_90842,plain,
class_Groups_Omonoid__mult(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90841,c_1447]) ).
tcf(c_90847,plain,
( class_Rings_Ocomm__ring__1(iPr_def_10)
| ~ class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1511]) ).
tcf(c_90848,plain,
class_Rings_Ocomm__ring__1(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90847,c_1455]) ).
tcf(c_90861,plain,
( class_Rings_Osemiring__0(iPr_def_10)
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1513]) ).
tcf(c_90862,plain,
class_Rings_Osemiring__0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90861,c_1448]) ).
tcf(c_90867,plain,
( class_Groups_Ogroup__add(iPr_def_10)
| ~ class_Groups_Oab__group__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1514]) ).
tcf(c_90868,plain,
class_Groups_Ogroup__add(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90867,c_1452]) ).
tcf(c_90873,plain,
( class_Rings_Omult__zero(iPr_def_10)
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1515]) ).
tcf(c_90874,plain,
class_Rings_Omult__zero(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90873,c_1448]) ).
tcf(c_90879,plain,
( class_Rings_Ocomm__ring(iPr_def_10)
| ~ class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1516]) ).
tcf(c_90880,plain,
class_Rings_Ocomm__ring(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90879,c_1460]) ).
tcf(c_90881,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X0)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X1)),
inference(superposition,[status(thm)],[c_16752,c_16953]) ).
tcf(c_90888,plain,
( class_Orderings_Oorder(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1517]) ).
tcf(c_90895,plain,
( class_Int_Oring__char__0(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1518]) ).
tcf(c_90902,plain,
( class_Rings_Osemiring(iPr_def_10)
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1519]) ).
tcf(c_90903,plain,
class_Rings_Osemiring(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90902,c_1448]) ).
tcf(c_90908,plain,
( class_Orderings_Oord(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1520]) ).
tcf(c_90927,plain,
( class_Groups_Ouminus(iPr_def_10)
| ~ class_Groups_Oab__group__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1521]) ).
tcf(c_90928,plain,
class_Groups_Ouminus(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90927,c_1452]) ).
tcf(c_90933,plain,
( class_Rings_Oring__1(iPr_def_10)
| ~ class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1522]) ).
tcf(c_90934,plain,
class_Rings_Oring__1(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90933,c_1455]) ).
tcf(c_90939,plain,
( class_Groups_Ominus(iPr_def_10)
| ~ class_Groups_Oab__group__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1523]) ).
tcf(c_90940,plain,
class_Groups_Ominus(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90939,c_1452]) ).
tcf(c_90945,plain,
( class_Power_Opower(iPr_def_10)
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1524]) ).
tcf(c_90946,plain,
class_Power_Opower(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90945,c_1447]) ).
tcf(c_90947,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),iPr_def_20) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_16961,c_72176]) ).
tcf(c_90948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),iPr_def_20)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,iPr_def_20),X3)),iPr_def_20),
inference(superposition,[status(thm)],[c_90947,c_16673]) ).
tcf(c_90949,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_90947,c_16953]) ).
tcf(c_90950,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_90947,c_16935]) ).
tcf(c_90951,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),iPr_def_20) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),iPr_def_20)),
inference(superposition,[status(thm)],[c_90947,c_16929]) ).
tcf(c_90952,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),iPr_def_20)),
inference(superposition,[status(thm)],[c_90947,c_16752]) ).
tcf(c_90953,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),iPr_def_20) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),iPr_def_20),iPr_def_20),
inference(superposition,[status(thm)],[c_90947,c_16929]) ).
tcf(c_90954,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),iPr_def_20),iPr_def_20),
inference(superposition,[status(thm)],[c_90947,c_16752]) ).
tcf(c_90955,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,iPr_def_20)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),iPr_def_20),
inference(superposition,[status(thm)],[c_90947,c_16953]) ).
tcf(c_90956,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,iPr_def_20)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),iPr_def_20),
inference(superposition,[status(thm)],[c_90947,c_16935]) ).
tcf(c_90957,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_90954,c_90947]) ).
tcf(c_90958,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),iPr_def_20) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_90953,c_90947]) ).
tcf(c_90972,plain,
( class_Groups_Ozero(iPr_def_10)
| ~ class_Groups_Ozero(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1525]) ).
tcf(c_90973,plain,
class_Groups_Ozero(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90972,c_1468]) ).
tcf(c_90978,plain,
( class_Rings_Oring(iPr_def_10)
| ~ class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1526]) ).
tcf(c_90979,plain,
class_Rings_Oring(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90978,c_1460]) ).
tcf(c_90984,plain,
( class_Rings_Oidom(iPr_def_10)
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1527]) ).
tcf(c_90985,plain,
class_Rings_Oidom(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90984,c_1470]) ).
tcf(c_90990,plain,
( class_Rings_Odvd(iPr_def_10)
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1529]) ).
tcf(c_90991,plain,
class_Rings_Odvd(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_90990,c_1447]) ).
tcf(c_90992,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X0) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_16967,c_72176]) ).
tcf(c_90993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,X1),X3)),X2)),
inference(superposition,[status(thm)],[c_90992,c_16673]) ).
tcf(c_90994,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X1)),
inference(superposition,[status(thm)],[c_90992,c_16953]) ).
tcf(c_90995,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X1)),
inference(superposition,[status(thm)],[c_90992,c_16935]) ).
tcf(c_90996,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,X0)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_90992,c_16929]) ).
tcf(c_90997,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,X0)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_90992,c_16752]) ).
tcf(c_90998,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,iPr_def_20)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),iPr_def_20),
inference(superposition,[status(thm)],[c_90992,c_16929]) ).
tcf(c_90999,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,iPr_def_20)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),iPr_def_20),
inference(superposition,[status(thm)],[c_90992,c_16752]) ).
tcf(c_91000,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X0),iPr_def_20),
inference(superposition,[status(thm)],[c_90992,c_16953]) ).
tcf(c_91001,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X0),iPr_def_20),
inference(superposition,[status(thm)],[c_90992,c_16935]) ).
tcf(c_91002,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_91001,c_90992]) ).
tcf(c_91003,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_91000,c_90992]) ).
tcf(c_91004,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,iPr_def_20)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,iPr_def_20)),
inference(light_normalisation,[status(thm)],[c_90999,c_90955]) ).
tcf(c_91005,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,iPr_def_20)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,iPr_def_20)),
inference(light_normalisation,[status(thm)],[c_90998,c_90956]) ).
tcf(c_91006,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,X0)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,X1)),
inference(light_normalisation,[status(thm)],[c_90997,c_90949]) ).
tcf(c_91007,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,X0)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,X1)),
inference(light_normalisation,[status(thm)],[c_90996,c_90950]) ).
tcf(c_91008,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,X0),X1)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),X1),
inference(light_normalisation,[status(thm)],[c_90993,c_90992]) ).
tcf(c_91009,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),X1),
inference(light_normalisation,[status(thm)],[c_91008,c_90593]) ).
tcf(c_91019,plain,
c_Groups_Ozero__class_Ozero(iPr_def_10) != v_p,
inference(light_normalisation,[status(thm)],[c_50,c_72166]) ).
tcf(c_91020,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X0)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X0),
inference(superposition,[status(thm)],[c_90498,c_16698]) ).
tcf(c_91030,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15),
inference(superposition,[status(thm)],[c_90482,c_474]) ).
tcf(c_91032,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK7,iPr_def_15),
inference(superposition,[status(thm)],[c_90482,c_651]) ).
tcf(c_91033,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,iPr_def_15),
inference(superposition,[status(thm)],[c_90483,c_651]) ).
tcf(c_91042,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20),
inference(superposition,[status(thm)],[c_90947,c_16973]) ).
tcf(c_91043,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20),
inference(superposition,[status(thm)],[c_90992,c_16973]) ).
tcf(c_91044,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2),
inference(superposition,[status(thm)],[c_16973,c_16698]) ).
tcf(c_91045,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_91043,c_90498]) ).
tcf(c_91047,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2),
inference(light_normalisation,[status(thm)],[c_91044,c_17554]) ).
tcf(c_91065,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != iPr_def_20,
inference(light_normalisation,[status(thm)],[c_19946,c_72176]) ).
tcf(c_91070,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != iPr_def_15,
inference(light_normalisation,[status(thm)],[c_51,c_72171]) ).
tcf(c_91087,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_90482,c_457]) ).
tcf(c_91089,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,X0) = X0,
inference(light_normalisation,[status(thm)],[c_17042,c_72176]) ).
tcf(c_91091,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,sK7),
inference(superposition,[status(thm)],[c_90482,c_458]) ).
tcf(c_91092,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,v_n____),
inference(superposition,[status(thm)],[c_90483,c_458]) ).
tcf(c_91110,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,X0,X0)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72166,c_1234]) ).
tcf(c_91118,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,iPr_def_20) = X0,
inference(light_normalisation,[status(thm)],[c_17048,c_72176]) ).
tcf(c_91120,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_440,c_165]) ).
tcf(c_91125,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72176,c_224]) ).
tcf(c_91132,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72176,c_362]) ).
tcf(c_91136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_17614,c_16673]) ).
tcf(c_91137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_17614,c_16673]) ).
tcf(c_91138,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_17614,c_16716]) ).
tcf(c_91139,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_17614,c_16704]) ).
tcf(c_91140,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),
inference(superposition,[status(thm)],[c_17614,c_16698]) ).
tcf(c_91141,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_17614,c_16716]) ).
tcf(c_91142,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_17614,c_16704]) ).
tcf(c_91144,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),
inference(light_normalisation,[status(thm)],[c_91142,c_17614]) ).
tcf(c_91145,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),
inference(light_normalisation,[status(thm)],[c_91141,c_17614]) ).
tcf(c_91150,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),
inference(superposition,[status(thm)],[c_16973,c_45742]) ).
tcf(c_91151,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),
inference(superposition,[status(thm)],[c_45742,c_16698]) ).
tcf(c_91152,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),
inference(light_normalisation,[status(thm)],[c_91151,c_16698]) ).
tcf(c_91175,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_695,c_663]) ).
tcf(c_91179,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1),
inference(superposition,[status(thm)],[c_90947,c_17554]) ).
tcf(c_91180,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1),
inference(superposition,[status(thm)],[c_90992,c_17554]) ).
tcf(c_91181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X3),X2),
inference(superposition,[status(thm)],[c_17554,c_16716]) ).
tcf(c_91182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X3),X2),
inference(superposition,[status(thm)],[c_17554,c_16704]) ).
tcf(c_91183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X1),
inference(superposition,[status(thm)],[c_17554,c_16716]) ).
tcf(c_91184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X1),
inference(superposition,[status(thm)],[c_17554,c_16704]) ).
tcf(c_91185,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),
inference(superposition,[status(thm)],[c_17554,c_17614]) ).
tcf(c_91186,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,iPr_def_20)) = iPr_def_20,
inference(superposition,[status(thm)],[c_17554,c_90491]) ).
tcf(c_91199,plain,
( ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Polynomial_Opos__poly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_72166,c_822]) ).
tcf(c_91202,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1098,c_1095]) ).
tcf(c_91217,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(iPr_def_11,X0),X0))
| ~ class_Rings_Ocomm__semiring__1(iPr_def_10) ),
inference(superposition,[status(thm)],[c_72167,c_88]) ).
tcf(c_91218,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(iPr_def_11,X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_91217,c_90792]) ).
tcf(c_91220,plain,
hBOOL(hAPP(iPr_def_12,v_p)),
inference(superposition,[status(thm)],[c_72168,c_91218]) ).
tcf(c_91226,plain,
( ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20) ),
inference(superposition,[status(thm)],[c_72176,c_223]) ).
tcf(c_91249,plain,
( ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20) ),
inference(superposition,[status(thm)],[c_72176,c_363]) ).
tcf(c_91252,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( X0 = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(light_normalisation,[status(thm)],[c_17598,c_72176]) ).
tcf(c_91262,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = X1 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_16698,c_91252]) ).
tcf(c_91263,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = X2 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_17554,c_91252]) ).
tcf(c_91290,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_551,c_101]) ).
tcf(c_91291,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_551,c_373]) ).
tcf(c_91292,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(superposition,[status(thm)],[c_551,c_165]) ).
tcf(c_91293,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0,
inference(superposition,[status(thm)],[c_551,c_129]) ).
tcf(c_91294,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_551,c_331]) ).
tcf(c_91305,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_912,c_911]) ).
tcf(c_91309,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK7,iPr_def_15),
inference(superposition,[status(thm)],[c_90482,c_91294]) ).
tcf(c_91310,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,iPr_def_15),
inference(superposition,[status(thm)],[c_90483,c_91294]) ).
tcf(c_91318,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15),
inference(superposition,[status(thm)],[c_90482,c_91291]) ).
tcf(c_91324,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,sK7),
inference(superposition,[status(thm)],[c_90482,c_91292]) ).
tcf(c_91325,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,v_n____),
inference(superposition,[status(thm)],[c_90483,c_91292]) ).
tcf(c_91331,plain,
sK7 != iPr_def_15,
inference(superposition,[status(thm)],[c_90482,c_91293]) ).
tcf(c_91332,plain,
v_n____ != iPr_def_15,
inference(superposition,[status(thm)],[c_90483,c_91293]) ).
tcf(c_91336,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),
inference(superposition,[status(thm)],[c_16973,c_17690]) ).
tcf(c_91337,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),
inference(superposition,[status(thm)],[c_45742,c_17690]) ).
tcf(c_91338,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,iPr_def_20)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,iPr_def_20),
inference(superposition,[status(thm)],[c_90498,c_17690]) ).
tcf(c_91339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X4),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3))),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),
inference(superposition,[status(thm)],[c_17690,c_16673]) ).
tcf(c_91340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X4),X3))),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),
inference(superposition,[status(thm)],[c_17690,c_16673]) ).
tcf(c_91341,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = X0 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_17690,c_91252]) ).
tcf(c_91342,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(superposition,[status(thm)],[c_17690,c_16716]) ).
tcf(c_91343,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(superposition,[status(thm)],[c_17690,c_16704]) ).
tcf(c_91344,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))),
inference(superposition,[status(thm)],[c_17690,c_16698]) ).
tcf(c_91345,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(superposition,[status(thm)],[c_17690,c_16716]) ).
tcf(c_91346,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(superposition,[status(thm)],[c_17690,c_16704]) ).
tcf(c_91347,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2)),
inference(superposition,[status(thm)],[c_17690,c_17554]) ).
tcf(c_91348,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X0)) = iPr_def_20,
inference(superposition,[status(thm)],[c_17690,c_90508]) ).
tcf(c_91356,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))),
inference(light_normalisation,[status(thm)],[c_91347,c_17554]) ).
tcf(c_91357,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(light_normalisation,[status(thm)],[c_91346,c_17690]) ).
tcf(c_91358,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(light_normalisation,[status(thm)],[c_91345,c_17690]) ).
tcf(c_91377,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),
inference(superposition,[status(thm)],[c_925,c_91175]) ).
tcf(c_91378,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),
inference(superposition,[status(thm)],[c_925,c_695]) ).
tcf(c_91388,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,sK7) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_90482,c_1066]) ).
tcf(c_91389,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,v_n____) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_90483,c_1066]) ).
tcf(c_91397,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = sK7,
inference(superposition,[status(thm)],[c_90482,c_1067]) ).
tcf(c_91398,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = v_n____,
inference(superposition,[status(thm)],[c_90483,c_1067]) ).
tcf(c_91410,plain,
v_n____ = sK7,
inference(demodulation,[status(thm)],[c_91397,c_91398]) ).
tcf(c_91419,plain,
! [X0: $i] : c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10),X0),
inference(light_normalisation,[status(thm)],[c_22698,c_72166]) ).
tcf(c_91420,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(iPr_def_10,X0,X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_23017,c_72166]) ).
tcf(c_91421,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(iPr_def_10)) = X0,
inference(light_normalisation,[status(thm)],[c_23023,c_72166]) ).
tcf(c_91432,plain,
( ~ class_Rings_Olinordered__semidom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_362,c_49959]) ).
tcf(c_91435,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0),X0),
inference(superposition,[status(thm)],[c_911,c_49959]) ).
tcf(c_91436,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),
inference(superposition,[status(thm)],[c_1095,c_49959]) ).
tcf(c_91444,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1098,c_91436]) ).
tcf(c_91453,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X0),
inference(superposition,[status(thm)],[c_331,c_50323]) ).
tcf(c_91454,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_373,c_50323]) ).
tcf(c_91457,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_11697,c_50323]) ).
tcf(c_91458,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(superposition,[status(thm)],[c_91294,c_50323]) ).
tcf(c_91459,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_91291,c_50323]) ).
tcf(c_91461,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_91318,c_50323]) ).
tcf(c_91462,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1) = iPr_def_20 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),X1) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_17702,c_91252]) ).
tcf(c_91463,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_17702,c_16716]) ).
tcf(c_91464,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_17702,c_16704]) ).
tcf(c_91465,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17702,c_16716]) ).
tcf(c_91466,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17702,c_16704]) ).
tcf(c_91479,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(iPr_def_11,X0),c_Groups_Ozero__class_Ozero(iPr_def_10)))
| ~ class_Rings_Ocomm__semiring__1(iPr_def_10) ),
inference(superposition,[status(thm)],[c_72167,c_66]) ).
tcf(c_91480,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),X0),iPr_def_20))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72176,c_66]) ).
tcf(c_91481,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),X0),iPr_def_20)),
inference(forward_subsumption_resolution,[status(thm)],[c_91480,c_1447]) ).
tcf(c_91482,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(iPr_def_11,X0),c_Groups_Ozero__class_Ozero(iPr_def_10))),
inference(forward_subsumption_resolution,[status(thm)],[c_91479,c_90792]) ).
tcf(c_91508,plain,
! [X0: $i] :
( ~ class_Rings_Olinordered__semidom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(superposition,[status(thm)],[c_227,c_50323]) ).
tcf(c_91519,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_301,c_363]) ).
tcf(c_91521,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Orderings_Olinorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_301,c_91249]) ).
tcf(c_91530,plain,
hBOOL(hAPP(iPr_def_12,c_Groups_Ozero__class_Ozero(iPr_def_10))),
inference(superposition,[status(thm)],[c_72168,c_91482]) ).
tcf(c_91535,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_912,c_91435]) ).
tcf(c_91541,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(iPr_def_11,c_Groups_Oone__class_Oone(iPr_def_10)),X0))
| ~ class_Rings_Ocomm__semiring__1(iPr_def_10) ),
inference(superposition,[status(thm)],[c_72167,c_311]) ).
tcf(c_91542,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(iPr_def_11,c_Groups_Oone__class_Oone(iPr_def_10)),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_91541,c_90792]) ).
tcf(c_91548,plain,
! [X0: $i] : c_Polynomial_Osmult(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) = X0,
inference(superposition,[status(thm)],[c_1360,c_352]) ).
tcf(c_91549,plain,
! [X0: $i] : c_Polynomial_Osmult(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X0,
inference(superposition,[status(thm)],[c_1408,c_352]) ).
tcf(c_91550,plain,
! [X0: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0) = X0,
inference(superposition,[status(thm)],[c_1447,c_352]) ).
tcf(c_91551,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osmult(tc_Polynomial_Opoly(X0),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X1) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_352]) ).
tcf(c_91552,plain,
! [X0: $i] : c_Polynomial_Osmult(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),X0) = X0,
inference(superposition,[status(thm)],[c_90792,c_352]) ).
tcf(c_91560,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2) = iPr_def_20 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_17708,c_91252]) ).
tcf(c_91561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17708,c_16716]) ).
tcf(c_91562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17708,c_16704]) ).
tcf(c_91563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17708,c_16716]) ).
tcf(c_91564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17708,c_16704]) ).
tcf(c_91587,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_421,c_49959]) ).
tcf(c_91589,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_421,c_165]) ).
tcf(c_91590,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Orderings_Olinorder(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_421,c_363]) ).
tcf(c_91591,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_421,c_91120]) ).
tcf(c_91592,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Orderings_Olinorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_421,c_91249]) ).
tcf(c_91593,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_421,c_91292]) ).
tcf(c_91603,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_91587,c_1414]) ).
tcf(c_91610,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)),
inference(superposition,[status(thm)],[c_90483,c_491]) ).
tcf(c_91611,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X1),
inference(superposition,[status(thm)],[c_491,c_50323]) ).
tcf(c_91617,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)),
inference(superposition,[status(thm)],[c_90483,c_492]) ).
tcf(c_91618,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X0),
inference(superposition,[status(thm)],[c_492,c_50323]) ).
tcf(c_91627,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(iPr_def_10)) = X0,
inference(superposition,[status(thm)],[c_90764,c_500]) ).
tcf(c_91629,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(demodulation,[status(thm)],[c_91617,c_551]) ).
tcf(c_91630,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_n____),
inference(superposition,[status(thm)],[c_91629,c_50323]) ).
tcf(c_91635,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(superposition,[status(thm)],[c_331,c_91603]) ).
tcf(c_91636,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(superposition,[status(thm)],[c_373,c_91603]) ).
tcf(c_91637,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_224,c_91603]) ).
tcf(c_91638,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_227,c_91603]) ).
tcf(c_91640,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(superposition,[status(thm)],[c_492,c_91603]) ).
tcf(c_91641,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
inference(superposition,[status(thm)],[c_491,c_91603]) ).
tcf(c_91642,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_11697,c_91603]) ).
tcf(c_91643,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91294,c_91603]) ).
tcf(c_91644,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91291,c_91603]) ).
tcf(c_91646,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15),
inference(superposition,[status(thm)],[c_91318,c_91603]) ).
tcf(c_91647,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91629,c_91603]) ).
tcf(c_91650,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(demodulation,[status(thm)],[c_91610,c_551]) ).
tcf(c_91651,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_91650,c_50323]) ).
tcf(c_91652,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91650,c_91603]) ).
tcf(c_91661,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0) = X0,
inference(superposition,[status(thm)],[c_90764,c_504]) ).
tcf(c_91663,plain,
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Oone__class_Oone(iPr_def_10))
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_91661,c_227]) ).
tcf(c_91672,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1)) = X1 )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1514,c_560]) ).
tcf(c_91673,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0)) = X0,
inference(superposition,[status(thm)],[c_90868,c_560]) ).
tcf(c_91682,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Olinordered__idom(X0) ),
inference(superposition,[status(thm)],[c_1481,c_571]) ).
tcf(c_91690,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1458,c_575]) ).
tcf(c_91692,plain,
c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10)) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_90868,c_575]) ).
tcf(c_91701,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_643]) ).
tcf(c_91713,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_644]) ).
tcf(c_91725,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = X1 )
| ~ class_Rings_Oidom(X0) ),
inference(superposition,[status(thm)],[c_1473,c_645]) ).
tcf(c_91733,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Rings_Olinordered__semidom(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_224,c_675]) ).
tcf(c_91735,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_679,c_675]) ).
tcf(c_91736,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_695,c_675]) ).
tcf(c_91737,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_91378,c_675]) ).
tcf(c_91745,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ class_Orderings_Olinorder(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_301,c_676]) ).
tcf(c_91750,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_661,c_676]) ).
tcf(c_91753,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),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_91175,c_676]) ).
tcf(c_91757,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_91745,c_1368]) ).
tcf(c_91767,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_91753,c_675]) ).
tcf(c_91768,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_91753,c_663]) ).
tcf(c_91776,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91757,c_675]) ).
tcf(c_91782,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_91757,c_675]) ).
tcf(c_91783,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_91757,c_663]) ).
tcf(c_91805,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_fun(X1,X0),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,X0),X2)) = X2 )
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(superposition,[status(thm)],[c_1326,c_870]) ).
tcf(c_91806,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) = X0,
inference(superposition,[status(thm)],[c_1427,c_870]) ).
tcf(c_91811,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != iPr_def_20,
inference(light_normalisation,[status(thm)],[c_19953,c_72176]) ).
tcf(c_91818,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(superposition,[status(thm)],[c_1373,c_1106]) ).
tcf(c_91819,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0,
inference(superposition,[status(thm)],[c_1458,c_1106]) ).
tcf(c_91821,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(iPr_def_10)) = X0,
inference(superposition,[status(thm)],[c_90868,c_1106]) ).
tcf(c_91822,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,iPr_def_20) = X0,
inference(light_normalisation,[status(thm)],[c_91819,c_72176]) ).
tcf(c_91830,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1452,c_1109]) ).
tcf(c_91831,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X1,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1505,c_1109]) ).
tcf(c_91832,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(iPr_def_10,X0,X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_90804,c_1109]) ).
tcf(c_91833,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_91830,c_72176]) ).
tcf(c_91846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3),X2)),iPr_def_20)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),iPr_def_20)),X2),
inference(superposition,[status(thm)],[c_91822,c_16673]) ).
tcf(c_91847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X2)),X3),
inference(superposition,[status(thm)],[c_91822,c_16673]) ).
tcf(c_91853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),X1)),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X1),
inference(superposition,[status(thm)],[c_91833,c_16673]) ).
tcf(c_91854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X3)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),X3),
inference(superposition,[status(thm)],[c_91833,c_16673]) ).
tcf(c_91855,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0),X1) = iPr_def_20,
inference(superposition,[status(thm)],[c_91833,c_16716]) ).
tcf(c_91856,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0)),X1) = iPr_def_20,
inference(superposition,[status(thm)],[c_91833,c_16929]) ).
tcf(c_91857,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X1)) = iPr_def_20,
inference(superposition,[status(thm)],[c_91833,c_16935]) ).
tcf(c_91860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X3)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),X3),
inference(light_normalisation,[status(thm)],[c_91854,c_16935]) ).
tcf(c_91861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X0)),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X0),
inference(light_normalisation,[status(thm)],[c_91853,c_91179]) ).
tcf(c_91862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),X3)),X1)),
inference(light_normalisation,[status(thm)],[c_91861,c_90508]) ).
tcf(c_91863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X2)),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),X3),X2),
inference(light_normalisation,[status(thm)],[c_91862,c_16929]) ).
tcf(c_91869,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_551,c_1144]) ).
tcf(c_91871,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,iPr_def_15) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_90483,c_1144]) ).
tcf(c_91874,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_91871,c_91436]) ).
tcf(c_91875,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____),
inference(superposition,[status(thm)],[c_91871,c_1095]) ).
tcf(c_91878,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_1098,c_1145]) ).
tcf(c_91884,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____)),
inference(superposition,[status(thm)],[c_91871,c_1145]) ).
tcf(c_91885,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_440,c_1145]) ).
tcf(c_91886,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_551,c_1145]) ).
tcf(c_91888,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),
inference(superposition,[status(thm)],[c_1145,c_50323]) ).
tcf(c_91889,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(superposition,[status(thm)],[c_1145,c_91603]) ).
tcf(c_91901,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_1214,c_50325]) ).
tcf(c_91905,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_90483,c_50325]) ).
tcf(c_91908,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_50325,c_91292]) ).
tcf(c_91915,plain,
! [X0: $i,X1: $i,X2: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1),X2),
inference(light_normalisation,[status(thm)],[c_22506,c_72166]) ).
tcf(c_91918,plain,
! [X0: $i,X1: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1)) = c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1),
inference(superposition,[status(thm)],[c_91550,c_91915]) ).
tcf(c_91919,plain,
! [X0: $i,X1: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1))) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_91915,c_91420]) ).
tcf(c_91920,plain,
! [X0: $i,X1: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Groups_Ozero__class_Ozero(iPr_def_10))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1),
inference(superposition,[status(thm)],[c_91915,c_91421]) ).
tcf(c_91927,plain,
c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1384,c_86]) ).
tcf(c_91928,plain,
c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1424,c_86]) ).
tcf(c_91929,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1468,c_86]) ).
tcf(c_91930,plain,
! [X0: $i] :
( ( c_Polynomial_Odegree(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_1525,c_86]) ).
tcf(c_91931,plain,
c_Polynomial_Odegree(iPr_def_10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_90973,c_86]) ).
tcf(c_91932,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(light_normalisation,[status(thm)],[c_91929,c_72166]) ).
tcf(c_91940,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1384,c_130]) ).
tcf(c_91941,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1424,c_130]) ).
tcf(c_91942,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1468,c_130]) ).
tcf(c_91943,plain,
! [X0: $i] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_1525,c_130]) ).
tcf(c_91944,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(iPr_def_10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_90973,c_130]) ).
tcf(c_91945,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(light_normalisation,[status(thm)],[c_91942,c_72166]) ).
tcf(c_91957,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_256,c_91603]) ).
tcf(c_91978,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X1 ) ),
inference(superposition,[status(thm)],[c_256,c_457]) ).
tcf(c_91979,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_256,c_458]) ).
tcf(c_91980,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_256,c_91435]) ).
tcf(c_91981,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_256,c_91436]) ).
tcf(c_91982,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_256,c_91087]) ).
tcf(c_92011,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_331,c_292]) ).
tcf(c_92012,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_373,c_292]) ).
tcf(c_92013,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_224,c_292]) ).
tcf(c_92014,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oone__class_Oone(X0)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_227,c_292]) ).
tcf(c_92022,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_11697,c_292]) ).
tcf(c_92025,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91294,c_292]) ).
tcf(c_92026,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_91125,c_292]) ).
tcf(c_92027,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91291,c_292]) ).
tcf(c_92029,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91318,c_292]) ).
tcf(c_92032,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91650,c_292]) ).
tcf(c_92047,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_91905,c_49959]) ).
tcf(c_92057,plain,
! [X0: $i,X1: $i] :
( 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,X0,X1) ),
inference(superposition,[status(thm)],[c_91901,c_49959]) ).
tcf(c_92072,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),X1),
inference(superposition,[status(thm)],[c_91901,c_91436]) ).
tcf(c_92080,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ( X0 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_256,c_92047]) ).
tcf(c_92084,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_492,c_92047]) ).
tcf(c_92085,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))),
inference(superposition,[status(thm)],[c_491,c_92047]) ).
tcf(c_92100,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X1),
inference(light_normalisation,[status(thm)],[c_22512,c_72166]) ).
tcf(c_92103,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X1)) = c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1),
inference(superposition,[status(thm)],[c_91673,c_92100]) ).
tcf(c_92104,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0),
inference(superposition,[status(thm)],[c_91692,c_92100]) ).
tcf(c_92105,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0))) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_92100,c_91420]) ).
tcf(c_92106,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(iPr_def_10))) = c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_92100,c_91421]) ).
tcf(c_92108,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1))) = c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1),
inference(light_normalisation,[status(thm)],[c_92103,c_92100]) ).
tcf(c_92119,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_331,c_295]) ).
tcf(c_92120,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_373,c_295]) ).
tcf(c_92121,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Orderings_Oorder(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_224,c_295]) ).
tcf(c_92122,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oone__class_Oone(X0)))
| ~ class_Orderings_Oorder(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_227,c_295]) ).
tcf(c_92131,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_11697,c_295]) ).
tcf(c_92134,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91294,c_295]) ).
tcf(c_92135,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Orderings_Oorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_91125,c_295]) ).
tcf(c_92136,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91291,c_295]) ).
tcf(c_92138,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91318,c_295]) ).
tcf(c_92141,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91650,c_295]) ).
tcf(c_92157,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_440,c_334]) ).
tcf(c_92158,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_551,c_334]) ).
tcf(c_92161,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(superposition,[status(thm)],[c_334,c_91603]) ).
tcf(c_92168,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
inference(superposition,[status(thm)],[c_334,c_457]) ).
tcf(c_92169,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1)),
inference(superposition,[status(thm)],[c_334,c_458]) ).
tcf(c_92170,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
inference(superposition,[status(thm)],[c_334,c_91435]) ).
tcf(c_92171,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(superposition,[status(thm)],[c_334,c_92047]) ).
tcf(c_92189,plain,
c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1360,c_390]) ).
tcf(c_92190,plain,
c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1408,c_390]) ).
tcf(c_92191,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1447,c_390]) ).
tcf(c_92192,plain,
! [X0: $i] :
( ( c_Polynomial_Odegree(tc_Polynomial_Opoly(X0),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_390]) ).
tcf(c_92193,plain,
c_Polynomial_Odegree(iPr_def_10,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(iPr_def_10))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_90792,c_390]) ).
tcf(c_92194,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(iPr_def_10)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(light_normalisation,[status(thm)],[c_92191,c_72166]) ).
tcf(c_92202,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Groups_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Polynomial_Odegree(X1,c_Polynomial_Omonom(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_403,c_49959]) ).
tcf(c_92203,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_403,c_164]) ).
tcf(c_92214,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_256,c_92057]) ).
tcf(c_92215,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_256,c_92057]) ).
tcf(c_92223,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(superposition,[status(thm)],[c_492,c_92057]) ).
tcf(c_92231,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,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91629,c_92057]) ).
tcf(c_92244,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_92157,c_50323]) ).
tcf(c_92246,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92157,c_91603]) ).
tcf(c_92255,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),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_92157,c_91435]) ).
tcf(c_92283,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_90483,c_50489]) ).
tcf(c_92284,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_50489,c_49959]) ).
tcf(c_92286,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_50489,c_91292]) ).
tcf(c_92297,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92283,c_50323]) ).
tcf(c_92298,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_92283,c_92057]) ).
tcf(c_92299,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_92283,c_91603]) ).
tcf(c_92300,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)
| ~ class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92283,c_223]) ).
tcf(c_92307,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),iPr_def_15),
inference(superposition,[status(thm)],[c_92283,c_91436]) ).
tcf(c_92321,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(superposition,[status(thm)],[c_92307,c_49959]) ).
tcf(c_92328,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_92299,c_164]) ).
tcf(c_92331,plain,
! [X0: $i,X1: $i] : c_Divides_Odiv__class_Omod(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1)) = c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1),
inference(light_normalisation,[status(thm)],[c_22518,c_72166]) ).
tcf(c_92336,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_92331,c_91420]) ).
tcf(c_92337,plain,
! [X0: $i,X1: $i,X2: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2))) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1),X2),
inference(superposition,[status(thm)],[c_92331,c_91915]) ).
tcf(c_92338,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1))) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X1),
inference(superposition,[status(thm)],[c_92331,c_92100]) ).
tcf(c_92340,plain,
! [X0: $i,X1: $i,X2: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2)),
inference(light_normalisation,[status(thm)],[c_92337,c_91915]) ).
tcf(c_92347,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_256,c_449]) ).
tcf(c_92351,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(superposition,[status(thm)],[c_334,c_449]) ).
tcf(c_92352,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2))),
inference(superposition,[status(thm)],[c_492,c_449]) ).
tcf(c_92353,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)))),
inference(superposition,[status(thm)],[c_491,c_449]) ).
tcf(c_92354,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92157,c_449]) ).
tcf(c_92363,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))),
inference(light_normalisation,[status(thm)],[c_92352,c_553]) ).
tcf(c_92375,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,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,X0,X1)) ),
inference(superposition,[status(thm)],[c_91901,c_463]) ).
tcf(c_92376,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_49961,c_463]) ).
tcf(c_92383,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_421,c_463]) ).
tcf(c_92384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_50489,c_463]) ).
tcf(c_92385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_50325,c_463]) ).
tcf(c_92386,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)),
inference(superposition,[status(thm)],[c_651,c_463]) ).
tcf(c_92387,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))),
inference(superposition,[status(thm)],[c_474,c_463]) ).
tcf(c_92388,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(superposition,[status(thm)],[c_911,c_463]) ).
tcf(c_92389,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_91905,c_463]) ).
tcf(c_92390,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1214,c_463]) ).
tcf(c_92394,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_90483,c_463]) ).
tcf(c_92397,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(light_normalisation,[status(thm)],[c_92386,c_553]) ).
tcf(c_92408,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_92383,c_1414]) ).
tcf(c_92419,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_91901,c_464]) ).
tcf(c_92420,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_49961,c_464]) ).
tcf(c_92427,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_421,c_464]) ).
tcf(c_92428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_50489,c_464]) ).
tcf(c_92429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_50325,c_464]) ).
tcf(c_92430,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2)),
inference(superposition,[status(thm)],[c_651,c_464]) ).
tcf(c_92431,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))),
inference(superposition,[status(thm)],[c_474,c_464]) ).
tcf(c_92432,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
inference(superposition,[status(thm)],[c_911,c_464]) ).
tcf(c_92433,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_91905,c_464]) ).
tcf(c_92438,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_90483,c_464]) ).
tcf(c_92451,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_92427,c_1414]) ).
tcf(c_92464,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_90483,c_632]) ).
tcf(c_92465,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_632,c_50323]) ).
tcf(c_92466,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1) ),
inference(superposition,[status(thm)],[c_632,c_92057]) ).
tcf(c_92467,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_632,c_91603]) ).
tcf(c_92468,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_632,c_295]) ).
tcf(c_92469,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_632,c_292]) ).
tcf(c_92474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_632,c_449]) ).
tcf(c_92475,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X1),
inference(superposition,[status(thm)],[c_632,c_457]) ).
tcf(c_92476,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),X0),
inference(superposition,[status(thm)],[c_632,c_458]) ).
tcf(c_92477,plain,
! [X0: $i,X1: $i] : ~ 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,X0,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X0),
inference(superposition,[status(thm)],[c_632,c_91435]) ).
tcf(c_92478,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_632,c_92047]) ).
tcf(c_92481,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X0),
inference(light_normalisation,[status(thm)],[c_92476,c_553]) ).
tcf(c_92498,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),iPr_def_15)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_256,c_92321]) ).
tcf(c_92511,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0) ),
inference(superposition,[status(thm)],[c_49961,c_92394]) ).
tcf(c_92518,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_421,c_92394]) ).
tcf(c_92519,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_50489,c_92394]) ).
tcf(c_92520,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_50325,c_92394]) ).
tcf(c_92521,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_651,c_92394]) ).
tcf(c_92522,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),
inference(superposition,[status(thm)],[c_474,c_92394]) ).
tcf(c_92523,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15)),
inference(superposition,[status(thm)],[c_911,c_92394]) ).
tcf(c_92531,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15) ),
inference(forward_subsumption_resolution,[status(thm)],[c_92518,c_1414]) ).
tcf(c_92542,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),v_n____),
inference(superposition,[status(thm)],[c_92521,c_49959]) ).
tcf(c_92547,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),v_n____),
inference(superposition,[status(thm)],[c_92522,c_49959]) ).
tcf(c_92559,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_92531,c_49959]) ).
tcf(c_92560,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v_n____ ) ),
inference(superposition,[status(thm)],[c_92531,c_164]) ).
tcf(c_92561,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_92531,c_49959]) ).
tcf(c_92562,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)),
inference(superposition,[status(thm)],[c_92531,c_165]) ).
tcf(c_92563,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92531,c_464]) ).
tcf(c_92564,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92531,c_463]) ).
tcf(c_92578,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0) = v_n____ ) ),
inference(superposition,[status(thm)],[c_256,c_92542]) ).
tcf(c_92586,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15) = v_n____ ) ),
inference(superposition,[status(thm)],[c_256,c_92547]) ).
tcf(c_92598,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ( X0 = v_n____ ) ),
inference(superposition,[status(thm)],[c_256,c_92464]) ).
tcf(c_92608,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15),v_n____),
inference(superposition,[status(thm)],[c_92523,c_49959]) ).
tcf(c_92615,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15) ),
inference(superposition,[status(thm)],[c_92157,c_92559]) ).
tcf(c_92616,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15) ),
inference(superposition,[status(thm)],[c_91901,c_92559]) ).
tcf(c_92626,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_227,c_92561]) ).
tcf(c_92627,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(superposition,[status(thm)],[c_334,c_92561]) ).
tcf(c_92628,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_632,c_92561]) ).
tcf(c_92629,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_492,c_92561]) ).
tcf(c_92630,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))),
inference(superposition,[status(thm)],[c_491,c_92561]) ).
tcf(c_92641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(light_normalisation,[status(thm)],[c_22551,c_72176]) ).
tcf(c_92651,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) ) ),
inference(superposition,[status(thm)],[c_16929,c_92641]) ).
tcf(c_92652,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) ) ),
inference(superposition,[status(thm)],[c_16935,c_92641]) ).
tcf(c_92653,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X1)) ) ),
inference(superposition,[status(thm)],[c_91833,c_92641]) ).
tcf(c_92655,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)) ) ),
inference(superposition,[status(thm)],[c_90992,c_92641]) ).
tcf(c_92657,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),iPr_def_20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1)) ) ),
inference(superposition,[status(thm)],[c_90992,c_92641]) ).
tcf(c_92660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X4)) ) ),
inference(superposition,[status(thm)],[c_92641,c_16673]) ).
tcf(c_92661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X5,X1))),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X5),X4)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X1)) ) ),
inference(superposition,[status(thm)],[c_92641,c_16673]) ).
tcf(c_92662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3) = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3) )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_92641,c_91252]) ).
tcf(c_92663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1))) ) ),
inference(superposition,[status(thm)],[c_92641,c_16716]) ).
tcf(c_92664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1))) ) ),
inference(superposition,[status(thm)],[c_92641,c_16704]) ).
tcf(c_92665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2))) ) ),
inference(superposition,[status(thm)],[c_92641,c_16716]) ).
tcf(c_92666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2))) ) ),
inference(superposition,[status(thm)],[c_92641,c_16704]) ).
tcf(c_92671,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,iPr_def_20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1)) ) ),
inference(light_normalisation,[status(thm)],[c_92657,c_90956]) ).
tcf(c_92675,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)) ) ),
inference(light_normalisation,[status(thm)],[c_92655,c_90950]) ).
tcf(c_92725,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_90483,c_633]) ).
tcf(c_92726,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_633,c_50323]) ).
tcf(c_92727,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1) ),
inference(superposition,[status(thm)],[c_633,c_92057]) ).
tcf(c_92728,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_633,c_91603]) ).
tcf(c_92729,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_633,c_295]) ).
tcf(c_92730,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_633,c_292]) ).
tcf(c_92735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_633,c_449]) ).
tcf(c_92736,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X2),
inference(superposition,[status(thm)],[c_633,c_457]) ).
tcf(c_92737,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),X1),
inference(superposition,[status(thm)],[c_633,c_458]) ).
tcf(c_92738,plain,
! [X0: $i,X1: $i] : ~ 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,X0,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X1),
inference(superposition,[status(thm)],[c_633,c_91435]) ).
tcf(c_92739,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_633,c_92561]) ).
tcf(c_92740,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_633,c_92047]) ).
tcf(c_92772,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_697,c_663]) ).
tcf(c_92780,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
inference(superposition,[status(thm)],[c_697,c_675]) ).
tcf(c_92781,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_697,c_663]) ).
tcf(c_92805,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_91389,c_1097]) ).
tcf(c_92807,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0) ),
inference(superposition,[status(thm)],[c_91871,c_1097]) ).
tcf(c_92809,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_1097,c_50323]) ).
tcf(c_92811,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1097,c_91603]) ).
tcf(c_92812,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1097,c_295]) ).
tcf(c_92813,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1097,c_292]) ).
tcf(c_92818,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2)),
inference(superposition,[status(thm)],[c_1097,c_91436]) ).
tcf(c_92819,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_1097,c_92559]) ).
tcf(c_92820,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_1097,c_92464]) ).
tcf(c_92825,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(light_normalisation,[status(thm)],[c_92818,c_1065]) ).
tcf(c_92847,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92157,c_92297]) ).
tcf(c_92848,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_91901,c_92297]) ).
tcf(c_92851,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_1097,c_92297]) ).
tcf(c_92860,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(superposition,[status(thm)],[c_1214,c_92387]) ).
tcf(c_92866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X3))),
inference(superposition,[status(thm)],[c_92387,c_464]) ).
tcf(c_92867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X3))),
inference(superposition,[status(thm)],[c_92387,c_463]) ).
tcf(c_92868,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1))),
inference(superposition,[status(thm)],[c_92387,c_92394]) ).
tcf(c_92879,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),
inference(superposition,[status(thm)],[c_90483,c_92431]) ).
tcf(c_92881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)))),
inference(superposition,[status(thm)],[c_92431,c_464]) ).
tcf(c_92882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3)))),
inference(superposition,[status(thm)],[c_92431,c_463]) ).
tcf(c_92883,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15))),
inference(superposition,[status(thm)],[c_92431,c_92394]) ).
tcf(c_92888,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_551,c_92879]) ).
tcf(c_92890,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_92879,c_49959]) ).
tcf(c_92896,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_92888,c_49959]) ).
tcf(c_92898,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_256,c_92890]) ).
tcf(c_92900,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),
inference(superposition,[status(thm)],[c_92157,c_92890]) ).
tcf(c_92909,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_551,c_92900]) ).
tcf(c_92911,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_92900,c_50323]) ).
tcf(c_92913,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),
inference(superposition,[status(thm)],[c_92900,c_91603]) ).
tcf(c_92914,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92900,c_295]) ).
tcf(c_92915,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92900,c_292]) ).
tcf(c_92920,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_92909,c_50323]) ).
tcf(c_92922,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_92909,c_91603]) ).
tcf(c_92923,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92909,c_295]) ).
tcf(c_92924,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92909,c_292]) ).
tcf(c_92925,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_256,c_92896]) ).
tcf(c_92938,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92438,c_49959]) ).
tcf(c_92941,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_92438,c_91120]) ).
tcf(c_92945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(light_normalisation,[status(thm)],[c_22563,c_72176]) ).
tcf(c_92955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3),X4) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3),X4))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3),X4))) ) ),
inference(superposition,[status(thm)],[c_16673,c_92945]) ).
tcf(c_92956,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) ) ),
inference(superposition,[status(thm)],[c_16752,c_92945]) ).
tcf(c_92957,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) ) ),
inference(superposition,[status(thm)],[c_16953,c_92945]) ).
tcf(c_92959,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)) ) ),
inference(superposition,[status(thm)],[c_90992,c_92945]) ).
tcf(c_92961,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),iPr_def_20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1)) ) ),
inference(superposition,[status(thm)],[c_90992,c_92945]) ).
tcf(c_92964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3) )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_92945,c_91252]) ).
tcf(c_92965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1))) ) ),
inference(superposition,[status(thm)],[c_92945,c_16716]) ).
tcf(c_92966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1))) ) ),
inference(superposition,[status(thm)],[c_92945,c_16704]) ).
tcf(c_92967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2))) ) ),
inference(superposition,[status(thm)],[c_92945,c_16716]) ).
tcf(c_92968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2))) ) ),
inference(superposition,[status(thm)],[c_92945,c_16704]) ).
tcf(c_92971,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,iPr_def_20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1)) ) ),
inference(light_normalisation,[status(thm)],[c_92961,c_90955]) ).
tcf(c_92975,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)) ) ),
inference(light_normalisation,[status(thm)],[c_92959,c_90949]) ).
tcf(c_93015,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_700,c_1243]) ).
tcf(c_93016,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
inference(superposition,[status(thm)],[c_891,c_1243]) ).
tcf(c_93018,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),
inference(superposition,[status(thm)],[c_1243,c_91378]) ).
tcf(c_93019,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),
inference(superposition,[status(thm)],[c_1243,c_91377]) ).
tcf(c_93020,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),
inference(superposition,[status(thm)],[c_1243,c_680]) ).
tcf(c_93021,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),
inference(superposition,[status(thm)],[c_1243,c_925]) ).
tcf(c_93030,plain,
! [X0: $i] : c_Polynomial_Osmult(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_1386,c_186]) ).
tcf(c_93031,plain,
! [X0: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_1470,c_186]) ).
tcf(c_93032,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osmult(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) )
| ~ class_Rings_Oidom(X0) ),
inference(superposition,[status(thm)],[c_1527,c_186]) ).
tcf(c_93033,plain,
! [X0: $i] : c_Polynomial_Osmult(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),
inference(superposition,[status(thm)],[c_90985,c_186]) ).
tcf(c_93034,plain,
! [X0: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,iPr_def_20,X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_93031,c_72166,c_72176]) ).
tcf(c_93046,plain,
! [X0: $i] : c_Polynomial_Osmult(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1409,c_189]) ).
tcf(c_93048,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osmult(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(superposition,[status(thm)],[c_1502,c_189]) ).
tcf(c_93058,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72176,c_226]) ).
tcf(c_93059,plain,
( ~ class_Rings_Olinordered__semidom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_226,c_50323]) ).
tcf(c_93060,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_226,c_92057]) ).
tcf(c_93061,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_226,c_91603]) ).
tcf(c_93062,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)))
| ~ class_Orderings_Oorder(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_226,c_295]) ).
tcf(c_93063,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_226,c_292]) ).
tcf(c_93064,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Rings_Olinordered__semidom(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_226,c_675]) ).
tcf(c_93080,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_421,c_92941]) ).
tcf(c_93081,plain,
! [X0: $i,X1: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,iPr_def_20,c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X1),
inference(superposition,[status(thm)],[c_93034,c_91915]) ).
tcf(c_93083,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15) = v_n____ ) ),
inference(superposition,[status(thm)],[c_256,c_92608]) ).
tcf(c_93091,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ) ),
inference(superposition,[status(thm)],[c_256,c_92725]) ).
tcf(c_93098,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_1097,c_92725]) ).
tcf(c_93100,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_92157,c_92725]) ).
tcf(c_93125,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),iPr_def_15),
inference(superposition,[status(thm)],[c_93100,c_91436]) ).
tcf(c_93127,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15) ),
inference(superposition,[status(thm)],[c_93100,c_92297]) ).
tcf(c_93136,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92805,c_50323]) ).
tcf(c_93137,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_92805,c_92057]) ).
tcf(c_93138,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_92805,c_91603]) ).
tcf(c_93139,plain,
( ~ class_Rings_Olinordered__semidom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92805,c_223]) ).
tcf(c_93140,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_92805,c_295]) ).
tcf(c_93141,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_92805,c_292]) ).
tcf(c_93163,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),X1)),
inference(superposition,[status(thm)],[c_551,c_92868]) ).
tcf(c_93168,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),v_n____),
inference(superposition,[status(thm)],[c_92868,c_49959]) ).
tcf(c_93172,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),X1)),
inference(superposition,[status(thm)],[c_551,c_92883]) ).
tcf(c_93177,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),v_n____),
inference(superposition,[status(thm)],[c_92883,c_49959]) ).
tcf(c_93180,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_700,c_93018]) ).
tcf(c_93181,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))),
inference(superposition,[status(thm)],[c_891,c_93018]) ).
tcf(c_93182,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_11748,c_93018]) ).
tcf(c_93183,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_91818,c_93018]) ).
tcf(c_93191,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_93182,c_663]) ).
tcf(c_93192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1) )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3) ) ),
inference(light_normalisation,[status(thm)],[c_22592,c_72176]) ).
tcf(c_93215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1) )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3) ) ),
inference(superposition,[status(thm)],[c_16698,c_93192]) ).
tcf(c_93216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4) ) ),
inference(superposition,[status(thm)],[c_17554,c_93192]) ).
tcf(c_93217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3) )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3) ) ),
inference(superposition,[status(thm)],[c_17690,c_93192]) ).
tcf(c_93218,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1) )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1) != X2 ) ),
inference(superposition,[status(thm)],[c_17614,c_93192]) ).
tcf(c_93219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X3) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),X1) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3) ) ),
inference(superposition,[status(thm)],[c_17702,c_93192]) ).
tcf(c_93220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X2)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4) ) ),
inference(superposition,[status(thm)],[c_17708,c_93192]) ).
tcf(c_93221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X5 = iPr_def_20 )
| ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1))),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)) )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X5) ) ),
inference(superposition,[status(thm)],[c_92641,c_93192]) ).
tcf(c_93222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X5 = iPr_def_20 )
| ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1))),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)) )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X5) ) ),
inference(superposition,[status(thm)],[c_92945,c_93192]) ).
tcf(c_93224,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X1) )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1) != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_90508,c_93192]) ).
tcf(c_93230,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1) )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1) != X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_93218,c_91065]) ).
tcf(c_93282,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X0) ),
inference(superposition,[status(thm)],[c_331,c_235]) ).
tcf(c_93283,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_373,c_235]) ).
tcf(c_93285,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(X0)
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_226,c_235]) ).
tcf(c_93286,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(X0)
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oone__class_Oone(X0)),X1) ),
inference(superposition,[status(thm)],[c_227,c_235]) ).
tcf(c_93291,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(superposition,[status(thm)],[c_334,c_235]) ).
tcf(c_93293,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92283,c_235]) ).
tcf(c_93298,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91757,c_235]) ).
tcf(c_93301,plain,
( ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_679,c_235]) ).
tcf(c_93302,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
inference(superposition,[status(thm)],[c_695,c_235]) ).
tcf(c_93305,plain,
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_11697,c_235]) ).
tcf(c_93306,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_92157,c_235]) ).
tcf(c_93307,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_91757,c_235]) ).
tcf(c_93308,plain,
( ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91753,c_235]) ).
tcf(c_93309,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(superposition,[status(thm)],[c_91294,c_235]) ).
tcf(c_93311,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91291,c_235]) ).
tcf(c_93313,plain,
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91318,c_235]) ).
tcf(c_93314,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0) ),
inference(superposition,[status(thm)],[c_91378,c_235]) ).
tcf(c_93315,plain,
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_n____) ),
inference(superposition,[status(thm)],[c_91629,c_235]) ).
tcf(c_93316,plain,
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91650,c_235]) ).
tcf(c_93318,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92900,c_235]) ).
tcf(c_93319,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92909,c_235]) ).
tcf(c_93320,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(superposition,[status(thm)],[c_93018,c_235]) ).
tcf(c_93321,plain,
( ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_93182,c_235]) ).
tcf(c_93322,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(forward_subsumption_resolution,[status(thm)],[c_93301,c_1376]) ).
tcf(c_93323,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_subsumption_resolution,[status(thm)],[c_93321,c_1376]) ).
tcf(c_93324,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_93314,c_1376]) ).
tcf(c_93325,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_93302,c_1376]) ).
tcf(c_93327,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_93320,c_1376]) ).
tcf(c_93328,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(forward_subsumption_resolution,[status(thm)],[c_93308,c_1376]) ).
tcf(c_93329,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_93307,c_1376]) ).
tcf(c_93333,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_93298,c_1376]) ).
tcf(c_93358,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X0) ),
inference(superposition,[status(thm)],[c_331,c_240]) ).
tcf(c_93359,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_373,c_240]) ).
tcf(c_93361,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(X0)
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_226,c_240]) ).
tcf(c_93362,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(X0)
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oone__class_Oone(X0)),X1) ),
inference(superposition,[status(thm)],[c_227,c_240]) ).
tcf(c_93367,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(superposition,[status(thm)],[c_334,c_240]) ).
tcf(c_93369,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92283,c_240]) ).
tcf(c_93374,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91757,c_240]) ).
tcf(c_93381,plain,
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_11697,c_240]) ).
tcf(c_93382,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_92157,c_240]) ).
tcf(c_93383,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_91757,c_240]) ).
tcf(c_93385,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(superposition,[status(thm)],[c_91294,c_240]) ).
tcf(c_93387,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91291,c_240]) ).
tcf(c_93389,plain,
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91318,c_240]) ).
tcf(c_93391,plain,
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_n____) ),
inference(superposition,[status(thm)],[c_91629,c_240]) ).
tcf(c_93392,plain,
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91650,c_240]) ).
tcf(c_93394,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92900,c_240]) ).
tcf(c_93395,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92909,c_240]) ).
tcf(c_93419,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X0) ),
inference(superposition,[status(thm)],[c_331,c_245]) ).
tcf(c_93420,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_373,c_245]) ).
tcf(c_93422,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_226,c_245]) ).
tcf(c_93423,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Oone__class_Oone(X0)),X1) ),
inference(superposition,[status(thm)],[c_227,c_245]) ).
tcf(c_93428,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(superposition,[status(thm)],[c_334,c_245]) ).
tcf(c_93430,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92283,c_245]) ).
tcf(c_93435,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91757,c_245]) ).
tcf(c_93442,plain,
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_11697,c_245]) ).
tcf(c_93443,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_92157,c_245]) ).
tcf(c_93444,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_91757,c_245]) ).
tcf(c_93446,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(superposition,[status(thm)],[c_91294,c_245]) ).
tcf(c_93448,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91291,c_245]) ).
tcf(c_93450,plain,
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91318,c_245]) ).
tcf(c_93452,plain,
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_n____) ),
inference(superposition,[status(thm)],[c_91629,c_245]) ).
tcf(c_93453,plain,
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91650,c_245]) ).
tcf(c_93455,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92900,c_245]) ).
tcf(c_93456,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92909,c_245]) ).
tcf(c_93479,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_91901,c_293]) ).
tcf(c_93487,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_421,c_293]) ).
tcf(c_93490,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_50489,c_293]) ).
tcf(c_93491,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_50325,c_293]) ).
tcf(c_93495,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_661,c_293]) ).
tcf(c_93503,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X0),X1,X1) ),
inference(superposition,[status(thm)],[c_1234,c_293]) ).
tcf(c_93508,plain,
! [X0: $i] :
( ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ class_Orderings_Opreorder(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,X0,X0) ),
inference(superposition,[status(thm)],[c_91110,c_293]) ).
tcf(c_93513,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_92531,c_293]) ).
tcf(c_93514,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_91905,c_293]) ).
tcf(c_93517,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_92531,c_293]) ).
tcf(c_93518,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_92511,c_293]) ).
tcf(c_93550,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_91757,c_93323]) ).
tcf(c_93555,plain,
( ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_93550,c_235]) ).
tcf(c_93558,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_93550,c_663]) ).
tcf(c_93559,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_subsumption_resolution,[status(thm)],[c_93555,c_1376]) ).
tcf(c_93576,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_700,c_93019]) ).
tcf(c_93577,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))),
inference(superposition,[status(thm)],[c_891,c_93019]) ).
tcf(c_93579,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_91818,c_93019]) ).
tcf(c_93587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3) ) ),
inference(light_normalisation,[status(thm)],[c_22607,c_72176]) ).
tcf(c_93603,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_90992,c_93587]) ).
tcf(c_93617,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_91901,c_300]) ).
tcf(c_93625,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_421,c_300]) ).
tcf(c_93628,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_50489,c_300]) ).
tcf(c_93629,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_50325,c_300]) ).
tcf(c_93633,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_661,c_300]) ).
tcf(c_93641,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X0),X1,X1) ),
inference(superposition,[status(thm)],[c_1234,c_300]) ).
tcf(c_93646,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,X0,X0) ),
inference(superposition,[status(thm)],[c_91110,c_300]) ).
tcf(c_93651,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_92531,c_300]) ).
tcf(c_93652,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_91905,c_300]) ).
tcf(c_93655,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_92531,c_300]) ).
tcf(c_93656,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_92511,c_300]) ).
tcf(c_93691,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_256,c_320]) ).
tcf(c_93693,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
inference(superposition,[status(thm)],[c_331,c_320]) ).
tcf(c_93695,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(superposition,[status(thm)],[c_334,c_320]) ).
tcf(c_93696,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(superposition,[status(thm)],[c_633,c_320]) ).
tcf(c_93697,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(superposition,[status(thm)],[c_632,c_320]) ).
tcf(c_93698,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1))),
inference(superposition,[status(thm)],[c_492,c_320]) ).
tcf(c_93699,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))),
inference(superposition,[status(thm)],[c_491,c_320]) ).
tcf(c_93701,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91294,c_320]) ).
tcf(c_93703,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(superposition,[status(thm)],[c_551,c_320]) ).
tcf(c_93725,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(superposition,[status(thm)],[c_1369,c_345]) ).
tcf(c_93726,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(superposition,[status(thm)],[c_1415,c_345]) ).
tcf(c_93727,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(superposition,[status(thm)],[c_1454,c_345]) ).
tcf(c_93728,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1510,c_345]) ).
tcf(c_93729,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(iPr_def_10),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(superposition,[status(thm)],[c_90842,c_345]) ).
tcf(c_93730,plain,
! [X0: $i] : hAPP(hAPP(iPr_def_13,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(light_normalisation,[status(thm)],[c_93729,c_72169]) ).
tcf(c_93738,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),X0) = X0,
inference(superposition,[status(thm)],[c_1357,c_346]) ).
tcf(c_93739,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),X0) = X0,
inference(superposition,[status(thm)],[c_1407,c_346]) ).
tcf(c_93740,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0) = X0,
inference(superposition,[status(thm)],[c_1446,c_346]) ).
tcf(c_93741,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1) = X1 )
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(superposition,[status(thm)],[c_1498,c_346]) ).
tcf(c_93742,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),X0) = X0,
inference(superposition,[status(thm)],[c_90764,c_346]) ).
tcf(c_93750,plain,
hAPP(iPr_def_14,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = v_q,
inference(superposition,[status(thm)],[c_72170,c_93730]) ).
tcf(c_93756,plain,
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_93138,c_164]) ).
tcf(c_93761,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(demodulation,[status(thm)],[c_93163,c_553]) ).
tcf(c_93768,plain,
! [X0: $i,X1: $i] : c_Divides_Odiv__class_Omod(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1),X1) = c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1),
inference(light_normalisation,[status(thm)],[c_22993,c_72166]) ).
tcf(c_93770,plain,
! [X0: $i] : c_Divides_Odiv__class_Omod(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_91420,c_93768]) ).
tcf(c_93771,plain,
! [X0: $i,X1: $i,X2: $i] : c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2)),X2) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2)),
inference(superposition,[status(thm)],[c_91915,c_93768]) ).
tcf(c_93772,plain,
! [X0: $i,X1: $i] : c_Divides_Odiv__class_Omod(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1)),X1) = c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1)),
inference(superposition,[status(thm)],[c_92100,c_93768]) ).
tcf(c_93773,plain,
! [X0: $i,X1: $i] : c_Divides_Odiv__class_Omod(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1)) = c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1),
inference(superposition,[status(thm)],[c_92331,c_93768]) ).
tcf(c_93774,plain,
! [X0: $i,X1: $i] : c_Divides_Odiv__class_Omod(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1)),X1) = c_Divides_Odiv__class_Omod(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1)),
inference(superposition,[status(thm)],[c_93768,c_92331]) ).
tcf(c_93784,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = X0,
inference(superposition,[status(thm)],[c_1357,c_347]) ).
tcf(c_93785,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Nat_Onat),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = X0,
inference(superposition,[status(thm)],[c_1407,c_347]) ).
tcf(c_93786,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0,
inference(superposition,[status(thm)],[c_1446,c_347]) ).
tcf(c_93787,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))) = X1 )
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(superposition,[status(thm)],[c_1498,c_347]) ).
tcf(c_93788,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(iPr_def_10),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) = X0,
inference(superposition,[status(thm)],[c_90764,c_347]) ).
tcf(c_93800,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_440,c_384]) ).
tcf(c_93801,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_551,c_384]) ).
tcf(c_93809,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_384,c_463]) ).
tcf(c_93832,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(superposition,[status(thm)],[c_50489,c_387]) ).
tcf(c_93839,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X2))),
inference(superposition,[status(thm)],[c_92387,c_387]) ).
tcf(c_93840,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))),
inference(superposition,[status(thm)],[c_92431,c_387]) ).
tcf(c_93841,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_440,c_387]) ).
tcf(c_93842,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(superposition,[status(thm)],[c_551,c_387]) ).
tcf(c_93857,plain,
! [X0: $i] : c_Polynomial_Omonom(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_1384,c_400]) ).
tcf(c_93858,plain,
! [X0: $i] : c_Polynomial_Omonom(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1424,c_400]) ).
tcf(c_93859,plain,
! [X0: $i] : c_Polynomial_Omonom(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_1468,c_400]) ).
tcf(c_93860,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Omonom(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) )
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_1525,c_400]) ).
tcf(c_93861,plain,
! [X0: $i] : c_Polynomial_Omonom(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),
inference(superposition,[status(thm)],[c_90973,c_400]) ).
tcf(c_93862,plain,
! [X0: $i] : c_Polynomial_Omonom(tc_Complex_Ocomplex,iPr_def_20,X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_93859,c_72166,c_72176]) ).
tcf(c_93870,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10)),X0)
| ~ class_Groups_Ozero(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_93862,c_403]) ).
tcf(c_93871,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ class_Groups_Ozero(tc_Complex_Ocomplex) ),
inference(light_normalisation,[status(thm)],[c_93870,c_91932]) ).
tcf(c_93874,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(superposition,[status(thm)],[c_93727,c_17708]) ).
tcf(c_93875,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_93727,c_17708]) ).
tcf(c_93877,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),
inference(light_normalisation,[status(thm)],[c_93874,c_93727]) ).
tcf(c_93879,plain,
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)))
| ~ class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_93738,c_227]) ).
tcf(c_93882,plain,
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_93739,c_227]) ).
tcf(c_93885,plain,
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(iPr_def_10)))
| ~ class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_93742,c_227]) ).
tcf(c_93892,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_256,c_93809]) ).
tcf(c_93893,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_256,c_93809]) ).
tcf(c_93896,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_224,c_93809]) ).
tcf(c_93897,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_226,c_93809]) ).
tcf(c_93898,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_227,c_93809]) ).
tcf(c_93899,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_93100,c_93809]) ).
tcf(c_93900,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_92157,c_93809]) ).
tcf(c_93901,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_91901,c_93809]) ).
tcf(c_93902,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(superposition,[status(thm)],[c_317,c_93809]) ).
tcf(c_93903,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(superposition,[status(thm)],[c_334,c_93809]) ).
tcf(c_93906,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_633,c_93809]) ).
tcf(c_93907,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_632,c_93809]) ).
tcf(c_93908,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(superposition,[status(thm)],[c_492,c_93809]) ).
tcf(c_93911,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(superposition,[status(thm)],[c_1145,c_93809]) ).
tcf(c_93913,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92157,c_93809]) ).
tcf(c_93914,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91294,c_93809]) ).
tcf(c_93950,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_93899,c_300]) ).
tcf(c_93951,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_93899,c_293]) ).
tcf(c_93964,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_93901,c_300]) ).
tcf(c_93965,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_93901,c_293]) ).
tcf(c_93967,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_93901,c_464]) ).
tcf(c_93968,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_93901,c_463]) ).
tcf(c_93974,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_93901,c_49959]) ).
tcf(c_93976,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_93901,c_300]) ).
tcf(c_93977,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_93901,c_293]) ).
tcf(c_93999,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != X1 ) ),
inference(superposition,[status(thm)],[c_551,c_444]) ).
tcf(c_94017,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1373,c_619]) ).
tcf(c_94018,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1458,c_619]) ).
tcf(c_94019,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1514,c_619]) ).
tcf(c_94020,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_90868,c_619]) ).
tcf(c_94021,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X0) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_94018,c_72176]) ).
tcf(c_94035,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) = iPr_def_20,
inference(superposition,[status(thm)],[c_16973,c_94021]) ).
tcf(c_94036,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = iPr_def_20,
inference(superposition,[status(thm)],[c_45742,c_94021]) ).
tcf(c_94037,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20) = iPr_def_20,
inference(superposition,[status(thm)],[c_90498,c_94021]) ).
tcf(c_94038,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),iPr_def_20)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_94021,c_227]) ).
tcf(c_94045,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = iPr_def_20,
inference(superposition,[status(thm)],[c_16973,c_94036]) ).
tcf(c_94050,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))),X0)
| ~ class_Groups_Ozero(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_93857,c_403]) ).
tcf(c_94051,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ class_Groups_Ozero(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_94050,c_91927]) ).
tcf(c_94052,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))),X0)
| ~ class_Groups_Ozero(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93858,c_403]) ).
tcf(c_94053,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ class_Groups_Ozero(tc_Nat_Onat) ),
inference(light_normalisation,[status(thm)],[c_94052,c_91928]) ).
tcf(c_94054,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(iPr_def_10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))),X0)
| ~ class_Groups_Ozero(iPr_def_10) ),
inference(superposition,[status(thm)],[c_93861,c_403]) ).
tcf(c_94055,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ class_Groups_Ozero(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_94054,c_91931]) ).
tcf(c_94062,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_93902,c_300]) ).
tcf(c_94063,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_93902,c_293]) ).
tcf(c_94072,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ) ),
inference(superposition,[status(thm)],[c_256,c_93974]) ).
tcf(c_94081,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_1097,c_93974]) ).
tcf(c_94090,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0)) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_91673,c_94020]) ).
tcf(c_94091,plain,
c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10)) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_91692,c_94020]) ).
tcf(c_94092,plain,
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10)),c_Groups_Ozero__class_Ozero(iPr_def_10))
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94020,c_227]) ).
tcf(c_94101,plain,
( ~ class_Orderings_Olinorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ),
inference(superposition,[status(thm)],[c_94038,c_245]) ).
tcf(c_94102,plain,
( ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ),
inference(superposition,[status(thm)],[c_94038,c_240]) ).
tcf(c_94103,plain,
( ~ class_Orderings_Oorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ),
inference(superposition,[status(thm)],[c_94038,c_235]) ).
tcf(c_94104,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),iPr_def_20)
| ~ class_Orderings_Oorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_94038,c_295]) ).
tcf(c_94105,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),iPr_def_20)
| ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_94038,c_292]) ).
tcf(c_94126,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),
inference(superposition,[status(thm)],[c_16973,c_37700]) ).
tcf(c_94127,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),
inference(superposition,[status(thm)],[c_45742,c_37700]) ).
tcf(c_94128,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X0),
inference(superposition,[status(thm)],[c_90498,c_37700]) ).
tcf(c_94129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X4),X3)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),X3),
inference(superposition,[status(thm)],[c_37700,c_16673]) ).
tcf(c_94131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_37700,c_92945]) ).
tcf(c_94132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_37700,c_92641]) ).
tcf(c_94133,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2),
inference(superposition,[status(thm)],[c_37700,c_17554]) ).
tcf(c_94134,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))),
inference(superposition,[status(thm)],[c_37700,c_16973]) ).
tcf(c_94135,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),
inference(superposition,[status(thm)],[c_37700,c_16953]) ).
tcf(c_94136,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),
inference(superposition,[status(thm)],[c_37700,c_16935]) ).
tcf(c_94137,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X2)),X1),
inference(superposition,[status(thm)],[c_37700,c_16929]) ).
tcf(c_94138,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X2)),X1),
inference(superposition,[status(thm)],[c_37700,c_16752]) ).
tcf(c_94139,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),X1),
inference(superposition,[status(thm)],[c_37700,c_16929]) ).
tcf(c_94140,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),X1),
inference(superposition,[status(thm)],[c_37700,c_16752]) ).
tcf(c_94141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X3) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3) ) ),
inference(superposition,[status(thm)],[c_37700,c_93587]) ).
tcf(c_94142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2),X1)) ) ),
inference(superposition,[status(thm)],[c_37700,c_92945]) ).
tcf(c_94143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2),X1)) ) ),
inference(superposition,[status(thm)],[c_37700,c_92641]) ).
tcf(c_94144,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),
inference(superposition,[status(thm)],[c_37700,c_16953]) ).
tcf(c_94145,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),
inference(superposition,[status(thm)],[c_37700,c_16935]) ).
tcf(c_94146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_37700,c_92945]) ).
tcf(c_94147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_37700,c_92641]) ).
tcf(c_94148,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20)) = iPr_def_20,
inference(superposition,[status(thm)],[c_37700,c_90947]) ).
tcf(c_94152,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),
inference(light_normalisation,[status(thm)],[c_94145,c_37700]) ).
tcf(c_94153,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),
inference(light_normalisation,[status(thm)],[c_94144,c_37700]) ).
tcf(c_94176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X4),X3)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),X3),
inference(light_normalisation,[status(thm)],[c_94129,c_37700]) ).
tcf(c_94199,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1373,c_621]) ).
tcf(c_94200,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1458,c_621]) ).
tcf(c_94201,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1514,c_621]) ).
tcf(c_94212,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0),
inference(superposition,[status(thm)],[c_1447,c_631]) ).
tcf(c_94213,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,X2) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X2,X1) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_631]) ).
tcf(c_94214,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(iPr_def_10,X0,X1) = c_Groups_Oplus__class_Oplus(iPr_def_10,X1,X0),
inference(superposition,[status(thm)],[c_90792,c_631]) ).
tcf(c_94226,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1340,c_647]) ).
tcf(c_94227,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Olinordered__idom(X0) ),
inference(superposition,[status(thm)],[c_1481,c_647]) ).
tcf(c_94256,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0))
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_94212,c_227]) ).
tcf(c_94257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X2)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X3),X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),X2),
inference(superposition,[status(thm)],[c_94212,c_16673]) ).
tcf(c_94258,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X0),X1),
inference(superposition,[status(thm)],[c_94212,c_16704]) ).
tcf(c_94259,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X0)),X1),
inference(superposition,[status(thm)],[c_94212,c_16752]) ).
tcf(c_94260,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X1)),
inference(superposition,[status(thm)],[c_94212,c_16953]) ).
tcf(c_94261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3)) ) ),
inference(superposition,[status(thm)],[c_94212,c_92945]) ).
tcf(c_94279,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,X0,c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),X0))
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94214,c_227]) ).
tcf(c_94289,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(superposition,[status(thm)],[c_256,c_50941]) ).
tcf(c_94298,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_1097,c_50941]) ).
tcf(c_94315,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_90483,c_91869]) ).
tcf(c_94323,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_94315,c_1145]) ).
tcf(c_94330,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_1098,c_91886]) ).
tcf(c_94337,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,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91871,c_91886]) ).
tcf(c_94342,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0),iPr_def_15),
inference(superposition,[status(thm)],[c_90483,c_91886]) ).
tcf(c_94343,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),
inference(superposition,[status(thm)],[c_91886,c_50323]) ).
tcf(c_94346,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91886,c_91603]) ).
tcf(c_94361,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0)),
inference(superposition,[status(thm)],[c_94342,c_50323]) ).
tcf(c_94364,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0),iPr_def_15),
inference(superposition,[status(thm)],[c_94342,c_91603]) ).
tcf(c_94374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),X3)),
inference(superposition,[status(thm)],[c_16698,c_39652]) ).
tcf(c_94375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X4)),
inference(superposition,[status(thm)],[c_17554,c_39652]) ).
tcf(c_94376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X1)),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X3))) ) ),
inference(superposition,[status(thm)],[c_92641,c_39652]) ).
tcf(c_94377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X1)),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X3))) ) ),
inference(superposition,[status(thm)],[c_92945,c_39652]) ).
tcf(c_94378,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),iPr_def_20),
inference(superposition,[status(thm)],[c_90508,c_39652]) ).
tcf(c_94379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3)),
inference(superposition,[status(thm)],[c_37700,c_39652]) ).
tcf(c_94381,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,iPr_def_20)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,iPr_def_20)),
inference(superposition,[status(thm)],[c_90947,c_39652]) ).
tcf(c_94382,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,iPr_def_20)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,iPr_def_20)),
inference(superposition,[status(thm)],[c_90992,c_39652]) ).
tcf(c_94383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X4))),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X5),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X4)),
inference(superposition,[status(thm)],[c_39652,c_16673]) ).
tcf(c_94384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4))),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X6),X5),X3)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X4))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X6),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4)))),X5),
inference(superposition,[status(thm)],[c_39652,c_16673]) ).
tcf(c_94386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X5 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X5),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X5),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)))) ) ),
inference(superposition,[status(thm)],[c_39652,c_92945]) ).
tcf(c_94387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X5 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X5),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X5),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)))) ) ),
inference(superposition,[status(thm)],[c_39652,c_92641]) ).
tcf(c_94388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X4)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3)),X4),
inference(superposition,[status(thm)],[c_39652,c_17554]) ).
tcf(c_94389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3))),
inference(superposition,[status(thm)],[c_39652,c_16973]) ).
tcf(c_94390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),X4)),
inference(superposition,[status(thm)],[c_39652,c_16953]) ).
tcf(c_94391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),X4)),
inference(superposition,[status(thm)],[c_39652,c_16935]) ).
tcf(c_94392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X4)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3))),
inference(superposition,[status(thm)],[c_39652,c_16929]) ).
tcf(c_94393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X4)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3))),
inference(superposition,[status(thm)],[c_39652,c_16752]) ).
tcf(c_94394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X4)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),
inference(superposition,[status(thm)],[c_39652,c_16929]) ).
tcf(c_94395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X4)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),
inference(superposition,[status(thm)],[c_39652,c_16752]) ).
tcf(c_94396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X5)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X4)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X5)))),
inference(superposition,[status(thm)],[c_39652,c_39652]) ).
tcf(c_94397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X5 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X5) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X5) ) ),
inference(superposition,[status(thm)],[c_39652,c_93587]) ).
tcf(c_94398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X5)) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X5))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X5))),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X5))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_39652,c_92945]) ).
tcf(c_94399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X5)) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X5))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X5))),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X5))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_39652,c_92641]) ).
tcf(c_94400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X4)))),
inference(superposition,[status(thm)],[c_39652,c_16953]) ).
tcf(c_94401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X4)))),
inference(superposition,[status(thm)],[c_39652,c_16935]) ).
tcf(c_94402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3)),
inference(superposition,[status(thm)],[c_39652,c_37700]) ).
tcf(c_94403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X5 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X5,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X5),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)))) ) ),
inference(superposition,[status(thm)],[c_39652,c_92945]) ).
tcf(c_94404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X5 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X5,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X5),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)))) ) ),
inference(superposition,[status(thm)],[c_39652,c_92641]) ).
tcf(c_94405,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X0)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = iPr_def_20,
inference(superposition,[status(thm)],[c_39652,c_90992]) ).
tcf(c_94406,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_94405,c_90508]) ).
tcf(c_94407,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X2)) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_94378,c_90947]) ).
tcf(c_94409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X4)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3))),
inference(light_normalisation,[status(thm)],[c_94395,c_39652]) ).
tcf(c_94410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X4)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3))),
inference(light_normalisation,[status(thm)],[c_94394,c_39652]) ).
tcf(c_94421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X5 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X5,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X5),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)))) ) ),
inference(light_normalisation,[status(thm)],[c_94404,c_39652]) ).
tcf(c_94425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X5 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X5,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X5),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)))) ) ),
inference(light_normalisation,[status(thm)],[c_94403,c_39652]) ).
tcf(c_94486,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 ) ),
inference(superposition,[status(thm)],[c_91782,c_662]) ).
tcf(c_94504,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_680,c_665]) ).
tcf(c_94505,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,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,X0,X1) ),
inference(superposition,[status(thm)],[c_925,c_665]) ).
tcf(c_94508,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) ),
inference(superposition,[status(thm)],[c_665,c_235]) ).
tcf(c_94509,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_665,c_295]) ).
tcf(c_94510,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_665,c_292]) ).
tcf(c_94514,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_665,c_675]) ).
tcf(c_94515,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_665,c_663]) ).
tcf(c_94516,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),
inference(superposition,[status(thm)],[c_665,c_664]) ).
tcf(c_94517,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),
inference(superposition,[status(thm)],[c_665,c_93325]) ).
tcf(c_94518,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0),
inference(superposition,[status(thm)],[c_665,c_93324]) ).
tcf(c_94529,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_94508,c_1376]) ).
tcf(c_94543,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91757,c_666]) ).
tcf(c_94544,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
| ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1 ) ),
inference(superposition,[status(thm)],[c_697,c_666]) ).
tcf(c_94551,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_680,c_666]) ).
tcf(c_94552,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)) ),
inference(superposition,[status(thm)],[c_925,c_666]) ).
tcf(c_94569,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Orderings_Olinorder(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_301,c_668]) ).
tcf(c_94574,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_661,c_668]) ).
tcf(c_94577,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_91750,c_668]) ).
tcf(c_94578,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_91175,c_668]) ).
tcf(c_94579,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(superposition,[status(thm)],[c_91377,c_668]) ).
tcf(c_94582,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X1) ),
inference(superposition,[status(thm)],[c_925,c_668]) ).
tcf(c_94589,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_94569,c_1368]) ).
tcf(c_94618,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_680,c_94516]) ).
tcf(c_94619,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(superposition,[status(thm)],[c_925,c_94516]) ).
tcf(c_94636,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(superposition,[status(thm)],[c_1243,c_94619]) ).
tcf(c_94640,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_1098,c_91889]) ).
tcf(c_94645,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)),
inference(superposition,[status(thm)],[c_91389,c_91889]) ).
tcf(c_94647,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____)),
inference(superposition,[status(thm)],[c_91871,c_91889]) ).
tcf(c_94648,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_94315,c_91889]) ).
tcf(c_94649,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_440,c_91889]) ).
tcf(c_94656,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(demodulation,[status(thm)],[c_91908,c_553]) ).
tcf(c_94658,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,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)),X0)),
inference(superposition,[status(thm)],[c_551,c_94656]) ).
tcf(c_94661,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))),
inference(superposition,[status(thm)],[c_551,c_94656]) ).
tcf(c_94663,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),
inference(superposition,[status(thm)],[c_90483,c_94656]) ).
tcf(c_94664,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0),
inference(superposition,[status(thm)],[c_94656,c_50323]) ).
tcf(c_94665,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_94656,c_93809]) ).
tcf(c_94666,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_94656,c_92057]) ).
tcf(c_94667,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_94656,c_91603]) ).
tcf(c_94668,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) ),
inference(superposition,[status(thm)],[c_94656,c_245]) ).
tcf(c_94669,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) ),
inference(superposition,[status(thm)],[c_94656,c_240]) ).
tcf(c_94670,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) ),
inference(superposition,[status(thm)],[c_94656,c_235]) ).
tcf(c_94671,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94656,c_295]) ).
tcf(c_94672,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94656,c_292]) ).
tcf(c_94673,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_94656,c_320]) ).
tcf(c_94674,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_94656,c_449]) ).
tcf(c_94675,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_94656,c_92561]) ).
tcf(c_94676,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_94656,c_92047]) ).
tcf(c_94684,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_551,c_94663]) ).
tcf(c_94686,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),X0),
inference(superposition,[status(thm)],[c_94663,c_50323]) ).
tcf(c_94689,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),
inference(superposition,[status(thm)],[c_94663,c_91603]) ).
tcf(c_94690,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),X0) ),
inference(superposition,[status(thm)],[c_94663,c_245]) ).
tcf(c_94691,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),X0) ),
inference(superposition,[status(thm)],[c_94663,c_240]) ).
tcf(c_94692,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),X0) ),
inference(superposition,[status(thm)],[c_94663,c_235]) ).
tcf(c_94693,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94663,c_295]) ).
tcf(c_94694,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94663,c_292]) ).
tcf(c_94695,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),iPr_def_15)),
inference(superposition,[status(thm)],[c_94663,c_320]) ).
tcf(c_94696,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15)),
inference(superposition,[status(thm)],[c_94663,c_449]) ).
tcf(c_94697,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15)),
inference(superposition,[status(thm)],[c_94663,c_92561]) ).
tcf(c_94698,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15)),
inference(superposition,[status(thm)],[c_94663,c_92047]) ).
tcf(c_94705,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),X0),
inference(superposition,[status(thm)],[c_94684,c_50323]) ).
tcf(c_94708,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_94684,c_91603]) ).
tcf(c_94709,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),X0) ),
inference(superposition,[status(thm)],[c_94684,c_245]) ).
tcf(c_94710,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),X0) ),
inference(superposition,[status(thm)],[c_94684,c_240]) ).
tcf(c_94711,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),X0) ),
inference(superposition,[status(thm)],[c_94684,c_235]) ).
tcf(c_94712,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94684,c_295]) ).
tcf(c_94713,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94684,c_292]) ).
tcf(c_94714,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
inference(superposition,[status(thm)],[c_94684,c_320]) ).
tcf(c_94715,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(superposition,[status(thm)],[c_94684,c_449]) ).
tcf(c_94720,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15),v_n____),
inference(superposition,[status(thm)],[c_94698,c_50323]) ).
tcf(c_94721,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15)),
inference(superposition,[status(thm)],[c_94698,c_93809]) ).
tcf(c_94722,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,iPr_def_15,iPr_def_15)),
inference(superposition,[status(thm)],[c_94698,c_92057]) ).
tcf(c_94724,plain,
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15),v_n____) ),
inference(superposition,[status(thm)],[c_94698,c_245]) ).
tcf(c_94725,plain,
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15),v_n____) ),
inference(superposition,[status(thm)],[c_94698,c_240]) ).
tcf(c_94726,plain,
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15),v_n____) ),
inference(superposition,[status(thm)],[c_94698,c_235]) ).
tcf(c_94727,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94698,c_295]) ).
tcf(c_94728,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94698,c_292]) ).
tcf(c_94729,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15))),
inference(demodulation,[status(thm)],[c_94696,c_553]) ).
tcf(c_94731,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15),X0)),
inference(superposition,[status(thm)],[c_551,c_94729]) ).
tcf(c_94734,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1))),
inference(superposition,[status(thm)],[c_551,c_94729]) ).
tcf(c_94736,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),X0),
inference(superposition,[status(thm)],[c_94729,c_50323]) ).
tcf(c_94737,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15))),
inference(superposition,[status(thm)],[c_94729,c_93809]) ).
tcf(c_94738,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15))),
inference(superposition,[status(thm)],[c_94729,c_92057]) ).
tcf(c_94739,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15))),
inference(superposition,[status(thm)],[c_94729,c_91603]) ).
tcf(c_94740,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),X0) ),
inference(superposition,[status(thm)],[c_94729,c_245]) ).
tcf(c_94741,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),X0) ),
inference(superposition,[status(thm)],[c_94729,c_240]) ).
tcf(c_94742,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),X0) ),
inference(superposition,[status(thm)],[c_94729,c_235]) ).
tcf(c_94743,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94729,c_295]) ).
tcf(c_94744,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94729,c_292]) ).
tcf(c_94745,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15))),
inference(superposition,[status(thm)],[c_94729,c_320]) ).
tcf(c_94746,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,iPr_def_15))),
inference(superposition,[status(thm)],[c_94729,c_449]) ).
tcf(c_94747,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))),
inference(superposition,[status(thm)],[c_94729,c_92561]) ).
tcf(c_94748,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))),
inference(superposition,[status(thm)],[c_94729,c_92047]) ).
tcf(c_94758,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
inference(superposition,[status(thm)],[c_551,c_94715]) ).
tcf(c_94761,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X0),
inference(superposition,[status(thm)],[c_94715,c_50323]) ).
tcf(c_94762,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(superposition,[status(thm)],[c_94715,c_93809]) ).
tcf(c_94763,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(superposition,[status(thm)],[c_94715,c_92057]) ).
tcf(c_94764,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(superposition,[status(thm)],[c_94715,c_91603]) ).
tcf(c_94768,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94715,c_295]) ).
tcf(c_94769,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94715,c_292]) ).
tcf(c_94770,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1))),
inference(superposition,[status(thm)],[c_94715,c_320]) ).
tcf(c_94771,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2))),
inference(superposition,[status(thm)],[c_94715,c_449]) ).
tcf(c_94772,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_94715,c_92561]) ).
tcf(c_94773,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_94715,c_92047]) ).
tcf(c_94774,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))),
inference(light_normalisation,[status(thm)],[c_94771,c_553]) ).
tcf(c_94778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X3,X0)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),
inference(demodulation,[status(thm)],[c_40877,c_94212]) ).
tcf(c_94779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X3,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X2)),
inference(superposition,[status(thm)],[c_37700,c_94778]) ).
tcf(c_94780,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,iPr_def_20)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X1)),
inference(superposition,[status(thm)],[c_90992,c_94778]) ).
tcf(c_94786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X0),X1)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X3)),
inference(superposition,[status(thm)],[c_16716,c_94778]) ).
tcf(c_94787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X0)),X1)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X3)),
inference(superposition,[status(thm)],[c_16929,c_94778]) ).
tcf(c_94788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1))),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X4)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X3)),
inference(superposition,[status(thm)],[c_16935,c_94778]) ).
tcf(c_94789,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),
inference(superposition,[status(thm)],[c_91833,c_94778]) ).
tcf(c_94790,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X1)),
inference(superposition,[status(thm)],[c_91822,c_94778]) ).
tcf(c_94791,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,iPr_def_20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X0)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,iPr_def_20))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),iPr_def_20)),
inference(superposition,[status(thm)],[c_91089,c_94778]) ).
tcf(c_94792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X0)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))),
inference(superposition,[status(thm)],[c_16716,c_94778]) ).
tcf(c_94793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X0)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),X3)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),
inference(superposition,[status(thm)],[c_16929,c_94778]) ).
tcf(c_94794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X0)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3))))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3))),
inference(superposition,[status(thm)],[c_16935,c_94778]) ).
tcf(c_94795,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),iPr_def_20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,iPr_def_20))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),
inference(superposition,[status(thm)],[c_91833,c_94778]) ).
tcf(c_94796,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X0)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,X1))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),iPr_def_20)),
inference(superposition,[status(thm)],[c_91822,c_94778]) ).
tcf(c_94797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3)) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3))),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3))) ) ),
inference(superposition,[status(thm)],[c_94778,c_92945]) ).
tcf(c_94798,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X1)),
inference(light_normalisation,[status(thm)],[c_94780,c_91822]) ).
tcf(c_94799,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X0)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,X1))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),iPr_def_20),
inference(light_normalisation,[status(thm)],[c_94796,c_90947]) ).
tcf(c_94800,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,iPr_def_20))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),
inference(light_normalisation,[status(thm)],[c_94795,c_90947]) ).
tcf(c_94801,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,iPr_def_20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X0)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,iPr_def_20))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),iPr_def_20),
inference(light_normalisation,[status(thm)],[c_94791,c_90947]) ).
tcf(c_94802,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X1)),
inference(light_normalisation,[status(thm)],[c_94790,c_91002]) ).
tcf(c_94803,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),
inference(light_normalisation,[status(thm)],[c_94789,c_16935]) ).
tcf(c_94826,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_925,c_669]) ).
tcf(c_94828,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_669,c_293]) ).
tcf(c_94829,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
| ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1 )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_669,c_662]) ).
tcf(c_94832,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_669,c_94619]) ).
tcf(c_94835,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_94828,c_1367]) ).
tcf(c_94847,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = X0,
inference(superposition,[status(thm)],[c_1447,c_698]) ).
tcf(c_94848,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_698]) ).
tcf(c_94849,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(iPr_def_10),X0),c_Groups_Oone__class_Oone(iPr_def_10)) = X0,
inference(superposition,[status(thm)],[c_90792,c_698]) ).
tcf(c_94859,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0) = X0,
inference(superposition,[status(thm)],[c_1447,c_699]) ).
tcf(c_94860,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))),X1) = X1 )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_699]) ).
tcf(c_94861,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(iPr_def_10),c_Groups_Oone__class_Oone(iPr_def_10)),X0) = X0,
inference(superposition,[status(thm)],[c_90792,c_699]) ).
tcf(c_94874,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))),
inference(demodulation,[status(thm)],[c_94731,c_553]) ).
tcf(c_94876,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),X1)),
inference(superposition,[status(thm)],[c_551,c_94874]) ).
tcf(c_94879,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))),
inference(superposition,[status(thm)],[c_551,c_94874]) ).
tcf(c_94881,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),X1),
inference(superposition,[status(thm)],[c_94874,c_50323]) ).
tcf(c_94882,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1))),
inference(superposition,[status(thm)],[c_94874,c_93809]) ).
tcf(c_94883,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1))),
inference(superposition,[status(thm)],[c_94874,c_92057]) ).
tcf(c_94884,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_94874,c_91603]) ).
tcf(c_94888,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94874,c_295]) ).
tcf(c_94889,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94874,c_292]) ).
tcf(c_94890,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))),
inference(superposition,[status(thm)],[c_94874,c_320]) ).
tcf(c_94891,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)))),
inference(superposition,[status(thm)],[c_94874,c_449]) ).
tcf(c_94892,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15))),
inference(superposition,[status(thm)],[c_94874,c_92561]) ).
tcf(c_94893,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15))),
inference(superposition,[status(thm)],[c_94874,c_92047]) ).
tcf(c_94903,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1),X0)),
inference(superposition,[status(thm)],[c_551,c_94734]) ).
tcf(c_94908,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),X0),
inference(superposition,[status(thm)],[c_94734,c_50323]) ).
tcf(c_94911,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1))),
inference(superposition,[status(thm)],[c_94734,c_91603]) ).
tcf(c_94912,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),X0) ),
inference(superposition,[status(thm)],[c_94734,c_245]) ).
tcf(c_94913,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),X0) ),
inference(superposition,[status(thm)],[c_94734,c_240]) ).
tcf(c_94914,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),X0) ),
inference(superposition,[status(thm)],[c_94734,c_235]) ).
tcf(c_94915,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94734,c_295]) ).
tcf(c_94916,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94734,c_292]) ).
tcf(c_94917,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1))),
inference(superposition,[status(thm)],[c_94734,c_320]) ).
tcf(c_94918,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X2))),
inference(superposition,[status(thm)],[c_94734,c_449]) ).
tcf(c_94926,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),v_n____),
inference(superposition,[status(thm)],[c_94748,c_50323]) ).
tcf(c_94927,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))),
inference(superposition,[status(thm)],[c_94748,c_93809]) ).
tcf(c_94928,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))),
inference(superposition,[status(thm)],[c_94748,c_92057]) ).
tcf(c_94930,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),v_n____) ),
inference(superposition,[status(thm)],[c_94748,c_245]) ).
tcf(c_94931,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),v_n____) ),
inference(superposition,[status(thm)],[c_94748,c_240]) ).
tcf(c_94932,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),v_n____) ),
inference(superposition,[status(thm)],[c_94748,c_235]) ).
tcf(c_94933,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94748,c_295]) ).
tcf(c_94934,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94748,c_292]) ).
tcf(c_94939,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15)),
inference(superposition,[status(thm)],[c_90483,c_94758]) ).
tcf(c_94940,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X1),
inference(superposition,[status(thm)],[c_94758,c_50323]) ).
tcf(c_94943,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
inference(superposition,[status(thm)],[c_94758,c_91603]) ).
tcf(c_94947,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94758,c_295]) ).
tcf(c_94948,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94758,c_292]) ).
tcf(c_94949,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))),
inference(superposition,[status(thm)],[c_94758,c_320]) ).
tcf(c_94950,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)))),
inference(superposition,[status(thm)],[c_94758,c_449]) ).
tcf(c_94955,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_94939,c_50323]) ).
tcf(c_94959,plain,
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_94939,c_245]) ).
tcf(c_94960,plain,
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_94939,c_240]) ).
tcf(c_94961,plain,
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_94939,c_235]) ).
tcf(c_94962,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94939,c_295]) ).
tcf(c_94963,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94939,c_292]) ).
tcf(c_94967,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),v_n____),
inference(superposition,[status(thm)],[c_94773,c_50323]) ).
tcf(c_94968,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_94773,c_93809]) ).
tcf(c_94969,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_94773,c_92057]) ).
tcf(c_94971,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),v_n____) ),
inference(superposition,[status(thm)],[c_94773,c_245]) ).
tcf(c_94972,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),v_n____) ),
inference(superposition,[status(thm)],[c_94773,c_240]) ).
tcf(c_94973,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),v_n____) ),
inference(superposition,[status(thm)],[c_94773,c_235]) ).
tcf(c_94974,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94773,c_295]) ).
tcf(c_94975,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94773,c_292]) ).
tcf(c_94977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X2),
inference(superposition,[status(thm)],[c_94847,c_16673]) ).
tcf(c_94979,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(superposition,[status(thm)],[c_94847,c_92945]) ).
tcf(c_94980,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(superposition,[status(thm)],[c_94847,c_92641]) ).
tcf(c_94981,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),
inference(superposition,[status(thm)],[c_94847,c_17554]) ).
tcf(c_94983,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_94847,c_16953]) ).
tcf(c_94984,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_94847,c_16935]) ).
tcf(c_94985,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
inference(superposition,[status(thm)],[c_94847,c_16929]) ).
tcf(c_94986,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
inference(superposition,[status(thm)],[c_94847,c_16752]) ).
tcf(c_94987,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1),
inference(superposition,[status(thm)],[c_94847,c_16929]) ).
tcf(c_94988,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1),
inference(superposition,[status(thm)],[c_94847,c_16752]) ).
tcf(c_94989,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)),
inference(superposition,[status(thm)],[c_94847,c_39652]) ).
tcf(c_94990,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) != X2 ) ),
inference(superposition,[status(thm)],[c_94847,c_93587]) ).
tcf(c_94991,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_94847,c_92945]) ).
tcf(c_94992,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_94847,c_92641]) ).
tcf(c_94993,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0),
inference(superposition,[status(thm)],[c_94847,c_16953]) ).
tcf(c_94994,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0),
inference(superposition,[status(thm)],[c_94847,c_16935]) ).
tcf(c_94995,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),
inference(superposition,[status(thm)],[c_94847,c_37700]) ).
tcf(c_94996,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(superposition,[status(thm)],[c_94847,c_92945]) ).
tcf(c_94997,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(superposition,[status(thm)],[c_94847,c_92641]) ).
tcf(c_94998,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),
inference(light_normalisation,[status(thm)],[c_94988,c_94847]) ).
tcf(c_94999,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),
inference(light_normalisation,[status(thm)],[c_94987,c_94847]) ).
tcf(c_95000,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1) = X0 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) != X2 ) ),
inference(light_normalisation,[status(thm)],[c_94990,c_17614]) ).
tcf(c_95001,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1) = X0 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) != X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95000,c_91065]) ).
tcf(c_95005,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(light_normalisation,[status(thm)],[c_94997,c_94847]) ).
tcf(c_95006,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95005,c_91065]) ).
tcf(c_95009,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(light_normalisation,[status(thm)],[c_94996,c_94847]) ).
tcf(c_95010,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95009,c_91065]) ).
tcf(c_95013,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(light_normalisation,[status(thm)],[c_94992,c_17614]) ).
tcf(c_95014,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95013,c_91065]) ).
tcf(c_95017,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(light_normalisation,[status(thm)],[c_94991,c_17614]) ).
tcf(c_95018,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95017,c_91065]) ).
tcf(c_95021,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_94980,c_91065]) ).
tcf(c_95024,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_94979,c_91065]) ).
tcf(c_95045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X3),X2)),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)),X2),
inference(superposition,[status(thm)],[c_94859,c_16673]) ).
tcf(c_95047,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0)) ) ),
inference(superposition,[status(thm)],[c_94859,c_92945]) ).
tcf(c_95048,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0)) ) ),
inference(superposition,[status(thm)],[c_94859,c_92641]) ).
tcf(c_95051,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1)),
inference(superposition,[status(thm)],[c_94859,c_16953]) ).
tcf(c_95052,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1)),
inference(superposition,[status(thm)],[c_94859,c_16935]) ).
tcf(c_95053,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_94859,c_16929]) ).
tcf(c_95054,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_94859,c_16752]) ).
tcf(c_95055,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X1),
inference(superposition,[status(thm)],[c_94859,c_16929]) ).
tcf(c_95056,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X1),
inference(superposition,[status(thm)],[c_94859,c_16752]) ).
tcf(c_95057,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),
inference(superposition,[status(thm)],[c_94859,c_39652]) ).
tcf(c_95058,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) != X2 ) ),
inference(superposition,[status(thm)],[c_94859,c_93587]) ).
tcf(c_95059,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1)) ) ),
inference(superposition,[status(thm)],[c_94859,c_92945]) ).
tcf(c_95060,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1)) ) ),
inference(superposition,[status(thm)],[c_94859,c_92641]) ).
tcf(c_95061,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0),X1),
inference(superposition,[status(thm)],[c_94859,c_16953]) ).
tcf(c_95062,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0),X1),
inference(superposition,[status(thm)],[c_94859,c_16935]) ).
tcf(c_95063,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1)),
inference(superposition,[status(thm)],[c_94859,c_94778]) ).
tcf(c_95064,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_94859,c_92945]) ).
tcf(c_95065,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_94859,c_92641]) ).
tcf(c_95066,plain,
! [X0: $i,X1: $i,X2: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),
inference(superposition,[status(thm)],[c_94859,c_39652]) ).
tcf(c_95067,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),
inference(light_normalisation,[status(thm)],[c_95062,c_94859]) ).
tcf(c_95068,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),
inference(light_normalisation,[status(thm)],[c_95061,c_94859]) ).
tcf(c_95086,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(light_normalisation,[status(thm)],[c_95065,c_17614]) ).
tcf(c_95087,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95086,c_91065]) ).
tcf(c_95090,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(light_normalisation,[status(thm)],[c_95064,c_17614]) ).
tcf(c_95091,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95090,c_91065]) ).
tcf(c_95094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X3),X2)),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)),X2),
inference(light_normalisation,[status(thm)],[c_95045,c_94859]) ).
tcf(c_95113,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),X1)),
inference(superposition,[status(thm)],[c_551,c_94879]) ).
tcf(c_95118,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),X1),
inference(superposition,[status(thm)],[c_94879,c_50323]) ).
tcf(c_95121,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))),
inference(superposition,[status(thm)],[c_94879,c_91603]) ).
tcf(c_95125,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94879,c_295]) ).
tcf(c_95126,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94879,c_292]) ).
tcf(c_95127,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),iPr_def_15))),
inference(superposition,[status(thm)],[c_94879,c_320]) ).
tcf(c_95128,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),iPr_def_15))),
inference(superposition,[status(thm)],[c_94879,c_449]) ).
tcf(c_95134,plain,
! [X0: $i] :
( ( hAPP(iPr_def_21,X0) = iPr_def_20 )
| ( hAPP(iPr_def_18,X0) != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_50016,c_72174,c_72176,c_72177]) ).
tcf(c_95141,plain,
( ( hAPP(iPr_def_21,sK21) = iPr_def_20 )
| ( iPr_def_19 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_72175,c_95134]) ).
tcf(c_95142,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_19 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_95141,c_72178]) ).
tcf(c_95176,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X0))
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72176,c_750]) ).
tcf(c_95179,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Olinordered__ring(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_900,c_750]) ).
tcf(c_95181,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Olinordered__ring(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_912,c_750]) ).
tcf(c_95183,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))))
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_37700,c_750]) ).
tcf(c_95184,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_94847,c_750]) ).
tcf(c_95186,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)))
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_39652,c_750]) ).
tcf(c_95187,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),iPr_def_20)
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_90947,c_750]) ).
tcf(c_95189,plain,
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Oone__class_Oone(iPr_def_10))
| ~ class_Rings_Olinordered__ring(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94849,c_750]) ).
tcf(c_95191,plain,
! [X0: $i] :
( ~ class_Rings_Olinordered__ring(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_750,c_49959]) ).
tcf(c_95192,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Olinordered__ring(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_750,c_300]) ).
tcf(c_95193,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Olinordered__ring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_750,c_293]) ).
tcf(c_95194,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X0))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ class_Rings_Olinordered__ring(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_750,c_662]) ).
tcf(c_95195,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20)
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex) ),
inference(light_normalisation,[status(thm)],[c_95187,c_72176]) ).
tcf(c_95200,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex) ),
inference(light_normalisation,[status(thm)],[c_95184,c_72176]) ).
tcf(c_95212,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X0))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95194,c_1358]) ).
tcf(c_95215,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)))
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex) ),
inference(light_normalisation,[status(thm)],[c_95186,c_72176]) ).
tcf(c_95225,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Olinorder(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20) ),
inference(superposition,[status(thm)],[c_95195,c_300]) ).
tcf(c_95226,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20) ),
inference(superposition,[status(thm)],[c_95195,c_293]) ).
tcf(c_95237,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Olinorder(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20) ),
inference(superposition,[status(thm)],[c_95200,c_300]) ).
tcf(c_95238,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20) ),
inference(superposition,[status(thm)],[c_95200,c_293]) ).
tcf(c_95253,plain,
( ~ class_Rings_Olinordered__ring(iPr_def_10)
| ~ class_Orderings_Olinorder(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_95189,c_300]) ).
tcf(c_95254,plain,
( ~ class_Rings_Olinordered__ring(iPr_def_10)
| ~ class_Orderings_Opreorder(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_95189,c_293]) ).
tcf(c_95262,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15),X0)),
inference(superposition,[status(thm)],[c_551,c_94893]) ).
tcf(c_95264,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15)),v_n____),
inference(superposition,[status(thm)],[c_94893,c_50323]) ).
tcf(c_95265,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15))),
inference(superposition,[status(thm)],[c_94893,c_93809]) ).
tcf(c_95266,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15))),
inference(superposition,[status(thm)],[c_94893,c_92057]) ).
tcf(c_95271,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94893,c_295]) ).
tcf(c_95272,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,iPr_def_15)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94893,c_292]) ).
tcf(c_95282,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
inference(demodulation,[status(thm)],[c_92084,c_552]) ).
tcf(c_95286,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),v_n____),
inference(superposition,[status(thm)],[c_95282,c_50323]) ).
tcf(c_95287,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
inference(superposition,[status(thm)],[c_95282,c_93809]) ).
tcf(c_95288,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
inference(superposition,[status(thm)],[c_95282,c_92057]) ).
tcf(c_95289,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
inference(superposition,[status(thm)],[c_95282,c_91603]) ).
tcf(c_95290,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),v_n____) ),
inference(superposition,[status(thm)],[c_95282,c_245]) ).
tcf(c_95291,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),v_n____) ),
inference(superposition,[status(thm)],[c_95282,c_240]) ).
tcf(c_95292,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),v_n____) ),
inference(superposition,[status(thm)],[c_95282,c_235]) ).
tcf(c_95293,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_95282,c_295]) ).
tcf(c_95294,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_95282,c_292]) ).
tcf(c_95298,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),v_n____),
inference(superposition,[status(thm)],[c_92085,c_50323]) ).
tcf(c_95299,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))),
inference(superposition,[status(thm)],[c_92085,c_93809]) ).
tcf(c_95300,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))),
inference(superposition,[status(thm)],[c_92085,c_92057]) ).
tcf(c_95319,plain,
c_Power_Opower_Opower(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)) = c_Power_Opower__class_Opower(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1383,c_884]) ).
tcf(c_95320,plain,
c_Power_Opower_Opower(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)) = c_Power_Opower__class_Opower(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1423,c_884]) ).
tcf(c_95321,plain,
c_Power_Opower_Opower(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex)) = c_Power_Opower__class_Opower(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1467,c_884]) ).
tcf(c_95322,plain,
! [X0: $i] :
( ( c_Power_Opower_Opower(tc_Polynomial_Opoly(X0),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0))) = c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1524,c_884]) ).
tcf(c_95323,plain,
c_Power_Opower_Opower(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),c_Groups_Otimes__class_Otimes(iPr_def_10)) = c_Power_Opower__class_Opower(iPr_def_10),
inference(superposition,[status(thm)],[c_90946,c_884]) ).
tcf(c_95324,plain,
c_Power_Opower_Opower(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),c_Groups_Otimes__class_Otimes(iPr_def_10)) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_95323,c_72169]) ).
tcf(c_95331,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X1) = X0,
inference(superposition,[status(thm)],[c_1373,c_1061]) ).
tcf(c_95332,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X1) = X0,
inference(superposition,[status(thm)],[c_1458,c_1061]) ).
tcf(c_95333,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,X2),X2) = X1 )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1514,c_1061]) ).
tcf(c_95334,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(iPr_def_10,c_Groups_Oplus__class_Oplus(iPr_def_10,X0,X1),X1) = X0,
inference(superposition,[status(thm)],[c_90868,c_1061]) ).
tcf(c_95342,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),X1) = X0,
inference(superposition,[status(thm)],[c_1373,c_1062]) ).
tcf(c_95343,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X1) = X0,
inference(superposition,[status(thm)],[c_1458,c_1062]) ).
tcf(c_95344,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X1,X2),X2) = X1 )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1514,c_1062]) ).
tcf(c_95345,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Ominus__class_Ominus(iPr_def_10,X0,X1),X1) = X0,
inference(superposition,[status(thm)],[c_90868,c_1062]) ).
tcf(c_95353,plain,
! [X0: $i,X1: $i] :
( 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,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_1066,c_1147]) ).
tcf(c_95354,plain,
! [X0: $i,X1: $i] :
( 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,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(superposition,[status(thm)],[c_1067,c_1147]) ).
tcf(c_95361,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15) ),
inference(superposition,[status(thm)],[c_91398,c_1147]) ).
tcf(c_95364,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_1147,c_50323]) ).
tcf(c_95365,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_93809]) ).
tcf(c_95367,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_91603]) ).
tcf(c_95368,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_1147,c_245]) ).
tcf(c_95369,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_1147,c_240]) ).
tcf(c_95370,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_1147,c_235]) ).
tcf(c_95371,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_295]) ).
tcf(c_95372,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_292]) ).
tcf(c_95383,plain,
! [X0: $i] : hAPP(hAPP(iPr_def_13,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(iPr_def_10),
inference(superposition,[status(thm)],[c_95324,c_960]) ).
tcf(c_95385,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(superposition,[status(thm)],[c_95319,c_960]) ).
tcf(c_95388,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_95321,c_960]) ).
tcf(c_95394,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_925,c_95331]) ).
tcf(c_95395,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = X0,
inference(superposition,[status(thm)],[c_1243,c_95331]) ).
tcf(c_95399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),X4)),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3),X4)),
inference(superposition,[status(thm)],[c_16673,c_95332]) ).
tcf(c_95400,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),
inference(superposition,[status(thm)],[c_16704,c_95332]) ).
tcf(c_95402,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),
inference(superposition,[status(thm)],[c_16752,c_95332]) ).
tcf(c_95403,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),
inference(superposition,[status(thm)],[c_16953,c_95332]) ).
tcf(c_95404,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = X0,
inference(superposition,[status(thm)],[c_94036,c_95332]) ).
tcf(c_95405,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_94212,c_95332]) ).
tcf(c_95408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3)),
inference(superposition,[status(thm)],[c_94778,c_95332]) ).
tcf(c_95409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X0)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,X1))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3)),
inference(superposition,[status(thm)],[c_95332,c_94778]) ).
tcf(c_95410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3),X2)),X4)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4)),X2),
inference(superposition,[status(thm)],[c_95332,c_16673]) ).
tcf(c_95411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X4)),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),X4),
inference(superposition,[status(thm)],[c_95332,c_16673]) ).
tcf(c_95412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,X0)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),
inference(superposition,[status(thm)],[c_95332,c_94778]) ).
tcf(c_95414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2)),
inference(demodulation,[status(thm)],[c_94778,c_95409]) ).
tcf(c_95426,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),
inference(superposition,[status(thm)],[c_16973,c_95404]) ).
tcf(c_95427,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,X0) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),
inference(superposition,[status(thm)],[c_45742,c_95404]) ).
tcf(c_95428,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20) = iPr_def_20,
inference(superposition,[status(thm)],[c_90498,c_95404]) ).
tcf(c_95429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3),X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),iPr_def_20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))),X2),
inference(superposition,[status(thm)],[c_95404,c_16673]) ).
tcf(c_95430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),X1)),X2),
inference(superposition,[status(thm)],[c_95404,c_16673]) ).
tcf(c_95431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),X1)),X2),
inference(light_normalisation,[status(thm)],[c_95430,c_90992]) ).
tcf(c_95432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3),X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))),X2),
inference(light_normalisation,[status(thm)],[c_95429,c_90947]) ).
tcf(c_95440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3),X2)),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),iPr_def_20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)),X2),
inference(superposition,[status(thm)],[c_95427,c_16673]) ).
tcf(c_95441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3),X2)),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)),X2),
inference(superposition,[status(thm)],[c_95427,c_16673]) ).
tcf(c_95444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),iPr_def_20),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3),X2)),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)),X2),
inference(light_normalisation,[status(thm)],[c_95441,c_90992]) ).
tcf(c_95445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3),X2)),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)),X2),
inference(light_normalisation,[status(thm)],[c_95440,c_90947]) ).
tcf(c_95451,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0)) = X0,
inference(superposition,[status(thm)],[c_94090,c_95334]) ).
tcf(c_95452,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(iPr_def_10,c_Groups_Oplus__class_Oplus(iPr_def_10,X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_94214,c_95334]) ).
tcf(c_95456,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) = X1,
inference(demodulation,[status(thm)],[c_95342,c_925]) ).
tcf(c_95462,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)) = X1,
inference(superposition,[status(thm)],[c_95456,c_95331]) ).
tcf(c_95463,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_95456,c_94619]) ).
tcf(c_95464,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_95456,c_93324]) ).
tcf(c_95465,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),
inference(superposition,[status(thm)],[c_95456,c_91378]) ).
tcf(c_95466,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),
inference(superposition,[status(thm)],[c_95456,c_91377]) ).
tcf(c_95482,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),
inference(superposition,[status(thm)],[c_95465,c_666]) ).
tcf(c_95501,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_256,c_1148]) ).
tcf(c_95503,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_93100,c_1148]) ).
tcf(c_95504,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92157,c_1148]) ).
tcf(c_95505,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_91901,c_1148]) ).
tcf(c_95508,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_1066,c_1148]) ).
tcf(c_95509,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_1067,c_1148]) ).
tcf(c_95510,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_1098,c_1148]) ).
tcf(c_95512,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_1100,c_1148]) ).
tcf(c_95513,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_1144,c_1148]) ).
tcf(c_95514,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91869,c_1148]) ).
tcf(c_95516,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____) ),
inference(superposition,[status(thm)],[c_91398,c_1148]) ).
tcf(c_95517,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,v_n____)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91871,c_1148]) ).
tcf(c_95518,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_94315,c_1148]) ).
tcf(c_95540,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),
inference(superposition,[status(thm)],[c_1458,c_1153]) ).
tcf(c_95542,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0) = c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_90868,c_1153]) ).
tcf(c_95549,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Int_Oint),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = X0,
inference(superposition,[status(thm)],[c_1364,c_1241]) ).
tcf(c_95550,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0,
inference(superposition,[status(thm)],[c_1452,c_1241]) ).
tcf(c_95551,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))) = X1 )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1505,c_1241]) ).
tcf(c_95552,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(iPr_def_10),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) = X0,
inference(superposition,[status(thm)],[c_90804,c_1241]) ).
tcf(c_95563,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1))
| ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(superposition,[status(thm)],[c_697,c_1246]) ).
tcf(c_95566,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_11748,c_1246]) ).
tcf(c_95567,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_93020,c_1246]) ).
tcf(c_95569,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_95331,c_1246]) ).
tcf(c_95581,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_91783,c_95463]) ).
tcf(c_95584,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_669,c_95463]) ).
tcf(c_95585,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_91782,c_95463]) ).
tcf(c_95587,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_93020,c_95463]) ).
tcf(c_95602,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)) = X1,
inference(demodulation,[status(thm)],[c_95343,c_94212]) ).
tcf(c_95604,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X0),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1),
inference(superposition,[status(thm)],[c_16716,c_95602]) ).
tcf(c_95605,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X0)),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),
inference(superposition,[status(thm)],[c_16929,c_95602]) ).
tcf(c_95606,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),
inference(superposition,[status(thm)],[c_16935,c_95602]) ).
tcf(c_95611,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = X1,
inference(superposition,[status(thm)],[c_95602,c_95332]) ).
tcf(c_95617,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(iPr_def_10,X0,c_Groups_Ominus__class_Ominus(iPr_def_10,X1,X0)) = X1,
inference(demodulation,[status(thm)],[c_95345,c_94214]) ).
tcf(c_95623,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(iPr_def_10,X0,c_Groups_Ominus__class_Ominus(iPr_def_10,X0,X1)) = X1,
inference(superposition,[status(thm)],[c_95617,c_95334]) ).
tcf(c_95625,plain,
hAPP(iPr_def_14,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(iPr_def_10),
inference(superposition,[status(thm)],[c_72170,c_95383]) ).
tcf(c_95631,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),
inference(superposition,[status(thm)],[c_1243,c_95394]) ).
tcf(c_95632,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_95394,c_1246]) ).
tcf(c_95642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),X4)),X3),
inference(superposition,[status(thm)],[c_16673,c_95405]) ).
tcf(c_95643,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),
inference(superposition,[status(thm)],[c_16704,c_95405]) ).
tcf(c_95645,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),
inference(superposition,[status(thm)],[c_16752,c_95405]) ).
tcf(c_95646,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),
inference(superposition,[status(thm)],[c_16953,c_95405]) ).
tcf(c_95651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3),X2)),X4)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X4,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4)),X2),
inference(superposition,[status(thm)],[c_95405,c_16673]) ).
tcf(c_95652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X4)),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3)),X4),
inference(superposition,[status(thm)],[c_95405,c_16673]) ).
tcf(c_95664,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
inference(superposition,[status(thm)],[c_93020,c_95462]) ).
tcf(c_95669,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_95462,c_1246]) ).
tcf(c_95670,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)) = X0,
inference(superposition,[status(thm)],[c_95462,c_93020]) ).
tcf(c_95671,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),X0),
inference(superposition,[status(thm)],[c_95462,c_93019]) ).
tcf(c_95672,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),X0),
inference(superposition,[status(thm)],[c_95462,c_93018]) ).
tcf(c_95693,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_93020,c_1247]) ).
tcf(c_95695,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X1) ),
inference(superposition,[status(thm)],[c_95331,c_1247]) ).
tcf(c_95696,plain,
! [X0: $i,X1: $i] :
( 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,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_95394,c_1247]) ).
tcf(c_95697,plain,
! [X0: $i,X1: $i] :
( 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,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)) ),
inference(superposition,[status(thm)],[c_95462,c_1247]) ).
tcf(c_95700,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)) ),
inference(superposition,[status(thm)],[c_1247,c_235]) ).
tcf(c_95701,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_1247,c_295]) ).
tcf(c_95702,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_1247,c_292]) ).
tcf(c_95703,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_1247,c_663]) ).
tcf(c_95717,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95700,c_1376]) ).
tcf(c_95727,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_93020,c_1251]) ).
tcf(c_95731,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) ),
inference(superposition,[status(thm)],[c_1251,c_293]) ).
tcf(c_95732,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_1251,c_662]) ).
tcf(c_95733,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) ),
inference(superposition,[status(thm)],[c_1251,c_668]) ).
tcf(c_95734,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_1251,c_676]) ).
tcf(c_95735,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),
inference(superposition,[status(thm)],[c_1251,c_94516]) ).
tcf(c_95736,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0),
inference(superposition,[status(thm)],[c_1251,c_94619]) ).
tcf(c_95744,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95731,c_1367]) ).
tcf(c_95759,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
| ~ class_Orderings_Olinorder(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_301,c_1252]) ).
tcf(c_95764,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91783,c_1252]) ).
tcf(c_95765,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) ),
inference(superposition,[status(thm)],[c_661,c_1252]) ).
tcf(c_95768,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_669,c_1252]) ).
tcf(c_95772,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),
inference(superposition,[status(thm)],[c_95466,c_1252]) ).
tcf(c_95774,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_93020,c_1252]) ).
tcf(c_95785,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95759,c_1368]) ).
tcf(c_95793,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(superposition,[status(thm)],[c_680,c_11908]) ).
tcf(c_95795,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(superposition,[status(thm)],[c_681,c_11908]) ).
tcf(c_95796,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(superposition,[status(thm)],[c_925,c_11908]) ).
tcf(c_95797,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1243,c_11908]) ).
tcf(c_95798,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(superposition,[status(thm)],[c_95456,c_11908]) ).
tcf(c_95809,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1),
inference(superposition,[status(thm)],[c_16716,c_95611]) ).
tcf(c_95810,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2)),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),
inference(superposition,[status(thm)],[c_16929,c_95611]) ).
tcf(c_95811,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),
inference(superposition,[status(thm)],[c_16935,c_95611]) ).
tcf(c_95817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3),X2)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X1))),X2),
inference(superposition,[status(thm)],[c_95611,c_16673]) ).
tcf(c_95818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X3)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X4)),X2)),X3),
inference(superposition,[status(thm)],[c_95611,c_16673]) ).
tcf(c_95819,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_95611,c_95427]) ).
tcf(c_95833,plain,
! [X0: $i] : c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Ominus__class_Ominus(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0)) = X0,
inference(superposition,[status(thm)],[c_95623,c_95542]) ).
tcf(c_95840,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))) ),
inference(superposition,[status(thm)],[c_95671,c_293]) ).
tcf(c_95842,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))),X0),
inference(superposition,[status(thm)],[c_95671,c_1252]) ).
tcf(c_95843,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_95840,c_1367]) ).
tcf(c_95855,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))),X0),
inference(superposition,[status(thm)],[c_95672,c_666]) ).
tcf(c_95861,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_551,c_92168]) ).
tcf(c_95863,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),X1),
inference(superposition,[status(thm)],[c_92168,c_50323]) ).
tcf(c_95864,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))),
inference(superposition,[status(thm)],[c_92168,c_93809]) ).
tcf(c_95865,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))),
inference(superposition,[status(thm)],[c_92168,c_92057]) ).
tcf(c_95866,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
inference(superposition,[status(thm)],[c_92168,c_91603]) ).
tcf(c_95870,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92168,c_295]) ).
tcf(c_95871,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92168,c_292]) ).
tcf(c_95872,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))),
inference(superposition,[status(thm)],[c_92168,c_320]) ).
tcf(c_95873,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)))),
inference(superposition,[status(thm)],[c_92168,c_449]) ).
tcf(c_95874,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15))),
inference(superposition,[status(thm)],[c_92168,c_92561]) ).
tcf(c_95875,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15))),
inference(superposition,[status(thm)],[c_92168,c_92047]) ).
tcf(c_95883,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),iPr_def_20),X0) = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_50949,c_72176]) ).
tcf(c_95890,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,iPr_def_20)),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1),iPr_def_20) ) ),
inference(superposition,[status(thm)],[c_95883,c_17708]) ).
tcf(c_95891,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X0)),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1)) ) ),
inference(superposition,[status(thm)],[c_95883,c_17708]) ).
tcf(c_95892,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20)),X0) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20) ) ),
inference(superposition,[status(thm)],[c_95883,c_17702]) ).
tcf(c_95895,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),iPr_def_20),X1) ) ),
inference(light_normalisation,[status(thm)],[c_95891,c_90508]) ).
tcf(c_95898,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1),iPr_def_20) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),iPr_def_20),X1) ) ),
inference(light_normalisation,[status(thm)],[c_95890,c_90491]) ).
tcf(c_95904,plain,
! [X0: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(light_normalisation,[status(thm)],[c_51464,c_72176]) ).
tcf(c_95917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3))),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3)) ) ),
inference(superposition,[status(thm)],[c_95904,c_16673]) ).
tcf(c_95918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3)) ) ),
inference(superposition,[status(thm)],[c_95904,c_16673]) ).
tcf(c_95921,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0),X1) ) ),
inference(superposition,[status(thm)],[c_95904,c_16716]) ).
tcf(c_95922,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0),X1) ) ),
inference(superposition,[status(thm)],[c_95904,c_16704]) ).
tcf(c_95923,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_95904,c_16698]) ).
tcf(c_95924,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X1) ) ),
inference(superposition,[status(thm)],[c_95904,c_16716]) ).
tcf(c_95925,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X1) ) ),
inference(superposition,[status(thm)],[c_95904,c_16704]) ).
tcf(c_95926,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1) )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_95904,c_93192]) ).
tcf(c_95927,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_95904,c_17554]) ).
tcf(c_95928,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X0)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_95904,c_17690]) ).
tcf(c_95929,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1) = iPr_def_20 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0)),X1) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_95904,c_17708]) ).
tcf(c_95930,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ) ),
inference(superposition,[status(thm)],[c_95904,c_39652]) ).
tcf(c_95953,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X2)) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_95930,c_94847]) ).
tcf(c_95958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3))),X3)) ) ),
inference(light_normalisation,[status(thm)],[c_95917,c_94847]) ).
tcf(c_95975,plain,
! [X0: $i] : hAPP(c_Polynomial_Opoly(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1361,c_68]) ).
tcf(c_95976,plain,
! [X0: $i] : hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1409,c_68]) ).
tcf(c_95977,plain,
! [X0: $i] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1448,c_68]) ).
tcf(c_95978,plain,
! [X0: $i,X1: $i] :
( ( hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(superposition,[status(thm)],[c_1502,c_68]) ).
tcf(c_95979,plain,
! [X0: $i] : hAPP(c_Polynomial_Opoly(iPr_def_10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))),X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_90798,c_68]) ).
tcf(c_95980,plain,
! [X0: $i] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10)),X0) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_95977,c_72166,c_72176]) ).
tcf(c_95994,plain,
! [X0: $i,X1: $i] :
( ( hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Oidom(X0) ),
inference(superposition,[status(thm)],[c_1527,c_78]) ).
tcf(c_96003,plain,
! [X0: $i] : c_Polynomial_Osynthetic__div(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_1361,c_125]) ).
tcf(c_96004,plain,
! [X0: $i] : c_Polynomial_Osynthetic__div(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1409,c_125]) ).
tcf(c_96005,plain,
! [X0: $i] : c_Polynomial_Osynthetic__div(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_1448,c_125]) ).
tcf(c_96006,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osynthetic__div(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(superposition,[status(thm)],[c_1502,c_125]) ).
tcf(c_96007,plain,
! [X0: $i] : c_Polynomial_Osynthetic__div(iPr_def_10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),
inference(superposition,[status(thm)],[c_90798,c_125]) ).
tcf(c_96008,plain,
! [X0: $i] : c_Polynomial_Osynthetic__div(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10),X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_96005,c_72166]) ).
tcf(c_96026,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_92376,c_50323]) ).
tcf(c_96030,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_92376,c_245]) ).
tcf(c_96031,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_92376,c_240]) ).
tcf(c_96032,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_92376,c_235]) ).
tcf(c_96039,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(superposition,[status(thm)],[c_92376,c_320]) ).
tcf(c_96058,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15) ),
inference(superposition,[status(thm)],[c_1214,c_92389]) ).
tcf(c_96063,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92389,c_50323]) ).
tcf(c_96064,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92389,c_93809]) ).
tcf(c_96065,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92389,c_92057]) ).
tcf(c_96067,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92389,c_245]) ).
tcf(c_96068,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92389,c_240]) ).
tcf(c_96069,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92389,c_235]) ).
tcf(c_96089,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_440,c_92408]) ).
tcf(c_96098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_92408,c_464]) ).
tcf(c_96099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_92408,c_463]) ).
tcf(c_96100,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_92408,c_91292]) ).
tcf(c_96132,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_96089,c_293]) ).
tcf(c_96153,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_92420,c_50323]) ).
tcf(c_96157,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_92420,c_245]) ).
tcf(c_96158,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_92420,c_240]) ).
tcf(c_96159,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_92420,c_235]) ).
tcf(c_96166,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(superposition,[status(thm)],[c_92420,c_320]) ).
tcf(c_96189,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92433,c_50323]) ).
tcf(c_96190,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92433,c_93809]) ).
tcf(c_96191,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92433,c_92057]) ).
tcf(c_96193,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92433,c_245]) ).
tcf(c_96194,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92433,c_240]) ).
tcf(c_96195,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92433,c_235]) ).
tcf(c_96221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_92451,c_464]) ).
tcf(c_96222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_92451,c_463]) ).
tcf(c_96223,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_92451,c_91292]) ).
tcf(c_96229,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = X1 ) ),
inference(superposition,[status(thm)],[c_256,c_92475]) ).
tcf(c_96232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),X2),
inference(superposition,[status(thm)],[c_633,c_92475]) ).
tcf(c_96235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),X1),
inference(superposition,[status(thm)],[c_632,c_92475]) ).
tcf(c_96240,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1214,c_92475]) ).
tcf(c_96258,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92519,c_49959]) ).
tcf(c_96259,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92519,c_300]) ).
tcf(c_96260,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92519,c_293]) ).
tcf(c_96276,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,X0),c_Polynomial_Odegree(tc_Int_Oint,X0))
| ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_91548,c_159]) ).
tcf(c_96277,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,X0),c_Polynomial_Odegree(tc_Nat_Onat,X0))
| ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91549,c_159]) ).
tcf(c_96278,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,X0),c_Polynomial_Odegree(tc_Complex_Ocomplex,X0))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_91550,c_159]) ).
tcf(c_96279,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(iPr_def_10,X0),c_Polynomial_Odegree(iPr_def_10,X0))
| ~ class_Rings_Ocomm__semiring__0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_91552,c_159]) ).
tcf(c_96280,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))),c_Polynomial_Odegree(tc_Int_Oint,X0))
| ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_93030,c_159]) ).
tcf(c_96281,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(iPr_def_10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))),c_Polynomial_Odegree(iPr_def_10,X0))
| ~ class_Rings_Ocomm__semiring__0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_93033,c_159]) ).
tcf(c_96282,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10)),c_Polynomial_Odegree(tc_Complex_Ocomplex,X0))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_93034,c_159]) ).
tcf(c_96283,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))),c_Polynomial_Odegree(tc_Nat_Onat,X0))
| ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93046,c_159]) ).
tcf(c_96284,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)),iPr_def_15)
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_72171,c_159]) ).
tcf(c_96285,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Polynomial_Osmult(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92190,c_159]) ).
tcf(c_96286,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Polynomial_Osmult(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91928,c_159]) ).
tcf(c_96287,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_91927,c_159]) ).
tcf(c_96288,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(iPr_def_10,c_Polynomial_Osmult(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_91931,c_159]) ).
tcf(c_96289,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(iPr_def_10))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_91932,c_159]) ).
tcf(c_96290,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_92189,c_159]) ).
tcf(c_96291,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(iPr_def_10,c_Polynomial_Osmult(iPr_def_10,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(iPr_def_10)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_92193,c_159]) ).
tcf(c_96292,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(iPr_def_10))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_92194,c_159]) ).
tcf(c_96293,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X2,X1))) ),
inference(superposition,[status(thm)],[c_159,c_49959]) ).
tcf(c_96296,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)),iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_96284,c_1448]) ).
tcf(c_96297,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,X0))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(light_normalisation,[status(thm)],[c_96282,c_91932]) ).
tcf(c_96298,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Nat_Onat,X0))
| ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
inference(light_normalisation,[status(thm)],[c_96283,c_91928]) ).
tcf(c_96299,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(iPr_def_10,X0))
| ~ class_Rings_Ocomm__semiring__0(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_96281,c_91931]) ).
tcf(c_96300,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Int_Oint,X0))
| ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_96280,c_91927]) ).
tcf(c_96301,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(iPr_def_10))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_subsumption_resolution,[status(thm)],[c_96292,c_1448]) ).
tcf(c_96302,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(iPr_def_10))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_subsumption_resolution,[status(thm)],[c_96289,c_1448]) ).
tcf(c_96305,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(iPr_def_10,c_Polynomial_Osmult(iPr_def_10,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(iPr_def_10)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_subsumption_resolution,[status(thm)],[c_96291,c_90798]) ).
tcf(c_96306,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_subsumption_resolution,[status(thm)],[c_96290,c_1361]) ).
tcf(c_96307,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(iPr_def_10,c_Polynomial_Osmult(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_subsumption_resolution,[status(thm)],[c_96288,c_90798]) ).
tcf(c_96308,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_subsumption_resolution,[status(thm)],[c_96287,c_1361]) ).
tcf(c_96309,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Polynomial_Osmult(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_subsumption_resolution,[status(thm)],[c_96286,c_1409]) ).
tcf(c_96310,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Polynomial_Osmult(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_subsumption_resolution,[status(thm)],[c_96285,c_1409]) ).
tcf(c_96325,plain,
! [X0: $i] : c_Polynomial_Osmult(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_1361,c_176]) ).
tcf(c_96326,plain,
! [X0: $i] : c_Polynomial_Osmult(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1409,c_176]) ).
tcf(c_96327,plain,
! [X0: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_1448,c_176]) ).
tcf(c_96328,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osmult(tc_Polynomial_Opoly(X0),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(superposition,[status(thm)],[c_1502,c_176]) ).
tcf(c_96329,plain,
! [X0: $i] : c_Polynomial_Osmult(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),
inference(superposition,[status(thm)],[c_90798,c_176]) ).
tcf(c_96330,plain,
! [X0: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(iPr_def_10)) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_96327,c_72166]) ).
tcf(c_96344,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osmult(tc_Polynomial_Opoly(X0),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) )
| ~ class_Rings_Oidom(X0) ),
inference(superposition,[status(thm)],[c_1527,c_187]) ).
tcf(c_96353,plain,
! [X0: $i] : c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1386,c_202]) ).
tcf(c_96354,plain,
! [X0: $i] : c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1470,c_202]) ).
tcf(c_96355,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Odegree(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Rings_Oidom(X0) ),
inference(superposition,[status(thm)],[c_1527,c_202]) ).
tcf(c_96356,plain,
! [X0: $i] : c_Polynomial_Odegree(iPr_def_10,c_Polynomial_Osmult(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_90985,c_202]) ).
tcf(c_96363,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),iPr_def_15),
inference(superposition,[status(thm)],[c_91550,c_96296]) ).
tcf(c_96364,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10)),iPr_def_15),
inference(superposition,[status(thm)],[c_93034,c_96296]) ).
tcf(c_96365,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p))),
inference(superposition,[status(thm)],[c_96296,c_49959]) ).
tcf(c_96368,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_96363,c_72171]) ).
tcf(c_96371,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10)),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10)))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_96330,c_159]) ).
tcf(c_96372,plain,
! [X0: $i,X1: $i] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X1)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X1),
inference(superposition,[status(thm)],[c_96330,c_91915]) ).
tcf(c_96373,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(light_normalisation,[status(thm)],[c_96371,c_91932]) ).
tcf(c_96375,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)),iPr_def_15)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_256,c_96365]) ).
tcf(c_96377,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)),
inference(superposition,[status(thm)],[c_91550,c_96365]) ).
tcf(c_96378,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10))),
inference(superposition,[status(thm)],[c_93034,c_96365]) ).
tcf(c_96379,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_96377,c_72171]) ).
tcf(c_96393,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92520,c_49959]) ).
tcf(c_96394,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92520,c_300]) ).
tcf(c_96395,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_92520,c_293]) ).
tcf(c_96425,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = X2 ) ),
inference(superposition,[status(thm)],[c_256,c_92736]) ).
tcf(c_96428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X3),
inference(superposition,[status(thm)],[c_633,c_92736]) ).
tcf(c_96431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X2),
inference(superposition,[status(thm)],[c_632,c_92736]) ).
tcf(c_96448,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_256,c_92938]) ).
tcf(c_96457,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_1097,c_92938]) ).
tcf(c_96459,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_92157,c_92938]) ).
tcf(c_96488,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_96459,c_1148]) ).
tcf(c_96489,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)),
inference(superposition,[status(thm)],[c_96459,c_91436]) ).
tcf(c_96504,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_256,c_93136]) ).
tcf(c_96507,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_96459,c_93136]) ).
tcf(c_96508,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_93100,c_93136]) ).
tcf(c_96509,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92157,c_93136]) ).
tcf(c_96510,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91901,c_93136]) ).
tcf(c_96514,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_1097,c_93136]) ).
tcf(c_96523,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1) != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_51469,c_72176]) ).
tcf(c_96536,plain,
! [X0: $i] : hAPP(c_Polynomial_Opoly(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint))),X0) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1360,c_302]) ).
tcf(c_96537,plain,
! [X0: $i] : hAPP(c_Polynomial_Opoly(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat))),X0) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1408,c_302]) ).
tcf(c_96538,plain,
! [X0: $i] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1447,c_302]) ).
tcf(c_96539,plain,
! [X0: $i,X1: $i] :
( ( hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(X0),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))),X1) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_302]) ).
tcf(c_96540,plain,
! [X0: $i] : hAPP(c_Polynomial_Opoly(iPr_def_10,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(iPr_def_10))),X0) = c_Groups_Oone__class_Oone(iPr_def_10),
inference(superposition,[status(thm)],[c_90792,c_302]) ).
tcf(c_96541,plain,
! [X0: $i] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(iPr_def_10)),X0) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(light_normalisation,[status(thm)],[c_96538,c_72166]) ).
tcf(c_96553,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1369,c_312]) ).
tcf(c_96555,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1454,c_312]) ).
tcf(c_96556,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1510,c_312]) ).
tcf(c_96557,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(iPr_def_10),c_Groups_Oone__class_Oone(iPr_def_10)),X0) = c_Groups_Oone__class_Oone(iPr_def_10),
inference(superposition,[status(thm)],[c_90842,c_312]) ).
tcf(c_96558,plain,
! [X0: $i] : hAPP(hAPP(iPr_def_13,c_Groups_Oone__class_Oone(iPr_def_10)),X0) = c_Groups_Oone__class_Oone(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_96557,c_72169]) ).
tcf(c_96571,plain,
( ~ class_Rings_Olinordered__semidom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_227,c_333]) ).
tcf(c_96578,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(superposition,[status(thm)],[c_92805,c_333]) ).
tcf(c_96579,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92283,c_333]) ).
tcf(c_96583,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_632,c_333]) ).
tcf(c_96586,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(superposition,[status(thm)],[c_1097,c_333]) ).
tcf(c_96590,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(superposition,[status(thm)],[c_91886,c_333]) ).
tcf(c_96596,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_94656,c_333]) ).
tcf(c_96603,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_440,c_333]) ).
tcf(c_96604,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_551,c_333]) ).
tcf(c_96629,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)) = v_n____ ) ),
inference(superposition,[status(thm)],[c_256,c_93168]) ).
tcf(c_96632,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),X1),v_n____),
inference(superposition,[status(thm)],[c_551,c_93168]) ).
tcf(c_96641,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)) = v_n____ ) ),
inference(superposition,[status(thm)],[c_256,c_93177]) ).
tcf(c_96644,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),X1),v_n____),
inference(superposition,[status(thm)],[c_551,c_93177]) ).
tcf(c_96656,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_91818,c_93327]) ).
tcf(c_96658,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_700,c_93327]) ).
tcf(c_96659,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),X0),
inference(superposition,[status(thm)],[c_891,c_93327]) ).
tcf(c_96671,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_665,c_93329]) ).
tcf(c_96685,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_1247,c_93333]) ).
tcf(c_96688,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_95672,c_93333]) ).
tcf(c_96691,plain,
! [X0: $i] :
( ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,X0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_93508,c_90827,c_93508]) ).
tcf(c_96713,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_421,c_93841]) ).
tcf(c_96714,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92451,c_93841]) ).
tcf(c_96715,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92408,c_93841]) ).
tcf(c_96716,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_50489,c_93841]) ).
tcf(c_96740,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)) ) ),
inference(light_normalisation,[status(thm)],[c_51471,c_72176]) ).
tcf(c_96751,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X0),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1)),X0),X2) ) ),
inference(superposition,[status(thm)],[c_16929,c_96740]) ).
tcf(c_96752,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2)),X1) ) ),
inference(superposition,[status(thm)],[c_16935,c_96740]) ).
tcf(c_96753,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X0),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1) ) ),
inference(superposition,[status(thm)],[c_91833,c_96740]) ).
tcf(c_96754,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X0)) ) ),
inference(superposition,[status(thm)],[c_91822,c_96740]) ).
tcf(c_96755,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X0),X2),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1) ) ),
inference(superposition,[status(thm)],[c_95611,c_96740]) ).
tcf(c_96756,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))) ) ),
inference(superposition,[status(thm)],[c_37700,c_96740]) ).
tcf(c_96759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),X4),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X0)) ) ),
inference(superposition,[status(thm)],[c_39652,c_96740]) ).
tcf(c_96762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X4),X3)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),X3) ) ),
inference(superposition,[status(thm)],[c_96740,c_16673]) ).
tcf(c_96763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X0))),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X3)),X0) ) ),
inference(superposition,[status(thm)],[c_96740,c_16673]) ).
tcf(c_96765,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0),X1) = X2 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_96740,c_91252]) ).
tcf(c_96766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X3),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X0)) ) ),
inference(superposition,[status(thm)],[c_96740,c_16716]) ).
tcf(c_96767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X3),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X0)) ) ),
inference(superposition,[status(thm)],[c_96740,c_16704]) ).
tcf(c_96768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X3)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) ) ),
inference(superposition,[status(thm)],[c_96740,c_16716]) ).
tcf(c_96769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X3)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) ) ),
inference(superposition,[status(thm)],[c_96740,c_16704]) ).
tcf(c_96770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0),X1)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2) )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4) ) ),
inference(superposition,[status(thm)],[c_96740,c_93192]) ).
tcf(c_96771,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))) ) ),
inference(superposition,[status(thm)],[c_96740,c_17690]) ).
tcf(c_96772,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(superposition,[status(thm)],[c_96740,c_17614]) ).
tcf(c_96773,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X0 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0) = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0)) ) ),
inference(superposition,[status(thm)],[c_96740,c_92641]) ).
tcf(c_96774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X3),X4),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X3,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)))) ) ),
inference(superposition,[status(thm)],[c_96740,c_39652]) ).
tcf(c_96776,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,iPr_def_20) ) ),
inference(light_normalisation,[status(thm)],[c_96754,c_90508]) ).
tcf(c_96781,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1) ) ),
inference(light_normalisation,[status(thm)],[c_96772,c_94859]) ).
tcf(c_96782,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[c_96781,c_91065]) ).
tcf(c_96792,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))) ) ),
inference(light_normalisation,[status(thm)],[c_96771,c_37700]) ).
tcf(c_96844,plain,
! [X0: $i] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_1361,c_396]) ).
tcf(c_96845,plain,
! [X0: $i] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1409,c_396]) ).
tcf(c_96846,plain,
! [X0: $i] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_1448,c_396]) ).
tcf(c_96847,plain,
! [X0: $i,X1: $i] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(superposition,[status(thm)],[c_1502,c_396]) ).
tcf(c_96848,plain,
! [X0: $i] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(iPr_def_10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),
inference(superposition,[status(thm)],[c_90798,c_396]) ).
tcf(c_96849,plain,
! [X0: $i] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10),X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_96846,c_72166]) ).
tcf(c_96861,plain,
! [X0: $i,X1: $i] : c_Polynomial_Odegree(tc_Int_Oint,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,X0,X1)) = c_Polynomial_Odegree(tc_Int_Oint,X0),
inference(superposition,[status(thm)],[c_1361,c_398]) ).
tcf(c_96862,plain,
! [X0: $i,X1: $i] : c_Polynomial_Odegree(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Nat_Onat,X0,X1)) = c_Polynomial_Odegree(tc_Nat_Onat,X0),
inference(superposition,[status(thm)],[c_1409,c_398]) ).
tcf(c_96863,plain,
! [X0: $i,X1: $i] : c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X0,X1)) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X0),
inference(superposition,[status(thm)],[c_1448,c_398]) ).
tcf(c_96864,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Odegree(tc_Polynomial_Opoly(X0),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Polynomial_Opoly(X0),X1,X2)) = c_Polynomial_Odegree(tc_Polynomial_Opoly(X0),X1) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(superposition,[status(thm)],[c_1502,c_398]) ).
tcf(c_96865,plain,
! [X0: $i,X1: $i] : c_Polynomial_Odegree(iPr_def_10,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(iPr_def_10,X0,X1)) = c_Polynomial_Odegree(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_90798,c_398]) ).
tcf(c_96895,plain,
( ~ class_Orderings_Olinorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_94092,c_245]) ).
tcf(c_96896,plain,
( ~ class_Orderings_Opreorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_94092,c_240]) ).
tcf(c_96897,plain,
( ~ class_Orderings_Oorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_94092,c_235]) ).
tcf(c_96898,plain,
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10)),c_Groups_Ozero__class_Ozero(iPr_def_10))
| ~ class_Orderings_Oorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94092,c_295]) ).
tcf(c_96899,plain,
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10)),c_Groups_Ozero__class_Ozero(iPr_def_10))
| ~ class_Orderings_Opreorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94092,c_292]) ).
tcf(c_96921,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_94212,c_94256]) ).
tcf(c_96923,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_95602,c_94256]) ).
tcf(c_96924,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0),X0) ),
inference(superposition,[status(thm)],[c_94256,c_245]) ).
tcf(c_96925,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0),X0) ),
inference(superposition,[status(thm)],[c_94256,c_240]) ).
tcf(c_96926,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0),X0) ),
inference(superposition,[status(thm)],[c_94256,c_235]) ).
tcf(c_96927,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0))
| ~ class_Orderings_Oorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_94256,c_295]) ).
tcf(c_96928,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0))
| ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_94256,c_292]) ).
tcf(c_96961,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,X0,c_Groups_Oplus__class_Oplus(iPr_def_10,X0,c_Groups_Oone__class_Oone(iPr_def_10)))
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94214,c_94279]) ).
tcf(c_96963,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ominus__class_Ominus(iPr_def_10,X0,c_Groups_Oone__class_Oone(iPr_def_10)),X0)
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_95617,c_94279]) ).
tcf(c_96964,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),X0),X0) ),
inference(superposition,[status(thm)],[c_94279,c_245]) ).
tcf(c_96965,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),X0),X0) ),
inference(superposition,[status(thm)],[c_94279,c_240]) ).
tcf(c_96966,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),X0),X0) ),
inference(superposition,[status(thm)],[c_94279,c_235]) ).
tcf(c_96967,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,X0,c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),X0))
| ~ class_Orderings_Oorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94279,c_295]) ).
tcf(c_96968,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,X0,c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),X0))
| ~ class_Orderings_Opreorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94279,c_292]) ).
tcf(c_96997,plain,
c_Orderings_Oord__class_Oless__eq(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(superposition,[status(thm)],[c_1098,c_94346]) ).
tcf(c_97004,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91871,c_94346]) ).
tcf(c_97028,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_669,c_94504]) ).
tcf(c_97040,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))
| ~ class_Rings_Olinordered__semidom(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_224,c_94551]) ).
tcf(c_97041,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| 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(superposition,[status(thm)],[c_91757,c_94551]) ).
tcf(c_97042,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 ) ),
inference(superposition,[status(thm)],[c_697,c_94551]) ).
tcf(c_97044,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(superposition,[status(thm)],[c_679,c_94551]) ).
tcf(c_97045,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91757,c_94551]) ).
tcf(c_97047,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_95465,c_94551]) ).
tcf(c_97048,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_95672,c_94551]) ).
tcf(c_97063,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
inference(superposition,[status(thm)],[c_97045,c_662]) ).
tcf(c_97064,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_97045,c_668]) ).
tcf(c_97068,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_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_97045,c_94516]) ).
tcf(c_97069,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),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_97045,c_94619]) ).
tcf(c_97084,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(superposition,[status(thm)],[c_91818,c_94636]) ).
tcf(c_97085,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))),
inference(superposition,[status(thm)],[c_95462,c_94636]) ).
tcf(c_97086,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_700,c_94636]) ).
tcf(c_97087,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),X0),
inference(superposition,[status(thm)],[c_891,c_94636]) ).
tcf(c_97093,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0)),
inference(superposition,[status(thm)],[c_551,c_94661]) ).
tcf(c_97098,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),X0),
inference(superposition,[status(thm)],[c_94661,c_50323]) ).
tcf(c_97101,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))),
inference(superposition,[status(thm)],[c_94661,c_91603]) ).
tcf(c_97102,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),X0) ),
inference(superposition,[status(thm)],[c_94661,c_245]) ).
tcf(c_97103,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),X0) ),
inference(superposition,[status(thm)],[c_94661,c_240]) ).
tcf(c_97104,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),X0) ),
inference(superposition,[status(thm)],[c_94661,c_235]) ).
tcf(c_97105,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94661,c_295]) ).
tcf(c_97106,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94661,c_292]) ).
tcf(c_97107,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))),
inference(superposition,[status(thm)],[c_94661,c_320]) ).
tcf(c_97108,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_94661,c_333]) ).
tcf(c_97109,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2))),
inference(superposition,[status(thm)],[c_94661,c_449]) ).
tcf(c_97114,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)) ) ),
inference(light_normalisation,[status(thm)],[c_51473,c_72176]) ).
tcf(c_97125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X3,X4),X2)),X1),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X1)),X2),X3) ) ),
inference(superposition,[status(thm)],[c_16673,c_97114]) ).
tcf(c_97127,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X0),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X1)),X0),X2) ) ),
inference(superposition,[status(thm)],[c_16752,c_97114]) ).
tcf(c_97128,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2)),X1) ) ),
inference(superposition,[status(thm)],[c_16953,c_97114]) ).
tcf(c_97129,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X0)),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1) ) ),
inference(superposition,[status(thm)],[c_94036,c_97114]) ).
tcf(c_97130,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) ) ),
inference(superposition,[status(thm)],[c_94212,c_97114]) ).
tcf(c_97131,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X0)) ) ),
inference(superposition,[status(thm)],[c_91118,c_97114]) ).
tcf(c_97132,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2) ) ),
inference(superposition,[status(thm)],[c_95602,c_97114]) ).
tcf(c_97133,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))) ) ),
inference(superposition,[status(thm)],[c_37700,c_97114]) ).
tcf(c_97136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)),X4),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,X0)) ) ),
inference(superposition,[status(thm)],[c_39652,c_97114]) ).
tcf(c_97140,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0),X1) = X2 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_97114,c_91252]) ).
tcf(c_97141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X3),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X0)) ) ),
inference(superposition,[status(thm)],[c_97114,c_16716]) ).
tcf(c_97142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X3),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X0)) ) ),
inference(superposition,[status(thm)],[c_97114,c_16704]) ).
tcf(c_97143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X3)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) ) ),
inference(superposition,[status(thm)],[c_97114,c_16716]) ).
tcf(c_97144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X3)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) ) ),
inference(superposition,[status(thm)],[c_97114,c_16704]) ).
tcf(c_97145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0),X1)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2) )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4) ) ),
inference(superposition,[status(thm)],[c_97114,c_93192]) ).
tcf(c_97146,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1),X2),X0)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))) ) ),
inference(superposition,[status(thm)],[c_97114,c_17690]) ).
tcf(c_97147,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(superposition,[status(thm)],[c_97114,c_17614]) ).
tcf(c_97148,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X0 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0)) ) ),
inference(superposition,[status(thm)],[c_97114,c_92945]) ).
tcf(c_97149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X3),X4),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)))) ) ),
inference(superposition,[status(thm)],[c_97114,c_39652]) ).
tcf(c_97151,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,iPr_def_20) ) ),
inference(light_normalisation,[status(thm)],[c_97131,c_90508]) ).
tcf(c_97156,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1) ) ),
inference(light_normalisation,[status(thm)],[c_97147,c_94859]) ).
tcf(c_97157,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[c_97156,c_91065]) ).
tcf(c_97169,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2),X0)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))) ) ),
inference(light_normalisation,[status(thm)],[c_97146,c_37700]) ).
tcf(c_97227,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_543]) ).
tcf(c_97228,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(iPr_def_10),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(iPr_def_10),
inference(superposition,[status(thm)],[c_90792,c_543]) ).
tcf(c_97236,plain,
c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_1364,c_597]) ).
tcf(c_97237,plain,
c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_1452,c_597]) ).
tcf(c_97238,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1505,c_597]) ).
tcf(c_97239,plain,
c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),
inference(superposition,[status(thm)],[c_90804,c_597]) ).
tcf(c_97249,plain,
! [X0: $i] : c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),X0)) = c_Polynomial_Odegree(tc_Int_Oint,X0),
inference(superposition,[status(thm)],[c_1364,c_598]) ).
tcf(c_97250,plain,
! [X0: $i] : c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0)) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X0),
inference(superposition,[status(thm)],[c_1452,c_598]) ).
tcf(c_97251,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Odegree(tc_Polynomial_Opoly(X0),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)),X1)) = c_Polynomial_Odegree(tc_Polynomial_Opoly(X0),X1) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1505,c_598]) ).
tcf(c_97252,plain,
! [X0: $i] : c_Polynomial_Odegree(iPr_def_10,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),X0)) = c_Polynomial_Odegree(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_90804,c_598]) ).
tcf(c_97253,plain,
! [X0: $i] : c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0)) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X0),
inference(light_normalisation,[status(thm)],[c_97250,c_72166]) ).
tcf(c_97270,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X2)
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_301,c_671]) ).
tcf(c_97274,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X2)
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_421,c_671]) ).
tcf(c_97275,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Rings_Olinordered__semidom(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_362,c_671]) ).
tcf(c_97276,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91783,c_671]) ).
tcf(c_97277,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_661,c_671]) ).
tcf(c_97280,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_669,c_671]) ).
tcf(c_97282,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X1))
| ~ class_Rings_Olinordered__ring(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_750,c_671]) ).
tcf(c_97283,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_985,c_671]) ).
tcf(c_97284,plain,
! [X0: $i,X1: $i] :
( 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,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_91750,c_671]) ).
tcf(c_97286,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_1251,c_671]) ).
tcf(c_97288,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,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,X0,X1) ),
inference(superposition,[status(thm)],[c_91377,c_671]) ).
tcf(c_97289,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91768,c_671]) ).
tcf(c_97290,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(superposition,[status(thm)],[c_93019,c_671]) ).
tcf(c_97291,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_93191,c_671]) ).
tcf(c_97292,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_93558,c_671]) ).
tcf(c_97293,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_95466,c_671]) ).
tcf(c_97294,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))) ),
inference(superposition,[status(thm)],[c_95671,c_671]) ).
tcf(c_97328,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_97270,c_1368]) ).
tcf(c_97335,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_97282,c_1358]) ).
tcf(c_97358,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_97253,c_159]) ).
tcf(c_97359,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_97358,c_1448]) ).
tcf(c_97366,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),v_n____),
inference(superposition,[status(thm)],[c_94676,c_50323]) ).
tcf(c_97367,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_94676,c_93809]) ).
tcf(c_97368,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_94676,c_92057]) ).
tcf(c_97370,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),v_n____) ),
inference(superposition,[status(thm)],[c_94676,c_245]) ).
tcf(c_97371,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),v_n____) ),
inference(superposition,[status(thm)],[c_94676,c_240]) ).
tcf(c_97372,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),v_n____) ),
inference(superposition,[status(thm)],[c_94676,c_235]) ).
tcf(c_97373,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94676,c_295]) ).
tcf(c_97374,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94676,c_292]) ).
tcf(c_97375,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))),
inference(demodulation,[status(thm)],[c_94695,c_553]) ).
tcf(c_97377,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),X1)),
inference(superposition,[status(thm)],[c_551,c_94737]) ).
tcf(c_97382,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_94737,c_49959]) ).
tcf(c_97389,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),X1)),
inference(superposition,[status(thm)],[c_551,c_94738]) ).
tcf(c_97394,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_94738,c_50323]) ).
tcf(c_97397,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15))),
inference(superposition,[status(thm)],[c_94738,c_91603]) ).
tcf(c_97398,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_94738,c_245]) ).
tcf(c_97399,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_94738,c_240]) ).
tcf(c_97400,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_94738,c_235]) ).
tcf(c_97401,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94738,c_295]) ).
tcf(c_97402,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94738,c_292]) ).
tcf(c_97407,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),X1)),
inference(superposition,[status(thm)],[c_551,c_94882]) ).
tcf(c_97412,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_94882,c_49959]) ).
tcf(c_97419,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),X1)),
inference(superposition,[status(thm)],[c_551,c_94883]) ).
tcf(c_97424,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_94883,c_50323]) ).
tcf(c_97427,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1))),
inference(superposition,[status(thm)],[c_94883,c_91603]) ).
tcf(c_97428,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_94883,c_245]) ).
tcf(c_97429,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_94883,c_240]) ).
tcf(c_97430,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_94883,c_235]) ).
tcf(c_97431,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94883,c_295]) ).
tcf(c_97432,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94883,c_292]) ).
tcf(c_97435,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2) ) ),
inference(light_normalisation,[status(thm)],[c_51475,c_72176]) ).
tcf(c_97455,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0)),X1) = X1 ) ),
inference(superposition,[status(thm)],[c_17614,c_97435]) ).
tcf(c_97462,plain,
! [X0: $i] :
( ( X0 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0)),iPr_def_20) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_90491,c_97435]) ).
tcf(c_97464,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0))
| ( X0 = iPr_def_20 )
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_97435,c_750]) ).
tcf(c_97506,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ( X0 = X1 )
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_301,c_672]) ).
tcf(c_97512,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91783,c_672]) ).
tcf(c_97516,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_669,c_672]) ).
tcf(c_97517,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91782,c_672]) ).
tcf(c_97518,plain,
! [X0: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ class_Rings_Olinordered__ring(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_750,c_672]) ).
tcf(c_97520,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_91750,c_672]) ).
tcf(c_97521,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_97045,c_672]) ).
tcf(c_97522,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1 )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) ),
inference(superposition,[status(thm)],[c_1251,c_672]) ).
tcf(c_97525,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_91768,c_672]) ).
tcf(c_97528,plain,
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_93558,c_672]) ).
tcf(c_97554,plain,
! [X0: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_97518,c_1358]) ).
tcf(c_97571,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1360,c_716]) ).
tcf(c_97574,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_716]) ).
tcf(c_97575,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(iPr_def_10),X0),c_Groups_Ozero__class_Ozero(iPr_def_10)) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_90792,c_716]) ).
tcf(c_97589,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1360,c_717]) ).
tcf(c_97592,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_717]) ).
tcf(c_97593,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10)),X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_90792,c_717]) ).
tcf(c_97617,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,iPr_def_15) ),
inference(superposition,[status(thm)],[c_92805,c_95361]) ).
tcf(c_97618,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____) ),
inference(superposition,[status(thm)],[c_92283,c_95361]) ).
tcf(c_97619,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_91982,c_95361]) ).
tcf(c_97628,plain,
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_97619,c_50323]) ).
tcf(c_97629,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_97619,c_93809]) ).
tcf(c_97631,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_97619,c_91603]) ).
tcf(c_97632,plain,
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_97619,c_245]) ).
tcf(c_97633,plain,
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_97619,c_240]) ).
tcf(c_97634,plain,
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_97619,c_235]) ).
tcf(c_97635,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97619,c_295]) ).
tcf(c_97636,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97619,c_292]) ).
tcf(c_97637,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_97619,c_92559]) ).
tcf(c_97645,plain,
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_97629,c_49959]) ).
tcf(c_97646,plain,
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_97629,c_300]) ).
tcf(c_97647,plain,
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_97629,c_293]) ).
tcf(c_97657,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_95388,c_17708]) ).
tcf(c_97659,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_95388,c_17708]) ).
tcf(c_97662,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(light_normalisation,[status(thm)],[c_97659,c_95388]) ).
tcf(c_97669,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_1066,c_95503]) ).
tcf(c_97670,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(superposition,[status(thm)],[c_1067,c_95503]) ).
tcf(c_97680,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_95503,c_50323]) ).
tcf(c_97683,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_95503,c_91603]) ).
tcf(c_97684,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_95503,c_245]) ).
tcf(c_97685,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_95503,c_240]) ).
tcf(c_97686,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_95503,c_235]) ).
tcf(c_97709,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_1066,c_95505]) ).
tcf(c_97710,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(superposition,[status(thm)],[c_1067,c_95505]) ).
tcf(c_97714,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_1144,c_95505]) ).
tcf(c_97715,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1) ),
inference(superposition,[status(thm)],[c_91869,c_95505]) ).
tcf(c_97717,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15) ),
inference(superposition,[status(thm)],[c_91398,c_95505]) ).
tcf(c_97720,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_95505,c_49959]) ).
tcf(c_97722,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_95505,c_300]) ).
tcf(c_97723,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_95505,c_293]) ).
tcf(c_97738,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X1) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_51477,c_72176]) ).
tcf(c_97746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3)) = X0 ) ),
inference(superposition,[status(thm)],[c_39652,c_97738]) ).
tcf(c_97749,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),X1) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) ) ),
inference(superposition,[status(thm)],[c_16698,c_97738]) ).
tcf(c_97750,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) ) ),
inference(superposition,[status(thm)],[c_17554,c_97738]) ).
tcf(c_97751,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_17690,c_97738]) ).
tcf(c_97753,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_17702,c_97738]) ).
tcf(c_97754,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X2) ) ),
inference(superposition,[status(thm)],[c_17708,c_97738]) ).
tcf(c_97755,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0),X1) ) ),
inference(superposition,[status(thm)],[c_96740,c_97738]) ).
tcf(c_97756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) ) ),
inference(superposition,[status(thm)],[c_92641,c_97738]) ).
tcf(c_97757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) ) ),
inference(superposition,[status(thm)],[c_92945,c_97738]) ).
tcf(c_97758,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0),X1) ) ),
inference(superposition,[status(thm)],[c_97114,c_97738]) ).
tcf(c_97761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3))),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3)),X4),X3)),X2)) ) ),
inference(superposition,[status(thm)],[c_97738,c_16673]) ).
tcf(c_97762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X2)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2)),X2) ) ),
inference(superposition,[status(thm)],[c_97738,c_16673]) ).
tcf(c_97763,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)) ) ),
inference(superposition,[status(thm)],[c_97738,c_97114]) ).
tcf(c_97764,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0) = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)) ) ),
inference(superposition,[status(thm)],[c_97738,c_96740]) ).
tcf(c_97766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3)) ) ),
inference(superposition,[status(thm)],[c_97738,c_92945]) ).
tcf(c_97767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3)) ) ),
inference(superposition,[status(thm)],[c_97738,c_92641]) ).
tcf(c_97768,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2) ) ),
inference(superposition,[status(thm)],[c_97738,c_17554]) ).
tcf(c_97769,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) ) ),
inference(superposition,[status(thm)],[c_97738,c_16973]) ).
tcf(c_97770,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2)) ) ),
inference(superposition,[status(thm)],[c_97738,c_16953]) ).
tcf(c_97771,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2)) ) ),
inference(superposition,[status(thm)],[c_97738,c_16935]) ).
tcf(c_97772,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) ) ),
inference(superposition,[status(thm)],[c_97738,c_16929]) ).
tcf(c_97773,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) ) ),
inference(superposition,[status(thm)],[c_97738,c_16752]) ).
tcf(c_97774,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),X1) ) ),
inference(superposition,[status(thm)],[c_97738,c_16929]) ).
tcf(c_97775,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),X1) ) ),
inference(superposition,[status(thm)],[c_97738,c_16752]) ).
tcf(c_97776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)) ) ),
inference(superposition,[status(thm)],[c_97738,c_39652]) ).
tcf(c_97777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) != X2 ) ),
inference(superposition,[status(thm)],[c_97738,c_93587]) ).
tcf(c_97778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3),X1)) ) ),
inference(superposition,[status(thm)],[c_97738,c_92945]) ).
tcf(c_97779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3),X1)) ) ),
inference(superposition,[status(thm)],[c_97738,c_92641]) ).
tcf(c_97780,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2),X0) ) ),
inference(superposition,[status(thm)],[c_97738,c_16953]) ).
tcf(c_97781,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2),X0) ) ),
inference(superposition,[status(thm)],[c_97738,c_16935]) ).
tcf(c_97783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_97738,c_92945]) ).
tcf(c_97784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))),X3) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_97738,c_92641]) ).
tcf(c_97785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_97738,c_39652]) ).
tcf(c_97965,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Oidom(X0) ),
inference(superposition,[status(thm)],[c_1486,c_720]) ).
tcf(c_97975,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Oidom(X0) ),
inference(superposition,[status(thm)],[c_1486,c_721]) ).
tcf(c_97983,plain,
! [X0: $i] :
( 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),X0),X0))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Rings_Olinordered__ring(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_256,c_807]) ).
tcf(c_97989,plain,
( ~ class_Rings_Olinordered__ring(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_900,c_807]) ).
tcf(c_97991,plain,
( ~ class_Rings_Olinordered__ring(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_912,c_807]) ).
tcf(c_97993,plain,
! [X0: $i] :
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_37700,c_807]) ).
tcf(c_97994,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_94847,c_807]) ).
tcf(c_97996,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_39652,c_807]) ).
tcf(c_97997,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_90947,c_807]) ).
tcf(c_97999,plain,
( ~ class_Rings_Olinordered__ring(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_94849,c_807]) ).
tcf(c_98001,plain,
! [X0: $i] :
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X0),iPr_def_20) ),
inference(superposition,[status(thm)],[c_72176,c_807]) ).
tcf(c_98002,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20) ),
inference(light_normalisation,[status(thm)],[c_97997,c_72176]) ).
tcf(c_98007,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20) ),
inference(light_normalisation,[status(thm)],[c_97994,c_72176]) ).
tcf(c_98016,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),iPr_def_20) ),
inference(light_normalisation,[status(thm)],[c_97996,c_72176]) ).
tcf(c_98060,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_97717,c_49959]) ).
tcf(c_98061,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v_n____ ) ),
inference(superposition,[status(thm)],[c_97717,c_164]) ).
tcf(c_98062,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_97717,c_300]) ).
tcf(c_98063,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_97717,c_293]) ).
tcf(c_98073,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____) ),
inference(superposition,[status(thm)],[c_97717,c_95361]) ).
tcf(c_98096,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ( X0 = v_n____ ) ),
inference(superposition,[status(thm)],[c_256,c_98060]) ).
tcf(c_98100,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15) ),
inference(superposition,[status(thm)],[c_92157,c_98060]) ).
tcf(c_98126,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v_n____ ) ),
inference(superposition,[status(thm)],[c_98061,c_95361]) ).
tcf(c_98142,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____) ),
inference(superposition,[status(thm)],[c_98100,c_95361]) ).
tcf(c_98146,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Divides_Odiv__class_Omod(iPr_def_10,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)) = c_Divides_Odiv__class_Omod(iPr_def_10,X0,X2) ) ),
inference(light_normalisation,[status(thm)],[c_51479,c_72166,c_72176]) ).
tcf(c_98159,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1),X1) = c_Groups_Ozero__class_Ozero(iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_98146,c_91420]) ).
tcf(c_98160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X3))) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1),X3) ) ),
inference(superposition,[status(thm)],[c_98146,c_91915]) ).
tcf(c_98161,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Divides_Odiv__class_Omod(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1),c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X1)) = c_Divides_Odiv__class_Omod(iPr_def_10,X0,X1) ) ),
inference(superposition,[status(thm)],[c_98146,c_93768]) ).
tcf(c_98162,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2))) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X2) ) ),
inference(superposition,[status(thm)],[c_98146,c_92100]) ).
tcf(c_98164,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Divides_Odiv__class_Omod(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)),X2) = c_Divides_Odiv__class_Omod(iPr_def_10,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)) ) ),
inference(superposition,[status(thm)],[c_98146,c_93768]) ).
tcf(c_98181,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_912,c_910]) ).
tcf(c_98186,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)),X0),
inference(superposition,[status(thm)],[c_910,c_49959]) ).
tcf(c_98187,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))),
inference(superposition,[status(thm)],[c_910,c_387]) ).
tcf(c_98190,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)))),
inference(superposition,[status(thm)],[c_910,c_464]) ).
tcf(c_98191,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))),
inference(superposition,[status(thm)],[c_910,c_463]) ).
tcf(c_98192,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),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_910,c_93841]) ).
tcf(c_98193,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15))),
inference(superposition,[status(thm)],[c_910,c_92394]) ).
tcf(c_98201,plain,
! [X0: $i] : c_Polynomial_Opcompose(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_1361,c_958]) ).
tcf(c_98202,plain,
! [X0: $i] : c_Polynomial_Opcompose(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1409,c_958]) ).
tcf(c_98203,plain,
! [X0: $i] : c_Polynomial_Opcompose(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_1448,c_958]) ).
tcf(c_98204,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Opcompose(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(superposition,[status(thm)],[c_1502,c_958]) ).
tcf(c_98205,plain,
! [X0: $i] : c_Polynomial_Opcompose(iPr_def_10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),
inference(superposition,[status(thm)],[c_90798,c_958]) ).
tcf(c_98206,plain,
! [X0: $i] : c_Polynomial_Opcompose(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10),X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_98203,c_72166]) ).
tcf(c_98248,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)),
inference(superposition,[status(thm)],[c_551,c_95861]) ).
tcf(c_98253,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),
inference(superposition,[status(thm)],[c_90483,c_95861]) ).
tcf(c_98254,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),
inference(superposition,[status(thm)],[c_95861,c_50323]) ).
tcf(c_98257,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_95861,c_91603]) ).
tcf(c_98258,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1) ),
inference(superposition,[status(thm)],[c_95861,c_245]) ).
tcf(c_98259,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1) ),
inference(superposition,[status(thm)],[c_95861,c_240]) ).
tcf(c_98260,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1) ),
inference(superposition,[status(thm)],[c_95861,c_235]) ).
tcf(c_98261,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_95861,c_295]) ).
tcf(c_98262,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_95861,c_292]) ).
tcf(c_98263,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_95861,c_320]) ).
tcf(c_98265,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_95861,c_449]) ).
tcf(c_98266,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_95861,c_92561]) ).
tcf(c_98267,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_95861,c_92047]) ).
tcf(c_98277,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_551,c_98253]) ).
tcf(c_98303,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) ) ),
inference(light_normalisation,[status(thm)],[c_51481,c_72176]) ).
tcf(c_98315,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2)),X1),X2) ) ),
inference(superposition,[status(thm)],[c_16929,c_98303]) ).
tcf(c_98316,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0),X2) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),X0) ) ),
inference(superposition,[status(thm)],[c_16935,c_98303]) ).
tcf(c_98317,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X0) ) ),
inference(superposition,[status(thm)],[c_91833,c_98303]) ).
tcf(c_98318,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1),X2) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1) ) ),
inference(superposition,[status(thm)],[c_95332,c_98303]) ).
tcf(c_98319,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X0),X1) ) ),
inference(superposition,[status(thm)],[c_95427,c_98303]) ).
tcf(c_98320,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X0),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0) ) ),
inference(superposition,[status(thm)],[c_95405,c_98303]) ).
tcf(c_98321,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2) ) ),
inference(superposition,[status(thm)],[c_37700,c_98303]) ).
tcf(c_98323,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ) ),
inference(superposition,[status(thm)],[c_94859,c_98303]) ).
tcf(c_98324,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2) = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),X2) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) ) ),
inference(superposition,[status(thm)],[c_97738,c_98303]) ).
tcf(c_98325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4))),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X4))) ) ),
inference(superposition,[status(thm)],[c_39652,c_98303]) ).
tcf(c_98328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X2) ) ),
inference(superposition,[status(thm)],[c_98303,c_16673]) ).
tcf(c_98329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),X4)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4)),X2)),X3) ) ),
inference(superposition,[status(thm)],[c_98303,c_16673]) ).
tcf(c_98330,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) ) ),
inference(superposition,[status(thm)],[c_98303,c_97738]) ).
tcf(c_98332,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = X1 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_98303,c_91252]) ).
tcf(c_98333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X3),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)) ) ),
inference(superposition,[status(thm)],[c_98303,c_16716]) ).
tcf(c_98334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X3),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)) ) ),
inference(superposition,[status(thm)],[c_98303,c_16704]) ).
tcf(c_98335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),X3)) ) ),
inference(superposition,[status(thm)],[c_98303,c_16716]) ).
tcf(c_98336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),X3)) ) ),
inference(superposition,[status(thm)],[c_98303,c_16704]) ).
tcf(c_98337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1) )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4) ) ),
inference(superposition,[status(thm)],[c_98303,c_93192]) ).
tcf(c_98338,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2)),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2) ) ),
inference(superposition,[status(thm)],[c_98303,c_17690]) ).
tcf(c_98339,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1) ) ),
inference(superposition,[status(thm)],[c_98303,c_17614]) ).
tcf(c_98340,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),X0)) ) ),
inference(superposition,[status(thm)],[c_98303,c_96740]) ).
tcf(c_98341,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1) = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),X1)) ) ),
inference(superposition,[status(thm)],[c_98303,c_92641]) ).
tcf(c_98342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),X4)),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),X4)) ) ),
inference(superposition,[status(thm)],[c_98303,c_39652]) ).
tcf(c_98344,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0),X1) = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_98317,c_90508]) ).
tcf(c_98348,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,X1) ) ),
inference(light_normalisation,[status(thm)],[c_98319,c_16973,c_90508]) ).
tcf(c_98351,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1) ) ),
inference(light_normalisation,[status(thm)],[c_98339,c_17614,c_95052]) ).
tcf(c_98365,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2)),X1),X2) ) ),
inference(light_normalisation,[status(thm)],[c_98315,c_17554]) ).
tcf(c_98368,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2)),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2) ) ),
inference(light_normalisation,[status(thm)],[c_98338,c_17690]) ).
tcf(c_98374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2) ) ),
inference(light_normalisation,[status(thm)],[c_98321,c_17690]) ).
tcf(c_98448,plain,
! [X0: $i,X1: $i] : hAPP(c_Polynomial_Ocoeff(tc_Int_Oint,c_Polynomial_Omonom(tc_Int_Oint,X0,X1)),X1) = X0,
inference(superposition,[status(thm)],[c_1384,c_1057]) ).
tcf(c_98449,plain,
! [X0: $i,X1: $i] : hAPP(c_Polynomial_Ocoeff(tc_Nat_Onat,c_Polynomial_Omonom(tc_Nat_Onat,X0,X1)),X1) = X0,
inference(superposition,[status(thm)],[c_1424,c_1057]) ).
tcf(c_98450,plain,
! [X0: $i,X1: $i] : hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),X1) = X0,
inference(superposition,[status(thm)],[c_1468,c_1057]) ).
tcf(c_98451,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_Polynomial_Ocoeff(tc_Polynomial_Opoly(X0),c_Polynomial_Omonom(tc_Polynomial_Opoly(X0),X1,X2)),X2) = X1 )
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_1525,c_1057]) ).
tcf(c_98452,plain,
! [X0: $i,X1: $i] : hAPP(c_Polynomial_Ocoeff(iPr_def_10,c_Polynomial_Omonom(iPr_def_10,X0,X1)),X1) = X0,
inference(superposition,[status(thm)],[c_90973,c_1057]) ).
tcf(c_98470,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X0,
inference(superposition,[status(thm)],[c_1136,c_318]) ).
tcf(c_98471,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1136,c_50323]) ).
tcf(c_98472,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_1136,c_93809]) ).
tcf(c_98473,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_1136,c_92057]) ).
tcf(c_98474,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_1136,c_91603]) ).
tcf(c_98475,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| ~ class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1136,c_223]) ).
tcf(c_98476,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1136,c_245]) ).
tcf(c_98477,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 )
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1136,c_240]) ).
tcf(c_98478,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 )
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1136,c_235]) ).
tcf(c_98481,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0)) = X0 )
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1136,c_296]) ).
tcf(c_98482,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0)) = X0 )
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1136,c_251]) ).
tcf(c_98483,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0)) = X0 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1136,c_249]) ).
tcf(c_98484,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0)) = X0,
inference(superposition,[status(thm)],[c_1136,c_337]) ).
tcf(c_98485,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ) ),
inference(superposition,[status(thm)],[c_1136,c_320]) ).
tcf(c_98486,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))) = X1 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1136,c_333]) ).
tcf(c_98487,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ) ),
inference(superposition,[status(thm)],[c_1136,c_449]) ).
tcf(c_98488,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),
inference(superposition,[status(thm)],[c_1136,c_457]) ).
tcf(c_98489,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(superposition,[status(thm)],[c_1136,c_458]) ).
tcf(c_98490,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0) )
| ~ class_Rings_Olinordered__ring(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1136,c_807]) ).
tcf(c_98491,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_1136,c_1148]) ).
tcf(c_98492,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0),
inference(superposition,[status(thm)],[c_1136,c_91435]) ).
tcf(c_98493,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))) = X0,
inference(superposition,[status(thm)],[c_1136,c_91436]) ).
tcf(c_98494,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_1136,c_93136]) ).
tcf(c_98495,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_1136,c_92938]) ).
tcf(c_98496,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0 ) ),
inference(superposition,[status(thm)],[c_1136,c_50941]) ).
tcf(c_98497,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0 ) ),
inference(superposition,[status(thm)],[c_1136,c_93974]) ).
tcf(c_98498,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0 ) ),
inference(superposition,[status(thm)],[c_1136,c_92725]) ).
tcf(c_98499,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = iPr_def_15,
inference(superposition,[status(thm)],[c_1136,c_91087]) ).
tcf(c_98500,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,v_n____)) = iPr_def_15,
inference(superposition,[status(thm)],[c_1136,c_91092]) ).
tcf(c_98501,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_1136,c_95361]) ).
tcf(c_98502,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0)) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1136,c_92561]) ).
tcf(c_98503,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0)) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1136,c_92047]) ).
tcf(c_98504,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))) = iPr_def_15,
inference(superposition,[status(thm)],[c_1136,c_92321]) ).
tcf(c_98505,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,v_n____)) = X0 ) ),
inference(superposition,[status(thm)],[c_1136,c_98060]) ).
tcf(c_98506,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,v_n____)) = X0 ) ),
inference(superposition,[status(thm)],[c_1136,c_92559]) ).
tcf(c_98507,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,v_n____)) = X0 ) ),
inference(superposition,[status(thm)],[c_1136,c_92464]) ).
tcf(c_98508,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)),
inference(superposition,[status(thm)],[c_1136,c_92475]) ).
tcf(c_98509,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),v_n____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),
inference(superposition,[status(thm)],[c_1136,c_92542]) ).
tcf(c_98510,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),v_n____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),
inference(superposition,[status(thm)],[c_1136,c_92547]) ).
tcf(c_98511,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15),v_n____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15),
inference(superposition,[status(thm)],[c_1136,c_92608]) ).
tcf(c_98512,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
inference(superposition,[status(thm)],[c_1136,c_92736]) ).
tcf(c_98513,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),
inference(superposition,[status(thm)],[c_1136,c_92890]) ).
tcf(c_98514,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),
inference(superposition,[status(thm)],[c_1136,c_92896]) ).
tcf(c_98515,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),v_n____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),
inference(superposition,[status(thm)],[c_1136,c_93168]) ).
tcf(c_98516,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),v_n____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),
inference(superposition,[status(thm)],[c_1136,c_93177]) ).
tcf(c_98517,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0))) = iPr_def_15,
inference(superposition,[status(thm)],[c_1136,c_94361]) ).
tcf(c_98518,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)))) = iPr_def_15,
inference(superposition,[status(thm)],[c_1136,c_96365]) ).
tcf(c_98548,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(light_normalisation,[status(thm)],[c_98501,c_94315]) ).
tcf(c_98557,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(forward_subsumption_resolution,[status(thm)],[c_98475,c_1401]) ).
tcf(c_98662,plain,
! [X0: $i] : hAPP(c_Polynomial_Ocoeff(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))),X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1384,c_1139]) ).
tcf(c_98663,plain,
! [X0: $i] : hAPP(c_Polynomial_Ocoeff(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1424,c_1139]) ).
tcf(c_98664,plain,
! [X0: $i] : hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1468,c_1139]) ).
tcf(c_98665,plain,
! [X0: $i,X1: $i] :
( ( hAPP(c_Polynomial_Ocoeff(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_1525,c_1139]) ).
tcf(c_98666,plain,
! [X0: $i] : hAPP(c_Polynomial_Ocoeff(iPr_def_10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))),X0) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(superposition,[status(thm)],[c_90973,c_1139]) ).
tcf(c_98667,plain,
! [X0: $i] : hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10)),X0) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_98664,c_72166,c_72176]) ).
tcf(c_98694,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(iPr_def_10)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_91550,c_96301]) ).
tcf(c_98695,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(iPr_def_10)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_93034,c_96301]) ).
tcf(c_98696,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(iPr_def_10)))),
inference(superposition,[status(thm)],[c_96301,c_49959]) ).
tcf(c_98697,plain,
! [X0: $i] : c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(iPr_def_10))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_96301,c_164]) ).
tcf(c_98706,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))),c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))))
| ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_96325,c_159]) ).
tcf(c_98707,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_98706,c_91927]) ).
tcf(c_98708,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))),c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))))
| ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_96326,c_159]) ).
tcf(c_98709,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
inference(light_normalisation,[status(thm)],[c_98708,c_91928]) ).
tcf(c_98710,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(iPr_def_10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))),c_Polynomial_Odegree(iPr_def_10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))))
| ~ class_Rings_Ocomm__semiring__0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_96329,c_159]) ).
tcf(c_98711,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_98710,c_91931]) ).
tcf(c_98712,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) ) ),
inference(light_normalisation,[status(thm)],[c_51483,c_72176]) ).
tcf(c_98724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),X4) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X3),X4)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),X4)),X3) ) ),
inference(superposition,[status(thm)],[c_16673,c_98712]) ).
tcf(c_98726,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2)),X1),X2) ) ),
inference(superposition,[status(thm)],[c_16752,c_98712]) ).
tcf(c_98727,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0),X2) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),X0) ) ),
inference(superposition,[status(thm)],[c_16953,c_98712]) ).
tcf(c_98728,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0),X1) ) ),
inference(superposition,[status(thm)],[c_94212,c_98712]) ).
tcf(c_98729,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X0),X1) ) ),
inference(superposition,[status(thm)],[c_91089,c_98712]) ).
tcf(c_98730,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2) ) ),
inference(superposition,[status(thm)],[c_37700,c_98712]) ).
tcf(c_98732,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ) ),
inference(superposition,[status(thm)],[c_94859,c_98712]) ).
tcf(c_98733,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),X2) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) ) ),
inference(superposition,[status(thm)],[c_97738,c_98712]) ).
tcf(c_98734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4))),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X4))) ) ),
inference(superposition,[status(thm)],[c_39652,c_98712]) ).
tcf(c_98737,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) ) ),
inference(superposition,[status(thm)],[c_98712,c_97738]) ).
tcf(c_98739,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_98712,c_91252]) ).
tcf(c_98740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X3),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)) ) ),
inference(superposition,[status(thm)],[c_98712,c_16716]) ).
tcf(c_98741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X3),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)) ) ),
inference(superposition,[status(thm)],[c_98712,c_16704]) ).
tcf(c_98742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),X3)) ) ),
inference(superposition,[status(thm)],[c_98712,c_16716]) ).
tcf(c_98743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),X3)) ) ),
inference(superposition,[status(thm)],[c_98712,c_16704]) ).
tcf(c_98744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1) )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4) ) ),
inference(superposition,[status(thm)],[c_98712,c_93192]) ).
tcf(c_98745,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2)),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2) ) ),
inference(superposition,[status(thm)],[c_98712,c_17690]) ).
tcf(c_98746,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1) ) ),
inference(superposition,[status(thm)],[c_98712,c_17614]) ).
tcf(c_98747,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),X1)) ) ),
inference(superposition,[status(thm)],[c_98712,c_92945]) ).
tcf(c_98748,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),X0)) ) ),
inference(superposition,[status(thm)],[c_98712,c_97114]) ).
tcf(c_98749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),X4)),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X3)),X4)) ) ),
inference(superposition,[status(thm)],[c_98712,c_39652]) ).
tcf(c_98751,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,X1) ) ),
inference(light_normalisation,[status(thm)],[c_98729,c_90508]) ).
tcf(c_98755,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1) ) ),
inference(light_normalisation,[status(thm)],[c_98746,c_17614,c_95051]) ).
tcf(c_98767,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2)),X1),X2) ) ),
inference(light_normalisation,[status(thm)],[c_98726,c_17554]) ).
tcf(c_98770,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2)),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2) ) ),
inference(light_normalisation,[status(thm)],[c_98745,c_17690]) ).
tcf(c_98776,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2) ) ),
inference(light_normalisation,[status(thm)],[c_98730,c_17690]) ).
tcf(c_98887,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),
inference(superposition,[status(thm)],[c_680,c_12534]) ).
tcf(c_98888,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),
inference(superposition,[status(thm)],[c_681,c_12534]) ).
tcf(c_98889,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0),
inference(superposition,[status(thm)],[c_925,c_12534]) ).
tcf(c_98890,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)),
inference(superposition,[status(thm)],[c_1243,c_12534]) ).
tcf(c_98891,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),
inference(superposition,[status(thm)],[c_95456,c_12534]) ).
tcf(c_98892,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)),
inference(superposition,[status(thm)],[c_12534,c_94636]) ).
tcf(c_98893,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)),
inference(superposition,[status(thm)],[c_12534,c_93327]) ).
tcf(c_98894,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))),
inference(superposition,[status(thm)],[c_12534,c_93019]) ).
tcf(c_98895,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))),
inference(superposition,[status(thm)],[c_12534,c_93018]) ).
tcf(c_98896,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
inference(superposition,[status(thm)],[c_12534,c_891]) ).
tcf(c_98897,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(superposition,[status(thm)],[c_12534,c_1243]) ).
tcf(c_98911,plain,
c_Polynomial_OpCons(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_1384,c_183]) ).
tcf(c_98912,plain,
c_Polynomial_OpCons(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1424,c_183]) ).
tcf(c_98913,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_1468,c_183]) ).
tcf(c_98914,plain,
! [X0: $i] :
( ( c_Polynomial_OpCons(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) )
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_1525,c_183]) ).
tcf(c_98915,plain,
c_Polynomial_OpCons(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),
inference(superposition,[status(thm)],[c_90973,c_183]) ).
tcf(c_98916,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ozero__class_Ozero(iPr_def_10)) = c_Groups_Ozero__class_Ozero(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_98913,c_72166,c_72176]) ).
tcf(c_98924,plain,
! [X0: $i] : c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_OpCons(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1384,c_198]) ).
tcf(c_98925,plain,
! [X0: $i] : c_Polynomial_Odegree(tc_Nat_Onat,c_Polynomial_OpCons(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1424,c_198]) ).
tcf(c_98926,plain,
! [X0: $i] : c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1468,c_198]) ).
tcf(c_98927,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Odegree(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(tc_Polynomial_Opoly(X0),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_1525,c_198]) ).
tcf(c_98928,plain,
! [X0: $i] : c_Polynomial_Odegree(iPr_def_10,c_Polynomial_OpCons(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_90973,c_198]) ).
tcf(c_98929,plain,
! [X0: $i] : c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(iPr_def_10))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(light_normalisation,[status(thm)],[c_98926,c_72166]) ).
tcf(c_98954,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(X0,X2,X1)
| ( X1 = X2 )
| ~ class_Orderings_Oorder(X0)
| ~ class_Rings_Olinordered__idom(X0) ),
inference(superposition,[status(thm)],[c_230,c_295]) ).
tcf(c_98955,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(X0,X2,X1)
| ( X1 = X2 )
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(superposition,[status(thm)],[c_230,c_292]) ).
tcf(c_99021,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_230,c_223]) ).
tcf(c_99025,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X1)
| c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ( X1 = X2 )
| ~ class_Orderings_Oorder(X0)
| ~ class_Rings_Olinordered__idom(X0) ),
inference(superposition,[status(thm)],[c_230,c_295]) ).
tcf(c_99026,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X1)
| c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ( X1 = X2 )
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(superposition,[status(thm)],[c_230,c_292]) ).
tcf(c_99032,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X1 )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_230,c_333]) ).
tcf(c_99041,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Olinordered__ring(X0)
| ~ class_Rings_Olinordered__idom(X0) ),
inference(superposition,[status(thm)],[c_230,c_807]) ).
tcf(c_99042,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_230,c_1148]) ).
tcf(c_99046,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_230,c_93136]) ).
tcf(c_99047,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_230,c_92938]) ).
tcf(c_99056,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_230,c_98007]) ).
tcf(c_99057,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_230,c_91226]) ).
tcf(c_99083,plain,
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Oone__class_Oone(iPr_def_10))
| ( c_Groups_Ozero__class_Ozero(iPr_def_10) = c_Groups_Oone__class_Oone(iPr_def_10) )
| ~ class_Rings_Olinordered__ring(iPr_def_10)
| ~ class_Rings_Olinordered__idom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_230,c_97999]) ).
tcf(c_99089,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[c_99057,c_91065]) ).
tcf(c_99093,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[c_99056,c_91065]) ).
tcf(c_99144,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_96555,c_17708]) ).
tcf(c_99147,plain,
! [X0: $i] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X0) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_96555,c_17702]) ).
tcf(c_99148,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1),
inference(light_normalisation,[status(thm)],[c_99144,c_17614]) ).
tcf(c_99154,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1136,c_96583]) ).
tcf(c_99155,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_256,c_96583]) ).
tcf(c_99158,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_230,c_96583]) ).
tcf(c_99167,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_1097,c_96583]) ).
tcf(c_99189,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),v_n____),
inference(demodulation,[status(thm)],[c_96632,c_553]) ).
tcf(c_99200,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,X1,X2))),c_Polynomial_Odegree(tc_Int_Oint,X1))
| ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_96861,c_159]) ).
tcf(c_99201,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,X1,X2))),c_Polynomial_Odegree(tc_Int_Oint,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_99200,c_1361]) ).
tcf(c_99203,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1)) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_51485,c_72176]) ).
tcf(c_99212,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_97738,c_99203]) ).
tcf(c_99215,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_16698,c_99203]) ).
tcf(c_99216,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)))) = X0 ) ),
inference(superposition,[status(thm)],[c_17554,c_99203]) ).
tcf(c_99217,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),X1))) = X0 ) ),
inference(superposition,[status(thm)],[c_17690,c_99203]) ).
tcf(c_99219,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1)),X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_17708,c_99203]) ).
tcf(c_99222,plain,
! [X0: $i] :
( ( X0 = iPr_def_20 )
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_99203,c_807]) ).
tcf(c_99224,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X1) ) ),
inference(superposition,[status(thm)],[c_99203,c_98712]) ).
tcf(c_99225,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X1) ) ),
inference(superposition,[status(thm)],[c_99203,c_98303]) ).
tcf(c_99227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2)),X3)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X4),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2))),X3) ) ),
inference(superposition,[status(thm)],[c_99203,c_16673]) ).
tcf(c_99228,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X0 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X1),X2) ) ),
inference(superposition,[status(thm)],[c_99203,c_97114]) ).
tcf(c_99229,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( X0 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1),X2) ) ),
inference(superposition,[status(thm)],[c_99203,c_96740]) ).
tcf(c_99231,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3))) ) ),
inference(superposition,[status(thm)],[c_99203,c_92945]) ).
tcf(c_99232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3))) ) ),
inference(superposition,[status(thm)],[c_99203,c_92641]) ).
tcf(c_99233,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2) ) ),
inference(superposition,[status(thm)],[c_99203,c_17554]) ).
tcf(c_99235,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)) ) ),
inference(superposition,[status(thm)],[c_99203,c_16953]) ).
tcf(c_99236,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1),X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)) ) ),
inference(superposition,[status(thm)],[c_99203,c_16935]) ).
tcf(c_99237,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2))) ) ),
inference(superposition,[status(thm)],[c_99203,c_16929]) ).
tcf(c_99238,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2))) ) ),
inference(superposition,[status(thm)],[c_99203,c_16752]) ).
tcf(c_99239,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2)),X1) ) ),
inference(superposition,[status(thm)],[c_99203,c_16929]) ).
tcf(c_99240,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2)),X1) ) ),
inference(superposition,[status(thm)],[c_99203,c_16752]) ).
tcf(c_99241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_99203,c_39652]) ).
tcf(c_99242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) != X2 ) ),
inference(superposition,[status(thm)],[c_99203,c_93587]) ).
tcf(c_99243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3)),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_99203,c_92945]) ).
tcf(c_99244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3)),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X3)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_99203,c_92641]) ).
tcf(c_99245,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0) ) ),
inference(superposition,[status(thm)],[c_99203,c_16953]) ).
tcf(c_99246,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0) ) ),
inference(superposition,[status(thm)],[c_99203,c_16935]) ).
tcf(c_99247,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) ) ),
inference(superposition,[status(thm)],[c_99203,c_37700]) ).
tcf(c_99249,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_99203,c_97738]) ).
tcf(c_99250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1))) ) ),
inference(superposition,[status(thm)],[c_99203,c_92945]) ).
tcf(c_99251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X3) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1))) ) ),
inference(superposition,[status(thm)],[c_99203,c_92641]) ).
tcf(c_99252,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_99203,c_39652]) ).
tcf(c_99253,plain,
! [X0: $i] :
( ( X0 = iPr_def_20 )
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0),iPr_def_20) ),
inference(light_normalisation,[status(thm)],[c_99222,c_72176]) ).
tcf(c_99425,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(X0,X2,X1)
| ( X1 = X2 )
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_250,c_295]) ).
tcf(c_99426,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(X0,X2,X1)
| ( X1 = X2 )
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(superposition,[status(thm)],[c_250,c_292]) ).
tcf(c_99492,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Orderings_Olinorder(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_250,c_223]) ).
tcf(c_99496,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X1)
| c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ( X1 = X2 )
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_250,c_295]) ).
tcf(c_99497,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X1)
| c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ( X1 = X2 )
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(superposition,[status(thm)],[c_250,c_292]) ).
tcf(c_99503,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X1 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_250,c_333]) ).
tcf(c_99512,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Olinordered__ring(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_250,c_807]) ).
tcf(c_99513,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_250,c_1148]) ).
tcf(c_99517,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_250,c_96583]) ).
tcf(c_99518,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_250,c_92938]) ).
tcf(c_99527,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Olinorder(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_250,c_98007]) ).
tcf(c_99528,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ~ class_Orderings_Olinorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_250,c_91226]) ).
tcf(c_99554,plain,
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Oone__class_Oone(iPr_def_10))
| ( c_Groups_Ozero__class_Ozero(iPr_def_10) = c_Groups_Oone__class_Oone(iPr_def_10) )
| ~ class_Rings_Olinordered__ring(iPr_def_10)
| ~ class_Orderings_Olinorder(iPr_def_10) ),
inference(superposition,[status(thm)],[c_250,c_97999]) ).
tcf(c_99561,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Olinorder(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[c_99527,c_91065]) ).
tcf(c_99635,plain,
c_Polynomial_OpCons(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_1360,c_307]) ).
tcf(c_99636,plain,
c_Polynomial_OpCons(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1408,c_307]) ).
tcf(c_99637,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_1447,c_307]) ).
tcf(c_99638,plain,
! [X0: $i] :
( ( c_Polynomial_OpCons(tc_Polynomial_Opoly(X0),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_307]) ).
tcf(c_99639,plain,
c_Polynomial_OpCons(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(iPr_def_10)),
inference(superposition,[status(thm)],[c_90792,c_307]) ).
tcf(c_99640,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(iPr_def_10)) = c_Groups_Oone__class_Oone(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_99637,c_72166]) ).
tcf(c_99648,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(X0)) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_1136,c_374]) ).
tcf(c_99652,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(superposition,[status(thm)],[c_373,c_374]) ).
tcf(c_99660,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(X0)) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_96459,c_374]) ).
tcf(c_99661,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_93100,c_374]) ).
tcf(c_99662,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_92157,c_374]) ).
tcf(c_99663,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_91901,c_374]) ).
tcf(c_99664,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_317,c_374]) ).
tcf(c_99666,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_633,c_374]) ).
tcf(c_99667,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ) ),
inference(superposition,[status(thm)],[c_92420,c_374]) ).
tcf(c_99668,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ) ),
inference(superposition,[status(thm)],[c_92376,c_374]) ).
tcf(c_99669,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_632,c_374]) ).
tcf(c_99672,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1147,c_374]) ).
tcf(c_99673,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_11697,c_374]) ).
tcf(c_99676,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_91291,c_374]) ).
tcf(c_99677,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(iPr_def_15)) = iPr_def_15,
inference(superposition,[status(thm)],[c_91318,c_374]) ).
tcf(c_99678,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_92168,c_374]) ).
tcf(c_99679,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),
inference(superposition,[status(thm)],[c_92900,c_374]) ).
tcf(c_99680,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),
inference(superposition,[status(thm)],[c_92909,c_374]) ).
tcf(c_99681,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_94656,c_374]) ).
tcf(c_99682,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(superposition,[status(thm)],[c_94661,c_374]) ).
tcf(c_99688,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),
inference(superposition,[status(thm)],[c_94738,c_374]) ).
tcf(c_99692,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),
inference(superposition,[status(thm)],[c_94883,c_374]) ).
tcf(c_99693,plain,
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(v_n____)) = v_n____ ) ),
inference(superposition,[status(thm)],[c_97619,c_374]) ).
tcf(c_99694,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,X0,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(superposition,[status(thm)],[c_95861,c_374]) ).
tcf(c_99753,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_440,c_452]) ).
tcf(c_99754,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_551,c_452]) ).
tcf(c_99756,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0) ),
inference(superposition,[status(thm)],[c_90483,c_452]) ).
tcf(c_99758,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_440,c_452]) ).
tcf(c_99759,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_551,c_452]) ).
tcf(c_99761,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_90483,c_452]) ).
tcf(c_99762,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(superposition,[status(thm)],[c_452,c_50323]) ).
tcf(c_99765,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_452,c_91603]) ).
tcf(c_99769,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_452,c_295]) ).
tcf(c_99770,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_452,c_292]) ).
tcf(c_99775,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_452,c_320]) ).
tcf(c_99776,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(superposition,[status(thm)],[c_452,c_333]) ).
tcf(c_99827,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),
inference(superposition,[status(thm)],[c_99677,c_92168]) ).
tcf(c_99828,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK9(iPr_def_15),X0),iPr_def_15),
inference(superposition,[status(thm)],[c_99677,c_91889]) ).
tcf(c_99829,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_99677,c_387]) ).
tcf(c_99830,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),X0) ),
inference(superposition,[status(thm)],[c_99677,c_384]) ).
tcf(c_99831,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_99677,c_320]) ).
tcf(c_99832,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK9(iPr_def_15),X0),iPr_def_15),
inference(superposition,[status(thm)],[c_99677,c_1145]) ).
tcf(c_99835,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,sK9(iPr_def_15)),
inference(superposition,[status(thm)],[c_99677,c_165]) ).
tcf(c_99836,plain,
sK9(iPr_def_15) != iPr_def_15,
inference(superposition,[status(thm)],[c_99677,c_129]) ).
tcf(c_99837,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),iPr_def_15),
inference(superposition,[status(thm)],[c_99677,c_331]) ).
tcf(c_99839,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),X0) ),
inference(superposition,[status(thm)],[c_99677,c_333]) ).
tcf(c_99840,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),X0) ),
inference(superposition,[status(thm)],[c_99677,c_334]) ).
tcf(c_99842,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK9(iPr_def_15),iPr_def_15) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_99677,c_91869]) ).
tcf(c_99844,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(iPr_def_15),iPr_def_15),
inference(superposition,[status(thm)],[c_99677,c_474]) ).
tcf(c_99854,plain,
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK9(iPr_def_15) )
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_99677,c_444]) ).
tcf(c_99855,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(iPr_def_15),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_99677,c_464]) ).
tcf(c_99860,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,sK9(iPr_def_15)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_99677,c_1067]) ).
tcf(c_99861,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = sK9(iPr_def_15),
inference(superposition,[status(thm)],[c_99677,c_1066]) ).
tcf(c_99863,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,sK9(iPr_def_15)),
inference(superposition,[status(thm)],[c_99677,c_457]) ).
tcf(c_99865,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(iPr_def_15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),
inference(superposition,[status(thm)],[c_99677,c_92431]) ).
tcf(c_99866,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,sK9(iPr_def_15)) ),
inference(superposition,[status(thm)],[c_99677,c_633]) ).
tcf(c_99867,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK9(iPr_def_15)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_99677,c_452]) ).
tcf(c_99869,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK9(iPr_def_15)),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_99677,c_452]) ).
tcf(c_99870,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),sK9(iPr_def_15)),
inference(superposition,[status(thm)],[c_99677,c_92736]) ).
tcf(c_99872,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(iPr_def_15),X0) ),
inference(superposition,[status(thm)],[c_99677,c_92451]) ).
tcf(c_99873,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(iPr_def_15),X0) ),
inference(superposition,[status(thm)],[c_99677,c_92420]) ).
tcf(c_99877,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),X0) ),
inference(superposition,[status(thm)],[c_99677,c_50489]) ).
tcf(c_99976,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK9(iPr_def_15),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,sK9(iPr_def_15))) = iPr_def_15,
inference(superposition,[status(thm)],[c_1136,c_99863]) ).
tcf(c_99983,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK9(iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_99976,c_99860]) ).
tcf(c_99985,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_551,c_99827]) ).
tcf(c_100002,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK9(iPr_def_15),X0)),
inference(superposition,[status(thm)],[c_99828,c_49959]) ).
tcf(c_100020,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(iPr_def_15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_551,c_99865]) ).
tcf(c_100029,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),sK9(iPr_def_15)),
inference(superposition,[status(thm)],[c_99985,c_50323]) ).
tcf(c_100045,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),X1) ) ),
inference(light_normalisation,[status(thm)],[c_51488,c_72176]) ).
tcf(c_100056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X3)),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X4),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),X3),X2) ) ),
inference(superposition,[status(thm)],[c_16673,c_100045]) ).
tcf(c_100058,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X1),X2) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2)),X1),X1) ) ),
inference(superposition,[status(thm)],[c_16752,c_100045]) ).
tcf(c_100059,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X0) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),X2) ) ),
inference(superposition,[status(thm)],[c_16953,c_100045]) ).
tcf(c_100060,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1),X0) ) ),
inference(superposition,[status(thm)],[c_94212,c_100045]) ).
tcf(c_100061,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1),X0) ) ),
inference(superposition,[status(thm)],[c_91089,c_100045]) ).
tcf(c_100062,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) ) ),
inference(superposition,[status(thm)],[c_37700,c_100045]) ).
tcf(c_100066,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1)),X2) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X1)) ) ),
inference(superposition,[status(thm)],[c_99203,c_100045]) ).
tcf(c_100067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X4)) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X4))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X4))),X1) ) ),
inference(superposition,[status(thm)],[c_39652,c_100045]) ).
tcf(c_100072,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1)) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_100045,c_91252]) ).
tcf(c_100073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X3),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) ) ),
inference(superposition,[status(thm)],[c_100045,c_16716]) ).
tcf(c_100074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X3),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) ) ),
inference(superposition,[status(thm)],[c_100045,c_16704]) ).
tcf(c_100075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X3) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3),X2)) ) ),
inference(superposition,[status(thm)],[c_100045,c_16716]) ).
tcf(c_100076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3),X2)) ) ),
inference(superposition,[status(thm)],[c_100045,c_16704]) ).
tcf(c_100077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1))),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1) )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4) ) ),
inference(superposition,[status(thm)],[c_100045,c_93192]) ).
tcf(c_100078,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),X1) ) ),
inference(superposition,[status(thm)],[c_100045,c_17690]) ).
tcf(c_100079,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1) ) ),
inference(superposition,[status(thm)],[c_100045,c_17614]) ).
tcf(c_100080,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X0),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X0),X0)) ) ),
inference(superposition,[status(thm)],[c_100045,c_97114]) ).
tcf(c_100081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X4) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X4))),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X4)),X3)) ) ),
inference(superposition,[status(thm)],[c_100045,c_39652]) ).
tcf(c_100085,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1) ) ),
inference(light_normalisation,[status(thm)],[c_100079,c_17614,c_94986]) ).
tcf(c_100095,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),X0) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),X2) ) ),
inference(light_normalisation,[status(thm)],[c_100059,c_17554]) ).
tcf(c_100187,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1214,c_455]) ).
tcf(c_100191,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_90483,c_455]) ).
tcf(c_100192,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),X0) ),
inference(superposition,[status(thm)],[c_99677,c_455]) ).
tcf(c_100193,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1214,c_455]) ).
tcf(c_100197,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_90483,c_455]) ).
tcf(c_100198,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,sK9(iPr_def_15)) ),
inference(superposition,[status(thm)],[c_99677,c_455]) ).
tcf(c_100199,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) ),
inference(superposition,[status(thm)],[c_455,c_50323]) ).
tcf(c_100202,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_455,c_91603]) ).
tcf(c_100206,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_455,c_295]) ).
tcf(c_100207,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_455,c_292]) ).
tcf(c_100212,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_455,c_320]) ).
tcf(c_100214,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_455,c_449]) ).
tcf(c_100247,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) ) ),
inference(superposition,[status(thm)],[c_1136,c_456]) ).
tcf(c_100248,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) ) ),
inference(superposition,[status(thm)],[c_256,c_456]) ).
tcf(c_100249,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) ) ),
inference(superposition,[status(thm)],[c_256,c_456]) ).
tcf(c_100269,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),iPr_def_15)),
inference(superposition,[status(thm)],[c_94879,c_456]) ).
tcf(c_100271,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)) ),
inference(superposition,[status(thm)],[c_1214,c_456]) ).
tcf(c_100273,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_551,c_456]) ).
tcf(c_100275,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0)) ),
inference(superposition,[status(thm)],[c_90483,c_456]) ).
tcf(c_100276,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(superposition,[status(thm)],[c_99677,c_456]) ).
tcf(c_100277,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,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),X0),X1) ),
inference(superposition,[status(thm)],[c_1214,c_456]) ).
tcf(c_100279,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(superposition,[status(thm)],[c_551,c_456]) ).
tcf(c_100281,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0),iPr_def_15) ),
inference(superposition,[status(thm)],[c_90483,c_456]) ).
tcf(c_100282,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,sK9(iPr_def_15))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),iPr_def_15) ),
inference(superposition,[status(thm)],[c_99677,c_456]) ).
tcf(c_100347,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) ),
inference(superposition,[status(thm)],[c_49961,c_470]) ).
tcf(c_100348,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) ),
inference(superposition,[status(thm)],[c_96089,c_470]) ).
tcf(c_100350,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(superposition,[status(thm)],[c_384,c_470]) ).
tcf(c_100364,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)) ),
inference(superposition,[status(thm)],[c_1214,c_470]) ).
tcf(c_100365,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_440,c_470]) ).
tcf(c_100366,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_551,c_470]) ).
tcf(c_100368,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0)) ),
inference(superposition,[status(thm)],[c_90483,c_470]) ).
tcf(c_100369,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(iPr_def_15),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(superposition,[status(thm)],[c_99677,c_470]) ).
tcf(c_100370,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,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),X0),X1) ),
inference(superposition,[status(thm)],[c_1214,c_470]) ).
tcf(c_100371,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_440,c_470]) ).
tcf(c_100372,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(superposition,[status(thm)],[c_551,c_470]) ).
tcf(c_100374,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0),iPr_def_15) ),
inference(superposition,[status(thm)],[c_90483,c_470]) ).
tcf(c_100375,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK9(iPr_def_15))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),iPr_def_15) ),
inference(superposition,[status(thm)],[c_99677,c_470]) ).
tcf(c_100414,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) != X1 ) ),
inference(superposition,[status(thm)],[c_1214,c_554]) ).
tcf(c_100416,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ) ),
inference(superposition,[status(thm)],[c_551,c_554]) ).
tcf(c_100418,plain,
! [X0: $i] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0) != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_90483,c_554]) ).
tcf(c_100419,plain,
! [X0: $i] :
( ( sK9(iPr_def_15) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_99677,c_554]) ).
tcf(c_100439,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,sK9(iPr_def_15)) ),
inference(superposition,[status(thm)],[c_99840,c_245]) ).
tcf(c_100440,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,sK9(iPr_def_15)) ),
inference(superposition,[status(thm)],[c_99840,c_240]) ).
tcf(c_100441,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,sK9(iPr_def_15)) ),
inference(superposition,[status(thm)],[c_99840,c_235]) ).
tcf(c_100450,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,sK9(iPr_def_15)) ),
inference(superposition,[status(thm)],[c_99840,c_96583]) ).
tcf(c_100452,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK9(iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_99840,c_50941]) ).
tcf(c_100453,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(iPr_def_15),X0) ),
inference(superposition,[status(thm)],[c_99840,c_93974]) ).
tcf(c_100475,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),X0) ),
inference(superposition,[status(thm)],[c_99842,c_1097]) ).
tcf(c_100479,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK9(iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_99842,c_94346]) ).
tcf(c_100480,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,sK9(iPr_def_15))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_99842,c_1148]) ).
tcf(c_100481,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(iPr_def_15))),
inference(superposition,[status(thm)],[c_99842,c_91889]) ).
tcf(c_100482,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,sK9(iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_99842,c_91886]) ).
tcf(c_100483,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(iPr_def_15))),
inference(superposition,[status(thm)],[c_99842,c_1145]) ).
tcf(c_100484,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(iPr_def_15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_99842,c_91436]) ).
tcf(c_100485,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK9(iPr_def_15)),
inference(superposition,[status(thm)],[c_99842,c_1095]) ).
tcf(c_100506,plain,
sK9(iPr_def_15) = v_n____,
inference(demodulation,[status(thm)],[c_99861,c_91398]) ).
tcf(c_100509,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15) ),
inference(demodulation,[status(thm)],[c_99840,c_100506]) ).
tcf(c_100521,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____) = iPr_def_15,
inference(demodulation,[status(thm)],[c_99677,c_100506]) ).
tcf(c_100536,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_100509,c_235]) ).
tcf(c_100543,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_100509,c_333]) ).
tcf(c_100559,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_100509,c_235]) ).
tcf(c_100566,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(iPr_def_15)) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_100509,c_374]) ).
tcf(c_100568,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_100509,c_449]) ).
tcf(c_100571,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15)),
inference(superposition,[status(thm)],[c_100509,c_91435]) ).
tcf(c_100575,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1))),
inference(superposition,[status(thm)],[c_100509,c_92475]) ).
tcf(c_100576,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15))),
inference(superposition,[status(thm)],[c_100509,c_92736]) ).
tcf(c_100594,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)) ) ),
inference(light_normalisation,[status(thm)],[c_51493,c_72176]) ).
tcf(c_100607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X3,X4),X2)),X4)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X4)),X2),X4) ) ),
inference(superposition,[status(thm)],[c_16673,c_100594]) ).
tcf(c_100609,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)),X2),X2) ) ),
inference(superposition,[status(thm)],[c_16752,c_100594]) ).
tcf(c_100610,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),X2) ) ),
inference(superposition,[status(thm)],[c_16953,c_100594]) ).
tcf(c_100611,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) ) ),
inference(superposition,[status(thm)],[c_94212,c_100594]) ).
tcf(c_100612,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,iPr_def_20,X1)) ) ),
inference(superposition,[status(thm)],[c_91089,c_100594]) ).
tcf(c_100613,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)) ) ),
inference(superposition,[status(thm)],[c_37700,c_100594]) ).
tcf(c_100614,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ) ),
inference(superposition,[status(thm)],[c_94847,c_100594]) ).
tcf(c_100615,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X1) ) ),
inference(superposition,[status(thm)],[c_94859,c_100594]) ).
tcf(c_100617,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X2)) ) ),
inference(superposition,[status(thm)],[c_99203,c_100594]) ).
tcf(c_100618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X4)) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X4))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X4)))) ) ),
inference(superposition,[status(thm)],[c_39652,c_100594]) ).
tcf(c_100620,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,iPr_def_20),X1) ) ),
inference(superposition,[status(thm)],[c_90992,c_100594]) ).
tcf(c_100621,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)) ) ),
inference(superposition,[status(thm)],[c_100594,c_97738]) ).
tcf(c_100623,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)) = X2 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_100594,c_91252]) ).
tcf(c_100624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X3),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) ) ),
inference(superposition,[status(thm)],[c_100594,c_16716]) ).
tcf(c_100625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X3),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) ) ),
inference(superposition,[status(thm)],[c_100594,c_16704]) ).
tcf(c_100626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X3) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3))) ) ),
inference(superposition,[status(thm)],[c_100594,c_16716]) ).
tcf(c_100627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3))) ) ),
inference(superposition,[status(thm)],[c_100594,c_16704]) ).
tcf(c_100628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2))),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X2) )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X4) ) ),
inference(superposition,[status(thm)],[c_100594,c_93192]) ).
tcf(c_100629,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2) = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))) ) ),
inference(superposition,[status(thm)],[c_100594,c_17690]) ).
tcf(c_100630,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(superposition,[status(thm)],[c_100594,c_17614]) ).
tcf(c_100631,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) ) ),
inference(superposition,[status(thm)],[c_100594,c_100045]) ).
tcf(c_100632,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) ) ),
inference(superposition,[status(thm)],[c_100594,c_98712]) ).
tcf(c_100633,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X1)) ) ),
inference(superposition,[status(thm)],[c_100594,c_97114]) ).
tcf(c_100634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X4) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X4))),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X4)))) ) ),
inference(superposition,[status(thm)],[c_100594,c_39652]) ).
tcf(c_100636,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) ) ),
inference(light_normalisation,[status(thm)],[c_100620,c_90510]) ).
tcf(c_100641,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0) ) ),
inference(light_normalisation,[status(thm)],[c_100614,c_97157]) ).
tcf(c_100642,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0) ) ),
inference(light_normalisation,[status(thm)],[c_100641,c_91139,c_97157]) ).
tcf(c_100643,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0) ) ),
inference(light_normalisation,[status(thm)],[c_100630,c_17614,c_94986]) ).
tcf(c_100644,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_100643,c_91065]) ).
tcf(c_100656,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),X2) ) ),
inference(light_normalisation,[status(thm)],[c_100610,c_17554]) ).
tcf(c_100711,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ),
inference(superposition,[status(thm)],[c_440,c_555]) ).
tcf(c_100714,plain,
! [X0: $i] :
( ( X0 = v_n____ )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_90483,c_555]) ).
tcf(c_100727,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) ) ),
inference(superposition,[status(thm)],[c_12534,c_572]) ).
tcf(c_100728,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) != X0 ) ),
inference(superposition,[status(thm)],[c_891,c_572]) ).
tcf(c_100729,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) ) ),
inference(superposition,[status(thm)],[c_16973,c_572]) ).
tcf(c_100730,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) != X0 ) ),
inference(superposition,[status(thm)],[c_45742,c_572]) ).
tcf(c_100731,plain,
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = iPr_def_20 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_90498,c_572]) ).
tcf(c_100732,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0) = c_Groups_Ozero__class_Ozero(iPr_def_10) )
| ~ class_Groups_Olinordered__ab__group__add(iPr_def_10)
| ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0) != X0 ) ),
inference(superposition,[status(thm)],[c_91673,c_572]) ).
tcf(c_100734,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0) = c_Groups_Ozero__class_Ozero(tc_HOL_Obool) )
| ~ class_Groups_Olinordered__ab__group__add(tc_HOL_Obool)
| ( c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0) != X0 ) ),
inference(superposition,[status(thm)],[c_91806,c_572]) ).
tcf(c_100743,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = iPr_def_20 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) != X0 ) ),
inference(light_normalisation,[status(thm)],[c_100730,c_72176]) ).
tcf(c_100747,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) != X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_100728,c_1340]) ).
tcf(c_100750,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_100727,c_1340]) ).
tcf(c_100753,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = iPr_def_20 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) ) ),
inference(light_normalisation,[status(thm)],[c_100729,c_72176]) ).
tcf(c_100773,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)) = X1,
inference(superposition,[status(thm)],[c_1373,c_591]) ).
tcf(c_100774,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1)) = X1,
inference(superposition,[status(thm)],[c_1458,c_591]) ).
tcf(c_100775,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1),X2)) = X2 )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1514,c_591]) ).
tcf(c_100776,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(iPr_def_10,X0,c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X1)) = X1,
inference(superposition,[status(thm)],[c_90868,c_591]) ).
tcf(c_100788,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) = X1,
inference(superposition,[status(thm)],[c_1373,c_592]) ).
tcf(c_100789,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)) = X1,
inference(superposition,[status(thm)],[c_1458,c_592]) ).
tcf(c_100790,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,X2)) = X2 )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1514,c_592]) ).
tcf(c_100791,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),c_Groups_Oplus__class_Oplus(iPr_def_10,X0,X1)) = X1,
inference(superposition,[status(thm)],[c_90868,c_592]) ).
tcf(c_100800,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15)),
inference(superposition,[status(thm)],[c_100571,c_93809]) ).
tcf(c_100801,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),iPr_def_15),iPr_def_15)),
inference(superposition,[status(thm)],[c_100571,c_92057]) ).
tcf(c_100811,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(light_normalisation,[status(thm)],[c_99829,c_100506]) ).
tcf(c_100832,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_50489,c_100811]) ).
tcf(c_100836,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15))),
inference(superposition,[status(thm)],[c_910,c_100811]) ).
tcf(c_100844,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0) ),
inference(light_normalisation,[status(thm)],[c_99830,c_100506]) ).
tcf(c_100851,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0)) = v_n____ ) ),
inference(superposition,[status(thm)],[c_1136,c_100844]) ).
tcf(c_100852,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| ( X0 = v_n____ ) ),
inference(superposition,[status(thm)],[c_256,c_100844]) ).
tcf(c_100854,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____)),
inference(superposition,[status(thm)],[c_331,c_100844]) ).
tcf(c_100855,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_227,c_100844]) ).
tcf(c_100860,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(superposition,[status(thm)],[c_334,c_100844]) ).
tcf(c_100861,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0) ),
inference(superposition,[status(thm)],[c_633,c_100844]) ).
tcf(c_100862,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92420,c_100844]) ).
tcf(c_100863,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92376,c_100844]) ).
tcf(c_100864,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0) ),
inference(superposition,[status(thm)],[c_632,c_100844]) ).
tcf(c_100865,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0))),
inference(superposition,[status(thm)],[c_492,c_100844]) ).
tcf(c_100866,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,v_n____))),
inference(superposition,[status(thm)],[c_491,c_100844]) ).
tcf(c_100867,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_92157,c_100844]) ).
tcf(c_100868,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91294,c_100844]) ).
tcf(c_100870,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_100509,c_100844]) ).
tcf(c_100871,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,iPr_def_15) ),
inference(superposition,[status(thm)],[c_100509,c_100844]) ).
tcf(c_100872,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____))),
inference(superposition,[status(thm)],[c_92168,c_100844]) ).
tcf(c_100873,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92433,c_100844]) ).
tcf(c_100874,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92389,c_100844]) ).
tcf(c_100875,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_98277,c_100844]) ).
tcf(c_100876,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),
inference(superposition,[status(thm)],[c_98253,c_100844]) ).
tcf(c_100877,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15)),
inference(superposition,[status(thm)],[c_100571,c_100844]) ).
tcf(c_100878,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_94656,c_100844]) ).
tcf(c_100879,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
inference(superposition,[status(thm)],[c_94661,c_100844]) ).
tcf(c_100880,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,iPr_def_15)),
inference(superposition,[status(thm)],[c_94663,c_100844]) ).
tcf(c_100881,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,v_n____)),
inference(superposition,[status(thm)],[c_94684,c_100844]) ).
tcf(c_100882,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0))),
inference(superposition,[status(thm)],[c_94715,c_100844]) ).
tcf(c_100883,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))),
inference(superposition,[status(thm)],[c_94729,c_100844]) ).
tcf(c_100884,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_94734,c_100844]) ).
tcf(c_100885,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,v_n____))),
inference(superposition,[status(thm)],[c_94758,c_100844]) ).
tcf(c_100886,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,v_n____))),
inference(superposition,[status(thm)],[c_94874,c_100844]) ).
tcf(c_100887,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,iPr_def_15))),
inference(superposition,[status(thm)],[c_94879,c_100844]) ).
tcf(c_100888,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_95861,c_100844]) ).
tcf(c_100903,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,iPr_def_15)
| ~ class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
inference(light_normalisation,[status(thm)],[c_100855,c_90483]) ).
tcf(c_100956,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(iPr_def_10) = X2 )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,X2),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))),X2)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),X2) ) ),
inference(light_normalisation,[status(thm)],[c_51540,c_72166]) ).
tcf(c_100972,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(iPr_def_10) = X1 )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(iPr_def_10)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(iPr_def_10))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1))),X1)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),X1) ) ),
inference(superposition,[status(thm)],[c_91420,c_100956]) ).
tcf(c_100974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Ozero__class_Ozero(iPr_def_10) = X3 )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Divides_Odiv__class_Omod(iPr_def_10,X2,X3))),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Divides_Odiv__class_Omod(iPr_def_10,X2,X3)))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X3)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,X3),c_Polynomial_Odegree(tc_Complex_Ocomplex,X3))),X3)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)),X3) ) ),
inference(superposition,[status(thm)],[c_91915,c_100956]) ).
tcf(c_100975,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(iPr_def_10) = X2 )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2))),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2)))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,X2),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))),X2)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1)),X2) ) ),
inference(superposition,[status(thm)],[c_92100,c_100956]) ).
tcf(c_100976,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(iPr_def_10) = X1 )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(iPr_def_10)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(iPr_def_10))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1))),X1)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(iPr_def_10)),X1) ) ),
inference(superposition,[status(thm)],[c_93770,c_100956]) ).
tcf(c_100977,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2) = c_Groups_Ozero__class_Ozero(iPr_def_10) )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2))),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2))),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2)),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2)))),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2))) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2)) ) ),
inference(superposition,[status(thm)],[c_92331,c_100956]) ).
tcf(c_100978,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(iPr_def_10) = X2 )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,X2),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))),X2)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2)),X2) ) ),
inference(superposition,[status(thm)],[c_93768,c_100956]) ).
tcf(c_100979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( c_Polynomial_Osmult(tc_Complex_Ocomplex,X3,X2) = c_Groups_Ozero__class_Ozero(iPr_def_10) )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2))),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X3,X2))),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X3,X2)),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X3,X2)))),c_Polynomial_Osmult(tc_Complex_Ocomplex,X3,X2))) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),c_Polynomial_Osmult(tc_Complex_Ocomplex,X3,X2)) ) ),
inference(superposition,[status(thm)],[c_98146,c_100956]) ).
tcf(c_100985,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(iPr_def_10) = v_p )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,v_p)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,v_p))),iPr_def_15),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),iPr_def_15)),v_p)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),v_p) ) ),
inference(superposition,[status(thm)],[c_72171,c_100956]) ).
tcf(c_100987,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ozero__class_Ozero(iPr_def_10) = c_Groups_Oone__class_Oone(iPr_def_10) )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Groups_Oone__class_Oone(iPr_def_10))),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Groups_Oone__class_Oone(iPr_def_10)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(iPr_def_10)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oone__class_Oone(iPr_def_10))) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),c_Groups_Oone__class_Oone(iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_92194,c_100956]) ).
tcf(c_100988,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2) = c_Groups_Ozero__class_Ozero(iPr_def_10) )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2))),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2)))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2)),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2))) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X2)) ) ),
inference(superposition,[status(thm)],[c_97253,c_100956]) ).
tcf(c_100989,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(iPr_def_10) = X2 )
| ( c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,X2),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))),X2) = c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2)),c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),X2)) ) ),
inference(superposition,[status(thm)],[c_100956,c_95623]) ).
tcf(c_100990,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(iPr_def_10) = X2 )
| ( c_Groups_Oplus__class_Oplus(iPr_def_10,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,X2),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))),X2),c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),X2)) = c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,X2)) ) ),
inference(superposition,[status(thm)],[c_100956,c_95617]) ).
tcf(c_100991,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,v_p)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,v_p))),iPr_def_15),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),iPr_def_15)),v_p)) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),v_p),
inference(forward_subsumption_resolution,[status(thm)],[c_100985,c_91019]) ).
tcf(c_101057,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_12534,c_602]) ).
tcf(c_101058,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_891,c_602]) ).
tcf(c_101059,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_16973,c_602]) ).
tcf(c_101060,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_45742,c_602]) ).
tcf(c_101061,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20)
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_90498,c_602]) ).
tcf(c_101062,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_91673,c_602]) ).
tcf(c_101064,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0),c_Groups_Ozero__class_Ozero(tc_HOL_Obool)) ),
inference(superposition,[status(thm)],[c_91806,c_602]) ).
tcf(c_101065,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X0) ),
inference(superposition,[status(thm)],[c_602,c_49959]) ).
tcf(c_101066,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_602,c_387]) ).
tcf(c_101067,plain,
! [X0: $i,X1: $i] :
( ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_602,c_300]) ).
tcf(c_101068,plain,
! [X0: $i,X1: $i] :
( ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_602,c_293]) ).
tcf(c_101069,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_602,c_464]) ).
tcf(c_101070,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_602,c_463]) ).
tcf(c_101071,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) ),
inference(superposition,[status(thm)],[c_602,c_672]) ).
tcf(c_101072,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_602,c_671]) ).
tcf(c_101073,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_602,c_662]) ).
tcf(c_101074,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_602,c_668]) ).
tcf(c_101089,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),iPr_def_20) ),
inference(light_normalisation,[status(thm)],[c_101060,c_72176]) ).
tcf(c_101093,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101058,c_1340]) ).
tcf(c_101104,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101072,c_1340]) ).
tcf(c_101108,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101073,c_1340]) ).
tcf(c_101118,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101071,c_1340]) ).
tcf(c_101122,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101074,c_1340]) ).
tcf(c_101128,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101057,c_1340]) ).
tcf(c_101131,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),iPr_def_20) ),
inference(light_normalisation,[status(thm)],[c_101059,c_72176]) ).
tcf(c_101153,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_162,c_603]) ).
tcf(c_101155,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93901,c_603]) ).
tcf(c_101156,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91901,c_603]) ).
tcf(c_101157,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_49961,c_603]) ).
tcf(c_101158,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_96089,c_603]) ).
tcf(c_101159,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))) ),
inference(superposition,[status(thm)],[c_384,c_603]) ).
tcf(c_101161,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_301,c_603]) ).
tcf(c_101162,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_421,c_603]) ).
tcf(c_101164,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))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_91783,c_603]) ).
tcf(c_101165,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_661,c_603]) ).
tcf(c_101167,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(superposition,[status(thm)],[c_669,c_603]) ).
tcf(c_101169,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_95505,c_603]) ).
tcf(c_101170,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93902,c_603]) ).
tcf(c_101171,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93901,c_603]) ).
tcf(c_101172,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93899,c_603]) ).
tcf(c_101173,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_92438,c_603]) ).
tcf(c_101174,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97717,c_603]) ).
tcf(c_101175,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92531,c_603]) ).
tcf(c_101176,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92511,c_603]) ).
tcf(c_101178,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)) ),
inference(superposition,[status(thm)],[c_12534,c_603]) ).
tcf(c_101179,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) ),
inference(superposition,[status(thm)],[c_891,c_603]) ).
tcf(c_101180,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) ),
inference(superposition,[status(thm)],[c_16973,c_603]) ).
tcf(c_101181,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X0) ),
inference(superposition,[status(thm)],[c_45742,c_603]) ).
tcf(c_101182,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20) ),
inference(superposition,[status(thm)],[c_90498,c_603]) ).
tcf(c_101183,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),c_Groups_Ozero__class_Ozero(iPr_def_10))
| ~ class_Groups_Olinordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X0) ),
inference(superposition,[status(thm)],[c_91673,c_603]) ).
tcf(c_101185,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0),c_Groups_Ozero__class_Ozero(tc_HOL_Obool))
| ~ class_Groups_Olinordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0),X0) ),
inference(superposition,[status(thm)],[c_91806,c_603]) ).
tcf(c_101202,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101165,c_1340]) ).
tcf(c_101214,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101172,c_91120]) ).
tcf(c_101217,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101171,c_91120]) ).
tcf(c_101226,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),iPr_def_20)
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X0) ),
inference(light_normalisation,[status(thm)],[c_101181,c_72176]) ).
tcf(c_101230,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101179,c_1340]) ).
tcf(c_101233,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101173,c_91120]) ).
tcf(c_101236,plain,
( ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101170,c_91120]) ).
tcf(c_101239,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))
| 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))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_101164,c_700]) ).
tcf(c_101248,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101167,c_1340]) ).
tcf(c_101254,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),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,X0,X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101178,c_1340]) ).
tcf(c_101257,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),iPr_def_20)
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) ),
inference(light_normalisation,[status(thm)],[c_101180,c_72176]) ).
tcf(c_101306,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ 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,X0,X1)) ),
inference(superposition,[status(thm)],[c_12534,c_606]) ).
tcf(c_101307,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(superposition,[status(thm)],[c_891,c_606]) ).
tcf(c_101308,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) ),
inference(superposition,[status(thm)],[c_16973,c_606]) ).
tcf(c_101309,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
inference(superposition,[status(thm)],[c_45742,c_606]) ).
tcf(c_101310,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20)
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),iPr_def_20) ),
inference(superposition,[status(thm)],[c_90498,c_606]) ).
tcf(c_101311,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0))
| ~ class_Groups_Olinordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_91673,c_606]) ).
tcf(c_101313,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X0,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) ),
inference(superposition,[status(thm)],[c_91806,c_606]) ).
tcf(c_101314,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0)) ),
inference(superposition,[status(thm)],[c_606,c_49959]) ).
tcf(c_101315,plain,
( ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_606,c_164]) ).
tcf(c_101316,plain,
! [X0: $i,X1: $i] :
( ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_606,c_300]) ).
tcf(c_101317,plain,
! [X0: $i,X1: $i] :
( ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_606,c_293]) ).
tcf(c_101318,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(superposition,[status(thm)],[c_606,c_672]) ).
tcf(c_101319,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ class_Groups_Olinordered__ab__group__add(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__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(superposition,[status(thm)],[c_606,c_671]) ).
tcf(c_101320,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_606,c_662]) ).
tcf(c_101321,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ 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(superposition,[status(thm)],[c_606,c_94504]) ).
tcf(c_101322,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_606,c_1252]) ).
tcf(c_101324,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101314,c_162]) ).
tcf(c_101333,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
inference(light_normalisation,[status(thm)],[c_101309,c_72176]) ).
tcf(c_101337,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101307,c_1340]) ).
tcf(c_101340,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))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ 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(light_normalisation,[status(thm)],[c_101321,c_700]) ).
tcf(c_101341,plain,
( ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101315,c_162]) ).
tcf(c_101352,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ 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,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101319,c_1340]) ).
tcf(c_101356,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101320,c_1340]) ).
tcf(c_101360,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101318,c_1340]) ).
tcf(c_101364,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101322,c_1340]) ).
tcf(c_101367,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ 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,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101306,c_1340]) ).
tcf(c_101370,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) ),
inference(light_normalisation,[status(thm)],[c_101308,c_72176]) ).
tcf(c_101429,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_301,c_607]) ).
tcf(c_101430,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_421,c_607]) ).
tcf(c_101431,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92451,c_607]) ).
tcf(c_101432,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92408,c_607]) ).
tcf(c_101433,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_50489,c_607]) ).
tcf(c_101434,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_50325,c_607]) ).
tcf(c_101436,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_661,c_607]) ).
tcf(c_101439,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))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_97045,c_607]) ).
tcf(c_101440,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0) ),
inference(superposition,[status(thm)],[c_1251,c_607]) ).
tcf(c_101441,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92531,c_607]) ).
tcf(c_101442,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91905,c_607]) ).
tcf(c_101445,plain,
! [X0: $i,X1: $i] :
( 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,X0,X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
inference(superposition,[status(thm)],[c_12534,c_607]) ).
tcf(c_101446,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(superposition,[status(thm)],[c_891,c_607]) ).
tcf(c_101447,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) ),
inference(superposition,[status(thm)],[c_16973,c_607]) ).
tcf(c_101448,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
inference(superposition,[status(thm)],[c_45742,c_607]) ).
tcf(c_101449,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),iPr_def_20)
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20) ),
inference(superposition,[status(thm)],[c_90498,c_607]) ).
tcf(c_101450,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0))
| ~ class_Groups_Olinordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless__eq(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_91673,c_607]) ).
tcf(c_101452,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X0,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) ),
inference(superposition,[status(thm)],[c_91806,c_607]) ).
tcf(c_101454,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101436,c_1340]) ).
tcf(c_101463,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
inference(light_normalisation,[status(thm)],[c_101448,c_72176]) ).
tcf(c_101467,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101446,c_1340]) ).
tcf(c_101470,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),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_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_101439,c_700]) ).
tcf(c_101479,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101440,c_1340]) ).
tcf(c_101482,plain,
! [X0: $i,X1: $i] :
( 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,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101445,c_1340]) ).
tcf(c_101485,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) ),
inference(light_normalisation,[status(thm)],[c_101447,c_72176]) ).
tcf(c_101499,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),X1)),
inference(superposition,[status(thm)],[c_551,c_100575]) ).
tcf(c_101514,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1))),
inference(superposition,[status(thm)],[c_100575,c_100844]) ).
tcf(c_101517,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),X1)),
inference(superposition,[status(thm)],[c_551,c_100576]) ).
tcf(c_101532,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15))),
inference(superposition,[status(thm)],[c_100576,c_100844]) ).
tcf(c_101534,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_100800,c_49959]) ).
tcf(c_101539,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_100801,c_50323]) ).
tcf(c_101542,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15)),
inference(superposition,[status(thm)],[c_100801,c_91603]) ).
tcf(c_101543,plain,
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_100801,c_245]) ).
tcf(c_101544,plain,
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_100801,c_240]) ).
tcf(c_101545,plain,
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_100801,c_235]) ).
tcf(c_101546,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_100801,c_295]) ).
tcf(c_101547,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_100801,c_292]) ).
tcf(c_101548,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15),
inference(superposition,[status(thm)],[c_100801,c_374]) ).
tcf(c_101567,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15) ),
inference(superposition,[status(thm)],[c_100867,c_300]) ).
tcf(c_101568,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15) ),
inference(superposition,[status(thm)],[c_100867,c_293]) ).
tcf(c_101570,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_100867,c_92394]) ).
tcf(c_101579,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101214,c_50323]) ).
tcf(c_101582,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101214,c_91603]) ).
tcf(c_101583,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101214,c_245]) ).
tcf(c_101584,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101214,c_240]) ).
tcf(c_101585,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101214,c_235]) ).
tcf(c_101606,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101217,c_49959]) ).
tcf(c_101608,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101217,c_300]) ).
tcf(c_101609,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101217,c_293]) ).
tcf(c_101610,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101217,c_603]) ).
tcf(c_101611,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101217,c_607]) ).
tcf(c_101623,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0))) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1136,c_101324]) ).
tcf(c_101624,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_256,c_101324]) ).
tcf(c_101630,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_96459,c_101324]) ).
tcf(c_101631,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93100,c_101324]) ).
tcf(c_101632,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92157,c_101324]) ).
tcf(c_101633,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91901,c_101324]) ).
tcf(c_101637,plain,
! [X0: $i,X1: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))) ),
inference(superposition,[status(thm)],[c_1097,c_101324]) ).
tcf(c_101638,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_100509,c_101324]) ).
tcf(c_101688,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____)) ),
inference(superposition,[status(thm)],[c_101638,c_50323]) ).
tcf(c_101691,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101638,c_91603]) ).
tcf(c_101692,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____)) ),
inference(superposition,[status(thm)],[c_101638,c_245]) ).
tcf(c_101693,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____)) ),
inference(superposition,[status(thm)],[c_101638,c_240]) ).
tcf(c_101694,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____)) ),
inference(superposition,[status(thm)],[c_101638,c_235]) ).
tcf(c_101711,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(demodulation,[status(thm)],[c_101499,c_553]) ).
tcf(c_101712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,iPr_def_20))),X3)),
inference(light_normalisation,[status(thm)],[c_90492,c_90592,c_90947]) ).
tcf(c_101720,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1))
| ~ class_Rings_Olinordered__idom(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_12534,c_608]) ).
tcf(c_101721,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ~ class_Rings_Olinordered__idom(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_891,c_608]) ).
tcf(c_101722,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)))
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_16973,c_608]) ).
tcf(c_101723,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X0)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_45742,c_608]) ).
tcf(c_101724,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_90498,c_608]) ).
tcf(c_101725,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X0)
| ~ class_Rings_Olinordered__idom(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_91673,c_608]) ).
tcf(c_101727,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0),X0)
| ~ class_Rings_Olinordered__idom(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0),c_Groups_Ozero__class_Ozero(tc_HOL_Obool)) ),
inference(superposition,[status(thm)],[c_91806,c_608]) ).
tcf(c_101732,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_608,c_245]) ).
tcf(c_101733,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_608,c_240]) ).
tcf(c_101734,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(X0)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_608,c_235]) ).
tcf(c_101735,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Orderings_Oorder(X0)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_608,c_295]) ).
tcf(c_101736,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_608,c_292]) ).
tcf(c_101737,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_608,c_374]) ).
tcf(c_101738,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_608,c_320]) ).
tcf(c_101739,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_608,c_449]) ).
tcf(c_101740,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_608,c_675]) ).
tcf(c_101741,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Rings_Olinordered__idom(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_608,c_663]) ).
tcf(c_101743,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_608,c_100844]) ).
tcf(c_101744,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_608,c_92561]) ).
tcf(c_101745,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_608,c_92047]) ).
tcf(c_101749,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101741,c_1359]) ).
tcf(c_101758,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X0)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),iPr_def_20) ),
inference(light_normalisation,[status(thm)],[c_101723,c_72176]) ).
tcf(c_101762,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101721,c_1359]) ).
tcf(c_101765,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Rings_Olinordered__idom(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(light_normalisation,[status(thm)],[c_101740,c_700]) ).
tcf(c_101786,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101720,c_1359]) ).
tcf(c_101789,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)))
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),iPr_def_20) ),
inference(light_normalisation,[status(thm)],[c_101722,c_72176]) ).
tcf(c_101824,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0))) = X0 )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1136,c_609]) ).
tcf(c_101825,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0) = X0 )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_256,c_609]) ).
tcf(c_101829,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X1 )
| ~ class_Orderings_Olinorder(X0)
| ~ class_Rings_Olinordered__idom(X0) ),
inference(superposition,[status(thm)],[c_250,c_609]) ).
tcf(c_101830,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X1 )
| ~ class_Rings_Olinordered__idom(X0) ),
inference(superposition,[status(thm)],[c_230,c_609]) ).
tcf(c_101831,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_96459,c_609]) ).
tcf(c_101832,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),iPr_def_15)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93100,c_609]) ).
tcf(c_101833,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92157,c_609]) ).
tcf(c_101834,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91901,c_609]) ).
tcf(c_101835,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_317,c_609]) ).
tcf(c_101836,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_92805,c_609]) ).
tcf(c_101837,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92283,c_609]) ).
tcf(c_101839,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Rings_Olinordered__idom(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_91757,c_609]) ).
tcf(c_101840,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X0 )
| ~ class_Rings_Olinordered__idom(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_697,c_609]) ).
tcf(c_101842,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))) ),
inference(superposition,[status(thm)],[c_1097,c_609]) ).
tcf(c_101843,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_100509,c_609]) ).
tcf(c_101845,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Rings_Olinordered__idom(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)) ),
inference(superposition,[status(thm)],[c_12534,c_609]) ).
tcf(c_101846,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Rings_Olinordered__idom(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) ),
inference(superposition,[status(thm)],[c_891,c_609]) ).
tcf(c_101847,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) ),
inference(superposition,[status(thm)],[c_16973,c_609]) ).
tcf(c_101848,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X0) ),
inference(superposition,[status(thm)],[c_45742,c_609]) ).
tcf(c_101849,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20) ),
inference(superposition,[status(thm)],[c_90498,c_609]) ).
tcf(c_101850,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),c_Groups_Ozero__class_Ozero(iPr_def_10))
| ~ class_Rings_Olinordered__idom(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X0) ),
inference(superposition,[status(thm)],[c_91673,c_609]) ).
tcf(c_101852,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0),c_Groups_Ozero__class_Ozero(tc_HOL_Obool))
| ~ class_Rings_Olinordered__idom(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0),X0) ),
inference(superposition,[status(thm)],[c_91806,c_609]) ).
tcf(c_101854,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101843,c_318]) ).
tcf(c_101857,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101837,c_318]) ).
tcf(c_101860,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101834,c_318]) ).
tcf(c_101863,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),iPr_def_15)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101832,c_318]) ).
tcf(c_101872,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),iPr_def_20)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X0) ),
inference(light_normalisation,[status(thm)],[c_101848,c_72176]) ).
tcf(c_101876,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101846,c_1359]) ).
tcf(c_101879,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))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Rings_Olinordered__idom(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_101839,c_700]) ).
tcf(c_101880,plain,
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101836,c_318]) ).
tcf(c_101883,plain,
( ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101835,c_318]) ).
tcf(c_101886,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101833,c_318]) ).
tcf(c_101889,plain,
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101831,c_318]) ).
tcf(c_101892,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101840,c_1359]) ).
tcf(c_101900,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0) = X0 )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101825,c_318]) ).
tcf(c_101904,plain,
! [X0: $i,X1: $i] :
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101842,c_318]) ).
tcf(c_101907,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0))) = X0 )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101824,c_318]) ).
tcf(c_101915,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,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,X0,X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101845,c_1359]) ).
tcf(c_101918,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),iPr_def_20)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) ),
inference(light_normalisation,[status(thm)],[c_101847,c_72176]) ).
tcf(c_101991,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
inference(superposition,[status(thm)],[c_12534,c_614]) ).
tcf(c_101992,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(superposition,[status(thm)],[c_891,c_614]) ).
tcf(c_101993,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) ),
inference(superposition,[status(thm)],[c_16973,c_614]) ).
tcf(c_101994,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
inference(superposition,[status(thm)],[c_45742,c_614]) ).
tcf(c_101995,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20)
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),iPr_def_20) ),
inference(superposition,[status(thm)],[c_90498,c_614]) ).
tcf(c_101996,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0))
| ~ class_Groups_Olinordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_91673,c_614]) ).
tcf(c_101998,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_HOL_Obool,X0,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) ),
inference(superposition,[status(thm)],[c_91806,c_614]) ).
tcf(c_101999,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_614,c_318]) ).
tcf(c_102000,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0)) ),
inference(superposition,[status(thm)],[c_614,c_50323]) ).
tcf(c_102001,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_614,c_93809]) ).
tcf(c_102003,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_614,c_91603]) ).
tcf(c_102004,plain,
! [X0: $i,X1: $i] :
( ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_614,c_245]) ).
tcf(c_102005,plain,
! [X0: $i,X1: $i] :
( ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_614,c_240]) ).
tcf(c_102006,plain,
! [X0: $i,X1: $i] :
( ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_614,c_235]) ).
tcf(c_102007,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(superposition,[status(thm)],[c_614,c_295]) ).
tcf(c_102008,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(superposition,[status(thm)],[c_614,c_292]) ).
tcf(c_102009,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))) ),
inference(superposition,[status(thm)],[c_614,c_333]) ).
tcf(c_102010,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_614,c_663]) ).
tcf(c_102011,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_614,c_666]) ).
tcf(c_102012,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_614,c_93333]) ).
tcf(c_102013,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_614,c_96583]) ).
tcf(c_102014,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_614,c_92938]) ).
tcf(c_102019,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____) ),
inference(superposition,[status(thm)],[c_614,c_98060]) ).
tcf(c_102029,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102010,c_1340]) ).
tcf(c_102044,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
inference(light_normalisation,[status(thm)],[c_101994,c_72176]) ).
tcf(c_102048,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101992,c_1340]) ).
tcf(c_102053,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))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(light_normalisation,[status(thm)],[c_102012,c_700]) ).
tcf(c_102074,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102011,c_1340]) ).
tcf(c_102077,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102009,c_373]) ).
tcf(c_102080,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_101991,c_1340]) ).
tcf(c_102083,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) ),
inference(light_normalisation,[status(thm)],[c_101993,c_72176]) ).
tcf(c_102118,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X0)) = c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0) )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1136,c_615]) ).
tcf(c_102119,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0))
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_256,c_615]) ).
tcf(c_102123,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X1 )
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_250,c_615]) ).
tcf(c_102124,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X1 )
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Rings_Olinordered__idom(X0) ),
inference(superposition,[status(thm)],[c_230,c_615]) ).
tcf(c_102126,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_633,c_615]) ).
tcf(c_102127,plain,
! [X0: $i,X1: $i] :
( 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,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92420,c_615]) ).
tcf(c_102128,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92376,c_615]) ).
tcf(c_102129,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_632,c_615]) ).
tcf(c_102131,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_697,c_615]) ).
tcf(c_102133,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0) ),
inference(superposition,[status(thm)],[c_665,c_615]) ).
tcf(c_102139,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
inference(superposition,[status(thm)],[c_12534,c_615]) ).
tcf(c_102140,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(superposition,[status(thm)],[c_891,c_615]) ).
tcf(c_102141,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) ),
inference(superposition,[status(thm)],[c_16973,c_615]) ).
tcf(c_102142,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
inference(superposition,[status(thm)],[c_45742,c_615]) ).
tcf(c_102143,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),iPr_def_20)
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20) ),
inference(superposition,[status(thm)],[c_90498,c_615]) ).
tcf(c_102144,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0))
| ~ class_Groups_Olinordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_91673,c_615]) ).
tcf(c_102146,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,X0,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) ),
inference(superposition,[status(thm)],[c_91806,c_615]) ).
tcf(c_102154,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
inference(light_normalisation,[status(thm)],[c_102142,c_72176]) ).
tcf(c_102158,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102140,c_1340]) ).
tcf(c_102161,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102131,c_1340]) ).
tcf(c_102184,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102133,c_1340]) ).
tcf(c_102197,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102139,c_1340]) ).
tcf(c_102200,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) ),
inference(light_normalisation,[status(thm)],[c_102141,c_72176]) ).
tcf(c_102260,plain,
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____)) ),
inference(superposition,[status(thm)],[c_101854,c_50323]) ).
tcf(c_102263,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101854,c_91603]) ).
tcf(c_102265,plain,
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____)) ),
inference(superposition,[status(thm)],[c_101854,c_240]) ).
tcf(c_102267,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101854,c_295]) ).
tcf(c_102287,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101631,c_50323]) ).
tcf(c_102290,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101631,c_91603]) ).
tcf(c_102291,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101631,c_245]) ).
tcf(c_102292,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101631,c_240]) ).
tcf(c_102293,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101631,c_235]) ).
tcf(c_102307,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101633,c_49959]) ).
tcf(c_102309,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101633,c_300]) ).
tcf(c_102310,plain,
! [X0: $i] :
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101633,c_293]) ).
tcf(c_102311,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101633,c_603]) ).
tcf(c_102324,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))) = iPr_def_15 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1136,c_101688]) ).
tcf(c_102325,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____) = iPr_def_15 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_256,c_101688]) ).
tcf(c_102342,plain,
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101857,c_293]) ).
tcf(c_102348,plain,
! [X0: $i] :
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101860,c_49959]) ).
tcf(c_102351,plain,
! [X0: $i] :
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101860,c_293]) ).
tcf(c_102353,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101860,c_607]) ).
tcf(c_102362,plain,
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101863,c_50323]) ).
tcf(c_102365,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),iPr_def_15)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101863,c_91603]) ).
tcf(c_102367,plain,
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_101863,c_240]) ).
tcf(c_102369,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),iPr_def_15)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101863,c_295]) ).
tcf(c_102381,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))) = iPr_def_15 )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1136,c_102260]) ).
tcf(c_102386,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____) = iPr_def_15 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_250,c_102260]) ).
tcf(c_102387,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____) = iPr_def_15 )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_230,c_102260]) ).
tcf(c_102399,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_680,c_670]) ).
tcf(c_102400,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_681,c_670]) ).
tcf(c_102401,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_925,c_670]) ).
tcf(c_102402,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) ),
inference(superposition,[status(thm)],[c_1243,c_670]) ).
tcf(c_102403,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_95456,c_670]) ).
tcf(c_102405,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_680,c_670]) ).
tcf(c_102406,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_681,c_670]) ).
tcf(c_102407,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_925,c_670]) ).
tcf(c_102408,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(superposition,[status(thm)],[c_1243,c_670]) ).
tcf(c_102409,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)) ),
inference(superposition,[status(thm)],[c_95456,c_670]) ).
tcf(c_102411,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)) ),
inference(superposition,[status(thm)],[c_670,c_293]) ).
tcf(c_102412,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)) ),
inference(superposition,[status(thm)],[c_670,c_672]) ).
tcf(c_102413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
inference(superposition,[status(thm)],[c_670,c_671]) ).
tcf(c_102414,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_670,c_662]) ).
tcf(c_102415,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_670,c_668]) ).
tcf(c_102438,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102411,c_1367]) ).
tcf(c_102474,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_925,c_674]) ).
tcf(c_102475,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(superposition,[status(thm)],[c_1243,c_674]) ).
tcf(c_102476,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_95456,c_674]) ).
tcf(c_102479,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_674,c_235]) ).
tcf(c_102480,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))
| ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_674,c_295]) ).
tcf(c_102481,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_674,c_292]) ).
tcf(c_102482,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_674,c_675]) ).
tcf(c_102483,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_674,c_663]) ).
tcf(c_102497,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102479,c_1376]) ).
tcf(c_102518,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_680,c_686]) ).
tcf(c_102519,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_681,c_686]) ).
tcf(c_102520,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_925,c_686]) ).
tcf(c_102521,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_1243,c_686]) ).
tcf(c_102522,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X0)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_95456,c_686]) ).
tcf(c_102525,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_681,c_686]) ).
tcf(c_102526,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_925,c_686]) ).
tcf(c_102527,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_1243,c_686]) ).
tcf(c_102528,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_95456,c_686]) ).
tcf(c_102531,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)) ),
inference(superposition,[status(thm)],[c_686,c_235]) ).
tcf(c_102532,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_686,c_295]) ).
tcf(c_102533,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_686,c_292]) ).
tcf(c_102537,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_686,c_663]) ).
tcf(c_102562,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102531,c_1376]) ).
tcf(c_102600,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(iPr_def_11,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(iPr_def_10),X0),X1)))
| ~ class_Rings_Ocomm__semiring__1(iPr_def_10) ),
inference(superposition,[status(thm)],[c_72167,c_731]) ).
tcf(c_102601,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)))
| ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_991,c_731]) ).
tcf(c_102603,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_887,c_731]) ).
tcf(c_102604,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0))
| ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_888,c_731]) ).
tcf(c_102607,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)))
| ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_993,c_731]) ).
tcf(c_102608,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1220,c_731]) ).
tcf(c_102611,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_37700,c_731]) ).
tcf(c_102612,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_94847,c_731]) ).
tcf(c_102613,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_94859,c_731]) ).
tcf(c_102614,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0)),X1))
| ( X0 = iPr_def_20 )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_97738,c_731]) ).
tcf(c_102616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_39652,c_731]) ).
tcf(c_102618,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),iPr_def_20),iPr_def_20))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_90992,c_731]) ).
tcf(c_102619,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(iPr_def_10),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94849,c_731]) ).
tcf(c_102620,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(iPr_def_10),c_Groups_Oone__class_Oone(iPr_def_10)),X0))
| ~ class_Rings_Ocomm__semiring__1(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94861,c_731]) ).
tcf(c_102622,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_102612,c_1447]) ).
tcf(c_102623,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_102603,c_1360]) ).
tcf(c_102625,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_102613,c_1447]) ).
tcf(c_102626,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_102604,c_1360]) ).
tcf(c_102627,plain,
! [X0: $i,X1: $i] : hBOOL(hAPP(hAPP(iPr_def_11,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(iPr_def_10),X0),X1))),
inference(forward_subsumption_resolution,[status(thm)],[c_102600,c_90792]) ).
tcf(c_102628,plain,
! [X0: $i,X1: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_102607,c_1408]) ).
tcf(c_102629,plain,
! [X0: $i,X1: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_102601,c_1360]) ).
tcf(c_102630,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0)),X1))
| ( X0 = iPr_def_20 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102614,c_1447]) ).
tcf(c_102633,plain,
! [X0: $i,X1: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_102611,c_1447]) ).
tcf(c_102634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3)))),
inference(forward_subsumption_resolution,[status(thm)],[c_102616,c_1447]) ).
tcf(c_102643,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Polynomial_Osmult(tc_Nat_Onat,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Nat_Onat,X1,X2))),c_Polynomial_Odegree(tc_Nat_Onat,X1))
| ~ class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_96862,c_159]) ).
tcf(c_102644,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Nat_Onat,c_Polynomial_Osmult(tc_Nat_Onat,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Nat_Onat,X1,X2))),c_Polynomial_Odegree(tc_Nat_Onat,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_102643,c_1409]) ).
tcf(c_102646,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X1,X2))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_96863,c_159]) ).
tcf(c_102647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X2,X3) = c_Groups_Ozero__class_Ozero(iPr_def_10) )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X2,X3))),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X2,X3)))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X2,X3)),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X2,X3))) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X2,X3)) ) ),
inference(superposition,[status(thm)],[c_96863,c_100956]) ).
tcf(c_102648,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X1,X2))),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_102646,c_1448]) ).
tcf(c_102653,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(iPr_def_10,c_Polynomial_Osmult(iPr_def_10,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(iPr_def_10,X1,X2))),c_Polynomial_Odegree(iPr_def_10,X1))
| ~ class_Rings_Ocomm__semiring__0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_96865,c_159]) ).
tcf(c_102654,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(iPr_def_10,c_Polynomial_Osmult(iPr_def_10,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(iPr_def_10,X1,X2))),c_Polynomial_Odegree(iPr_def_10,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_102653,c_90798]) ).
tcf(c_102687,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ),
inference(superposition,[status(thm)],[c_96923,c_245]) ).
tcf(c_102688,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ),
inference(superposition,[status(thm)],[c_96923,c_240]) ).
tcf(c_102689,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ),
inference(superposition,[status(thm)],[c_96923,c_235]) ).
tcf(c_102690,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0)
| ~ class_Orderings_Oorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_96923,c_295]) ).
tcf(c_102691,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0)
| ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_96923,c_292]) ).
tcf(c_102714,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),X0),X1) ) ),
inference(superposition,[status(thm)],[c_95904,c_90499]) ).
tcf(c_102715,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X2),X1),
inference(superposition,[status(thm)],[c_16698,c_90499]) ).
tcf(c_102716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X3),X2),
inference(superposition,[status(thm)],[c_17554,c_90499]) ).
tcf(c_102717,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(superposition,[status(thm)],[c_17690,c_90499]) ).
tcf(c_102718,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_17614,c_90499]) ).
tcf(c_102719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),X3),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) ) ),
inference(superposition,[status(thm)],[c_100594,c_90499]) ).
tcf(c_102720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),X3),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) ) ),
inference(superposition,[status(thm)],[c_100045,c_90499]) ).
tcf(c_102721,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_17702,c_90499]) ).
tcf(c_102722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X2)),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17708,c_90499]) ).
tcf(c_102723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2)),X3),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X0)) ) ),
inference(superposition,[status(thm)],[c_96740,c_90499]) ).
tcf(c_102724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),X3),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)) ) ),
inference(superposition,[status(thm)],[c_98303,c_90499]) ).
tcf(c_102725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1))) ) ),
inference(superposition,[status(thm)],[c_92641,c_90499]) ).
tcf(c_102726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1))) ) ),
inference(superposition,[status(thm)],[c_92945,c_90499]) ).
tcf(c_102727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),X3),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)) ) ),
inference(superposition,[status(thm)],[c_98712,c_90499]) ).
tcf(c_102728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2)),X3),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X0)) ) ),
inference(superposition,[status(thm)],[c_97114,c_90499]) ).
tcf(c_102729,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,iPr_def_20)),
inference(superposition,[status(thm)],[c_90491,c_90499]) ).
tcf(c_102730,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20),X0),X1),
inference(superposition,[status(thm)],[c_90508,c_90499]) ).
tcf(c_102731,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),X1) ) ),
inference(superposition,[status(thm)],[c_95904,c_90499]) ).
tcf(c_102732,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),X1),
inference(superposition,[status(thm)],[c_16698,c_90499]) ).
tcf(c_102733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X1),
inference(superposition,[status(thm)],[c_17554,c_90499]) ).
tcf(c_102734,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(superposition,[status(thm)],[c_17690,c_90499]) ).
tcf(c_102735,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_17614,c_90499]) ).
tcf(c_102736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3))) ) ),
inference(superposition,[status(thm)],[c_100594,c_90499]) ).
tcf(c_102737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3),X2)) ) ),
inference(superposition,[status(thm)],[c_100045,c_90499]) ).
tcf(c_102738,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17702,c_90499]) ).
tcf(c_102739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17708,c_90499]) ).
tcf(c_102740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X3)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) ) ),
inference(superposition,[status(thm)],[c_96740,c_90499]) ).
tcf(c_102741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),X3)) ) ),
inference(superposition,[status(thm)],[c_98303,c_90499]) ).
tcf(c_102742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2))),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2))) ) ),
inference(superposition,[status(thm)],[c_92641,c_90499]) ).
tcf(c_102743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2))),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2))) ) ),
inference(superposition,[status(thm)],[c_92945,c_90499]) ).
tcf(c_102744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),X3)) ) ),
inference(superposition,[status(thm)],[c_98712,c_90499]) ).
tcf(c_102745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X3)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) ) ),
inference(superposition,[status(thm)],[c_97114,c_90499]) ).
tcf(c_102746,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,iPr_def_20)),iPr_def_20),
inference(superposition,[status(thm)],[c_90491,c_90499]) ).
tcf(c_102747,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),iPr_def_20) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),iPr_def_20),X1),
inference(superposition,[status(thm)],[c_90508,c_90499]) ).
tcf(c_102748,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),
inference(superposition,[status(thm)],[c_90499,c_95405]) ).
tcf(c_102749,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),
inference(superposition,[status(thm)],[c_90499,c_95332]) ).
tcf(c_102750,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2),X0),X1),
inference(superposition,[status(thm)],[c_90499,c_94212]) ).
tcf(c_102752,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_102746,c_90491,c_90498]) ).
tcf(c_102753,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),
inference(light_normalisation,[status(thm)],[c_102730,c_90498,c_91089]) ).
tcf(c_102754,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,iPr_def_20)),
inference(light_normalisation,[status(thm)],[c_102729,c_90498]) ).
tcf(c_102755,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),
inference(light_normalisation,[status(thm)],[c_102735,c_17614]) ).
tcf(c_102760,plain,
! [X0: $i,X1: $i,X2: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),
inference(light_normalisation,[status(thm)],[c_102732,c_91357]) ).
tcf(c_102761,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2),X1),
inference(light_normalisation,[status(thm)],[c_102715,c_45742]) ).
tcf(c_102762,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(light_normalisation,[status(thm)],[c_102734,c_17690]) ).
tcf(c_102763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X3),X2),
inference(light_normalisation,[status(thm)],[c_102716,c_16973,c_91356]) ).
tcf(c_102864,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(iPr_def_11,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(iPr_def_10),X1),X0)))
| ~ class_Rings_Ocomm__semiring__1(iPr_def_10) ),
inference(superposition,[status(thm)],[c_72167,c_732]) ).
tcf(c_102865,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)))
| ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_991,c_732]) ).
tcf(c_102871,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)))
| ~ class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_993,c_732]) ).
tcf(c_102875,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_37700,c_732]) ).
tcf(c_102878,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),X0),X1))
| ( X0 = iPr_def_20 )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_97738,c_732]) ).
tcf(c_102879,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0)),X1))
| ( X0 = iPr_def_20 )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_99203,c_732]) ).
tcf(c_102880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2))))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_39652,c_732]) ).
tcf(c_102885,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),X0),X1))
| ( X0 = iPr_def_20 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102878,c_1447]) ).
tcf(c_102888,plain,
! [X0: $i,X1: $i] : hBOOL(hAPP(hAPP(iPr_def_11,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(iPr_def_10),X1),X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_102864,c_90792]) ).
tcf(c_102889,plain,
! [X0: $i,X1: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))),
inference(forward_subsumption_resolution,[status(thm)],[c_102871,c_1408]) ).
tcf(c_102890,plain,
! [X0: $i,X1: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1))),
inference(forward_subsumption_resolution,[status(thm)],[c_102865,c_1360]) ).
tcf(c_102891,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X0)),X1))
| ( X0 = iPr_def_20 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102879,c_1447]) ).
tcf(c_102894,plain,
! [X0: $i,X1: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)))),
inference(forward_subsumption_resolution,[status(thm)],[c_102875,c_1447]) ).
tcf(c_102895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)))),
inference(forward_subsumption_resolution,[status(thm)],[c_102880,c_1447]) ).
tcf(c_102920,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Rings_Odvd(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1220,c_736]) ).
tcf(c_102927,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),X1),X1))
| ( X0 = iPr_def_20 )
| ~ class_Rings_Odvd(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_99203,c_736]) ).
tcf(c_102930,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex),iPr_def_20),iPr_def_20))
| ~ class_Rings_Odvd(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_90992,c_736]) ).
tcf(c_102931,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(iPr_def_10),X0),X0))
| ~ class_Rings_Odvd(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94849,c_736]) ).
tcf(c_102932,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(iPr_def_10),c_Groups_Oone__class_Oone(iPr_def_10)),X0))
| ~ class_Rings_Odvd(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94861,c_736]) ).
tcf(c_102933,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(iPr_def_11,X0),X0))
| ~ class_Rings_Odvd(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_102931,c_72167]) ).
tcf(c_102934,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(iPr_def_11,c_Groups_Oone__class_Oone(iPr_def_10)),X0))
| ~ class_Rings_Odvd(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_102932,c_72167]) ).
tcf(c_102939,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1342,c_826]) ).
tcf(c_102940,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1437,c_826]) ).
tcf(c_102941,plain,
! [X0: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Oidom(X0) ),
inference(superposition,[status(thm)],[c_1483,c_826]) ).
tcf(c_102942,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(iPr_def_10),c_Groups_Oone__class_Oone(iPr_def_10)),c_Groups_Oone__class_Oone(iPr_def_10)) = c_Groups_Oone__class_Oone(iPr_def_10),
inference(superposition,[status(thm)],[c_90626,c_826]) ).
tcf(c_102949,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),
inference(superposition,[status(thm)],[c_1364,c_1060]) ).
tcf(c_102950,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0),
inference(superposition,[status(thm)],[c_1452,c_1060]) ).
tcf(c_102951,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X2,X1) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1505,c_1060]) ).
tcf(c_102952,plain,
! [X0: $i,X1: $i] : c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Ominus__class_Ominus(iPr_def_10,X0,X1)) = c_Groups_Ominus__class_Ominus(iPr_def_10,X1,X0),
inference(superposition,[status(thm)],[c_90804,c_1060]) ).
tcf(c_102970,plain,
! [X0: $i] :
( ~ class_Orderings_Olinorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,X0,c_Groups_Ominus__class_Ominus(iPr_def_10,X0,c_Groups_Oone__class_Oone(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_96963,c_245]) ).
tcf(c_102971,plain,
! [X0: $i] :
( ~ class_Orderings_Opreorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,X0,c_Groups_Ominus__class_Ominus(iPr_def_10,X0,c_Groups_Oone__class_Oone(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_96963,c_240]) ).
tcf(c_102972,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,X0,c_Groups_Ominus__class_Ominus(iPr_def_10,X0,c_Groups_Oone__class_Oone(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_96963,c_235]) ).
tcf(c_102973,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ominus__class_Ominus(iPr_def_10,X0,c_Groups_Oone__class_Oone(iPr_def_10)),X0)
| ~ class_Orderings_Oorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_96963,c_295]) ).
tcf(c_102974,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ominus__class_Ominus(iPr_def_10,X0,c_Groups_Oone__class_Oone(iPr_def_10)),X0)
| ~ class_Orderings_Opreorder(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_96963,c_292]) ).
tcf(c_103027,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),X1))),c_Polynomial_Odegree(tc_Int_Oint,X1))
| ~ class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_97249,c_159]) ).
tcf(c_103028,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Int_Oint,c_Polynomial_Osmult(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),X1))),c_Polynomial_Odegree(tc_Int_Oint,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_103027,c_1361]) ).
tcf(c_103030,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(iPr_def_10,c_Polynomial_Osmult(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),X1))),c_Polynomial_Odegree(iPr_def_10,X1))
| ~ class_Rings_Ocomm__semiring__0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_97252,c_159]) ).
tcf(c_103031,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(iPr_def_10,c_Polynomial_Osmult(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),X1))),c_Polynomial_Odegree(iPr_def_10,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_103030,c_90798]) ).
tcf(c_103043,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ 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(superposition,[status(thm)],[c_606,c_97283]) ).
tcf(c_103045,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_661,c_97283]) ).
tcf(c_103048,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_669,c_97283]) ).
tcf(c_103052,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(superposition,[status(thm)],[c_95466,c_97283]) ).
tcf(c_103057,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))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint)
| ~ 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(light_normalisation,[status(thm)],[c_103043,c_700]) ).
tcf(c_103064,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_103045,c_300]) ).
tcf(c_103065,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_103045,c_293]) ).
tcf(c_103067,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_103045,c_672]) ).
tcf(c_103068,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(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__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_103045,c_671]) ).
tcf(c_103070,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| 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,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_103045,c_668]) ).
tcf(c_103074,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_103045,c_300]) ).
tcf(c_103075,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_103045,c_293]) ).
tcf(c_103076,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))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_103045,c_603]) ).
tcf(c_103077,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_103045,c_672]) ).
tcf(c_103078,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_103045,c_671]) ).
tcf(c_103082,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_103045,c_1252]) ).
tcf(c_103087,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_103075,c_1367]) ).
tcf(c_103093,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_103065,c_1367]) ).
tcf(c_103109,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))
| 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))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_103076,c_700]) ).
tcf(c_103154,plain,
! [X0: $i,X1: $i] : hAPP(c_Polynomial_Ocoeff(tc_Int_Oint,c_Polynomial_OpCons(tc_Int_Oint,X0,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(superposition,[status(thm)],[c_1384,c_1114]) ).
tcf(c_103155,plain,
! [X0: $i,X1: $i] : hAPP(c_Polynomial_Ocoeff(tc_Nat_Onat,c_Polynomial_OpCons(tc_Nat_Onat,X0,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(superposition,[status(thm)],[c_1424,c_1114]) ).
tcf(c_103156,plain,
! [X0: $i,X1: $i] : hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(superposition,[status(thm)],[c_1468,c_1114]) ).
tcf(c_103157,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_Polynomial_Ocoeff(tc_Polynomial_Opoly(X0),c_Polynomial_OpCons(tc_Polynomial_Opoly(X0),X1,X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_1525,c_1114]) ).
tcf(c_103158,plain,
! [X0: $i,X1: $i] : hAPP(c_Polynomial_Ocoeff(iPr_def_10,c_Polynomial_OpCons(iPr_def_10,X0,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(superposition,[status(thm)],[c_90973,c_1114]) ).
tcf(c_103172,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_93901,c_1118]) ).
tcf(c_103173,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_91901,c_1118]) ).
tcf(c_103174,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_49961,c_1118]) ).
tcf(c_103175,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_96089,c_1118]) ).
tcf(c_103176,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1),X0),
inference(superposition,[status(thm)],[c_344,c_1118]) ).
tcf(c_103177,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_384,c_1118]) ).
tcf(c_103180,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1),X0)
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_50432,c_1118]) ).
tcf(c_103181,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1),X0)
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_420,c_1118]) ).
tcf(c_103182,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1),X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_417,c_1118]) ).
tcf(c_103184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X3),X2)
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_403,c_1118]) ).
tcf(c_103185,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_92451,c_1118]) ).
tcf(c_103186,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_92408,c_1118]) ).
tcf(c_103188,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_50325,c_1118]) ).
tcf(c_103190,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),X1),
inference(superposition,[status(thm)],[c_474,c_1118]) ).
tcf(c_103191,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_606,c_1118]) ).
tcf(c_103192,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),X1),X0),
inference(superposition,[status(thm)],[c_1095,c_1118]) ).
tcf(c_103193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_95505,c_1118]) ).
tcf(c_103194,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_93902,c_1118]) ).
tcf(c_103195,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(superposition,[status(thm)],[c_93901,c_1118]) ).
tcf(c_103196,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(superposition,[status(thm)],[c_93899,c_1118]) ).
tcf(c_103197,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92438,c_1118]) ).
tcf(c_103198,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_91889,c_1118]) ).
tcf(c_103199,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X2),
inference(superposition,[status(thm)],[c_92387,c_1118]) ).
tcf(c_103200,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0),X1) ),
inference(superposition,[status(thm)],[c_97717,c_1118]) ).
tcf(c_103201,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_92531,c_1118]) ).
tcf(c_103202,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0),X1) ),
inference(superposition,[status(thm)],[c_92511,c_1118]) ).
tcf(c_103203,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),X2),
inference(superposition,[status(thm)],[c_92431,c_1118]) ).
tcf(c_103204,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0),X1) ),
inference(superposition,[status(thm)],[c_92564,c_1118]) ).
tcf(c_103205,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0),X1) ),
inference(superposition,[status(thm)],[c_92563,c_1118]) ).
tcf(c_103206,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0),X1) ),
inference(superposition,[status(thm)],[c_92520,c_1118]) ).
tcf(c_103207,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0),X1) ),
inference(superposition,[status(thm)],[c_92519,c_1118]) ).
tcf(c_103209,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,iPr_def_15),X0),
inference(superposition,[status(thm)],[c_92522,c_1118]) ).
tcf(c_103210,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),X1),
inference(superposition,[status(thm)],[c_92868,c_1118]) ).
tcf(c_103211,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15),X0),
inference(superposition,[status(thm)],[c_92879,c_1118]) ).
tcf(c_103212,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),X1),
inference(superposition,[status(thm)],[c_92883,c_1118]) ).
tcf(c_103214,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(superposition,[status(thm)],[c_94346,c_1118]) ).
tcf(c_103215,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),X1),
inference(superposition,[status(thm)],[c_94737,c_1118]) ).
tcf(c_103216,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),X1),
inference(superposition,[status(thm)],[c_94882,c_1118]) ).
tcf(c_103217,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),X1)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101217,c_1118]) ).
tcf(c_103218,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),X1)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101860,c_1118]) ).
tcf(c_103219,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),X1)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101633,c_1118]) ).
tcf(c_103220,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1214,c_1118]) ).
tcf(c_103221,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_440,c_1118]) ).
tcf(c_103222,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_551,c_1118]) ).
tcf(c_103224,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_n____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_90483,c_1118]) ).
tcf(c_103262,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(light_normalisation,[status(thm)],[c_103182,c_1067]) ).
tcf(c_103263,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0)
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(light_normalisation,[status(thm)],[c_103181,c_1067]) ).
tcf(c_103264,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0)
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(light_normalisation,[status(thm)],[c_103180,c_1067]) ).
tcf(c_103269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) ),
inference(light_normalisation,[status(thm)],[c_103193,c_1065]) ).
tcf(c_103290,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_103191,c_162]) ).
tcf(c_103344,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_93901,c_1119]) ).
tcf(c_103345,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_91901,c_1119]) ).
tcf(c_103346,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_49961,c_1119]) ).
tcf(c_103347,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_96089,c_1119]) ).
tcf(c_103348,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X1)),
inference(superposition,[status(thm)],[c_344,c_1119]) ).
tcf(c_103355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_92451,c_1119]) ).
tcf(c_103356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_92408,c_1119]) ).
tcf(c_103357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_50489,c_1119]) ).
tcf(c_103358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_50325,c_1119]) ).
tcf(c_103359,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2),X1)),
inference(superposition,[status(thm)],[c_651,c_1119]) ).
tcf(c_103360,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)),X2)),
inference(superposition,[status(thm)],[c_474,c_1119]) ).
tcf(c_103361,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_602,c_1119]) ).
tcf(c_103362,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))),X1)),
inference(superposition,[status(thm)],[c_910,c_1119]) ).
tcf(c_103363,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X1)),
inference(superposition,[status(thm)],[c_911,c_1119]) ).
tcf(c_103366,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1)),
inference(superposition,[status(thm)],[c_91889,c_1119]) ).
tcf(c_103367,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)) ),
inference(superposition,[status(thm)],[c_92531,c_1119]) ).
tcf(c_103368,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)) ),
inference(superposition,[status(thm)],[c_91905,c_1119]) ).
tcf(c_103370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X3)),X2)),
inference(superposition,[status(thm)],[c_92387,c_1119]) ).
tcf(c_103371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3))),X3)),
inference(superposition,[status(thm)],[c_92431,c_1119]) ).
tcf(c_103372,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)),
inference(superposition,[status(thm)],[c_94346,c_1119]) ).
tcf(c_103374,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1066,c_1119]) ).
tcf(c_103375,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1067,c_1119]) ).
tcf(c_103376,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_1098,c_1119]) ).
tcf(c_103377,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1099,c_1119]) ).
tcf(c_103378,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_1100,c_1119]) ).
tcf(c_103379,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_1144,c_1119]) ).
tcf(c_103380,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_91869,c_1119]) ).
tcf(c_103381,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,v_n____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_91389,c_1119]) ).
tcf(c_103382,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0) ),
inference(superposition,[status(thm)],[c_91398,c_1119]) ).
tcf(c_103469,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ) ),
inference(superposition,[status(thm)],[c_1136,c_1137]) ).
tcf(c_103470,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_256,c_1137]) ).
tcf(c_103472,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X1)),
inference(superposition,[status(thm)],[c_331,c_1137]) ).
tcf(c_103478,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X2)) ),
inference(superposition,[status(thm)],[c_334,c_1137]) ).
tcf(c_103479,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_452,c_1137]) ).
tcf(c_103480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_633,c_1137]) ).
tcf(c_103481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_92420,c_1137]) ).
tcf(c_103482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_92376,c_1137]) ).
tcf(c_103483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_632,c_1137]) ).
tcf(c_103484,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_455,c_1137]) ).
tcf(c_103485,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)),X1)),
inference(superposition,[status(thm)],[c_492,c_1137]) ).
tcf(c_103486,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))),X2)),
inference(superposition,[status(thm)],[c_491,c_1137]) ).
tcf(c_103487,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X1))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_608,c_1137]) ).
tcf(c_103488,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92157,c_1137]) ).
tcf(c_103489,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)),
inference(superposition,[status(thm)],[c_91294,c_1137]) ).
tcf(c_103490,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X1)) ),
inference(superposition,[status(thm)],[c_100509,c_1137]) ).
tcf(c_103491,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))),X2)),
inference(superposition,[status(thm)],[c_92168,c_1137]) ).
tcf(c_103492,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)),
inference(superposition,[status(thm)],[c_94656,c_1137]) ).
tcf(c_103493,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)),X1)),
inference(superposition,[status(thm)],[c_94661,c_1137]) ).
tcf(c_103494,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15),X1)),
inference(superposition,[status(thm)],[c_94663,c_1137]) ).
tcf(c_103495,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X1)),
inference(superposition,[status(thm)],[c_94684,c_1137]) ).
tcf(c_103496,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)),X1)),
inference(superposition,[status(thm)],[c_94715,c_1137]) ).
tcf(c_103497,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,iPr_def_15)),X1)),
inference(superposition,[status(thm)],[c_94729,c_1137]) ).
tcf(c_103498,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X2)),X1)),
inference(superposition,[status(thm)],[c_94734,c_1137]) ).
tcf(c_103499,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))),X2)),
inference(superposition,[status(thm)],[c_94758,c_1137]) ).
tcf(c_103500,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))),X2)),
inference(superposition,[status(thm)],[c_94874,c_1137]) ).
tcf(c_103501,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),iPr_def_15)),X2)),
inference(superposition,[status(thm)],[c_94879,c_1137]) ).
tcf(c_103502,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)),
inference(superposition,[status(thm)],[c_95861,c_1137]) ).
tcf(c_103504,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_440,c_1137]) ).
tcf(c_103505,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_551,c_1137]) ).
tcf(c_103507,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_90483,c_1137]) ).
tcf(c_103520,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X1)),
inference(light_normalisation,[status(thm)],[c_103496,c_553]) ).
tcf(c_103523,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X1)),
inference(light_normalisation,[status(thm)],[c_103485,c_553]) ).
tcf(c_103617,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1))),
inference(superposition,[status(thm)],[c_103210,c_49959]) ).
tcf(c_103618,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_103210,c_164]) ).
tcf(c_103621,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),X1),X2),
inference(superposition,[status(thm)],[c_103210,c_1118]) ).
tcf(c_103632,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15))),
inference(superposition,[status(thm)],[c_103212,c_49959]) ).
tcf(c_103633,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_103212,c_164]) ).
tcf(c_103636,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),X1),X2),
inference(superposition,[status(thm)],[c_103212,c_1118]) ).
tcf(c_103643,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))),
inference(demodulation,[status(thm)],[c_103348,c_551]) ).
tcf(c_103644,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_1214,c_103643]) ).
tcf(c_103645,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(superposition,[status(thm)],[c_1066,c_103643]) ).
tcf(c_103646,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(superposition,[status(thm)],[c_1067,c_103643]) ).
tcf(c_103647,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_1098,c_103643]) ).
tcf(c_103648,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)),
inference(superposition,[status(thm)],[c_1099,c_103643]) ).
tcf(c_103649,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_1100,c_103643]) ).
tcf(c_103650,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_1144,c_103643]) ).
tcf(c_103651,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91869,c_103643]) ).
tcf(c_103654,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91871,c_103643]) ).
tcf(c_103655,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_94315,c_103643]) ).
tcf(c_103656,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X1),
inference(superposition,[status(thm)],[c_103643,c_49959]) ).
tcf(c_103657,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1))),
inference(superposition,[status(thm)],[c_103643,c_387]) ).
tcf(c_103660,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1))),
inference(superposition,[status(thm)],[c_103643,c_464]) ).
tcf(c_103661,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1))),
inference(superposition,[status(thm)],[c_103643,c_463]) ).
tcf(c_103662,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X1),
inference(superposition,[status(thm)],[c_103643,c_1118]) ).
tcf(c_103663,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1)),
inference(superposition,[status(thm)],[c_103643,c_470]) ).
tcf(c_103664,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1)),X2)),
inference(superposition,[status(thm)],[c_103643,c_1119]) ).
tcf(c_103665,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
inference(superposition,[status(thm)],[c_103643,c_93841]) ).
tcf(c_103666,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_103643,c_100811]) ).
tcf(c_103667,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_103643,c_92394]) ).
tcf(c_103745,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(superposition,[status(thm)],[c_1214,c_103646]) ).
tcf(c_103746,plain,
! [X0: $i] : 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),X0),X0),
inference(superposition,[status(thm)],[c_440,c_103646]) ).
tcf(c_103749,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____),iPr_def_15),
inference(superposition,[status(thm)],[c_90483,c_103646]) ).
tcf(c_103750,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(superposition,[status(thm)],[c_103646,c_49959]) ).
tcf(c_103756,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0),X1),
inference(superposition,[status(thm)],[c_103646,c_1118]) ).
tcf(c_103766,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(superposition,[status(thm)],[c_1098,c_103662]) ).
tcf(c_103767,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1099,c_103662]) ).
tcf(c_103768,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(superposition,[status(thm)],[c_1100,c_103662]) ).
tcf(c_103769,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(superposition,[status(thm)],[c_1144,c_103662]) ).
tcf(c_103770,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(superposition,[status(thm)],[c_91869,c_103662]) ).
tcf(c_103771,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_n____),
inference(superposition,[status(thm)],[c_91389,c_103662]) ).
tcf(c_103772,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_91398,c_103662]) ).
tcf(c_103773,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),iPr_def_15),
inference(superposition,[status(thm)],[c_91871,c_103662]) ).
tcf(c_103774,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),iPr_def_15),
inference(superposition,[status(thm)],[c_94315,c_103662]) ).
tcf(c_103775,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))),
inference(superposition,[status(thm)],[c_103662,c_49959]) ).
tcf(c_103776,plain,
! [X0: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_103662,c_164]) ).
tcf(c_103779,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X2),X1),
inference(superposition,[status(thm)],[c_103662,c_1118]) ).
tcf(c_103790,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,v_n____),
inference(demodulation,[status(thm)],[c_103771,c_91398]) ).
tcf(c_103793,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_1214,c_103666]) ).
tcf(c_103794,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)),
inference(superposition,[status(thm)],[c_1099,c_103666]) ).
tcf(c_103795,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_1100,c_103666]) ).
tcf(c_103796,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_1144,c_103666]) ).
tcf(c_103797,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91869,c_103666]) ).
tcf(c_103798,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91389,c_103666]) ).
tcf(c_103799,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____)),
inference(superposition,[status(thm)],[c_91398,c_103666]) ).
tcf(c_103800,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0)),v_n____),
inference(superposition,[status(thm)],[c_103666,c_50323]) ).
tcf(c_103801,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_103666,c_93809]) ).
tcf(c_103802,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_103666,c_92057]) ).
tcf(c_103809,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_n____),
inference(superposition,[status(thm)],[c_103666,c_333]) ).
tcf(c_103810,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_103666,c_100844]) ).
tcf(c_103818,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,v_n____),
inference(demodulation,[status(thm)],[c_103809,c_91398]) ).
tcf(c_103822,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1) ) ),
inference(superposition,[status(thm)],[c_95904,c_90501]) ).
tcf(c_103824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),X2),
inference(superposition,[status(thm)],[c_17554,c_90501]) ).
tcf(c_103825,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(superposition,[status(thm)],[c_17690,c_90501]) ).
tcf(c_103826,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_17614,c_90501]) ).
tcf(c_103827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2))) ) ),
inference(superposition,[status(thm)],[c_100594,c_90501]) ).
tcf(c_103828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2))) ) ),
inference(superposition,[status(thm)],[c_100045,c_90501]) ).
tcf(c_103829,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1)))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_17702,c_90501]) ).
tcf(c_103830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17708,c_90501]) ).
tcf(c_103831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X0))) ) ),
inference(superposition,[status(thm)],[c_96740,c_90501]) ).
tcf(c_103832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) ) ),
inference(superposition,[status(thm)],[c_98303,c_90501]) ).
tcf(c_103833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)))) ) ),
inference(superposition,[status(thm)],[c_92641,c_90501]) ).
tcf(c_103834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)))) ) ),
inference(superposition,[status(thm)],[c_92945,c_90501]) ).
tcf(c_103835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) ) ),
inference(superposition,[status(thm)],[c_98712,c_90501]) ).
tcf(c_103836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3)),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X0))) ) ),
inference(superposition,[status(thm)],[c_97114,c_90501]) ).
tcf(c_103837,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,iPr_def_20))),
inference(superposition,[status(thm)],[c_90491,c_90501]) ).
tcf(c_103838,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1),
inference(superposition,[status(thm)],[c_90508,c_90501]) ).
tcf(c_103839,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X1) ) ),
inference(superposition,[status(thm)],[c_95904,c_90501]) ).
tcf(c_103840,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),X1),
inference(superposition,[status(thm)],[c_16698,c_90501]) ).
tcf(c_103841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X1),
inference(superposition,[status(thm)],[c_17554,c_90501]) ).
tcf(c_103842,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(superposition,[status(thm)],[c_17690,c_90501]) ).
tcf(c_103843,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_17614,c_90501]) ).
tcf(c_103844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)))),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3)))) ) ),
inference(superposition,[status(thm)],[c_100594,c_90501]) ).
tcf(c_103845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)))),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3),X2))) ) ),
inference(superposition,[status(thm)],[c_100045,c_90501]) ).
tcf(c_103846,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1)),X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17702,c_90501]) ).
tcf(c_103847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)),X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),X2))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17708,c_90501]) ).
tcf(c_103848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X3))),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)))) ) ),
inference(superposition,[status(thm)],[c_96740,c_90501]) ).
tcf(c_103849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)))),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),X3))) ) ),
inference(superposition,[status(thm)],[c_98303,c_90501]) ).
tcf(c_103850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)))) ) ),
inference(superposition,[status(thm)],[c_92641,c_90501]) ).
tcf(c_103851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)))) ) ),
inference(superposition,[status(thm)],[c_92945,c_90501]) ).
tcf(c_103852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)))),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),X3))) ) ),
inference(superposition,[status(thm)],[c_98712,c_90501]) ).
tcf(c_103853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X3))),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)))) ) ),
inference(superposition,[status(thm)],[c_97114,c_90501]) ).
tcf(c_103854,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,iPr_def_20),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20)),
inference(superposition,[status(thm)],[c_90491,c_90501]) ).
tcf(c_103855,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20)),X1),
inference(superposition,[status(thm)],[c_90508,c_90501]) ).
tcf(c_103856,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2)),
inference(superposition,[status(thm)],[c_90501,c_95405]) ).
tcf(c_103857,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),
inference(superposition,[status(thm)],[c_90501,c_95332]) ).
tcf(c_103859,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1) = iPr_def_20,
inference(superposition,[status(thm)],[c_90501,c_94036]) ).
tcf(c_103860,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1),
inference(superposition,[status(thm)],[c_90501,c_94212]) ).
tcf(c_103862,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),iPr_def_20) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),
inference(light_normalisation,[status(thm)],[c_103855,c_90498,c_91118]) ).
tcf(c_103863,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),iPr_def_20) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_103854,c_90491,c_90498]) ).
tcf(c_103864,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(light_normalisation,[status(thm)],[c_103843,c_17614]) ).
tcf(c_103869,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(light_normalisation,[status(thm)],[c_103842,c_17690]) ).
tcf(c_103996,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))) = X2 ) ),
inference(superposition,[status(thm)],[c_1136,c_1138]) ).
tcf(c_103997,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_256,c_1138]) ).
tcf(c_104003,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_96459,c_1138]) ).
tcf(c_104004,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),X1) ),
inference(superposition,[status(thm)],[c_93100,c_1138]) ).
tcf(c_104005,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),X1) ),
inference(superposition,[status(thm)],[c_92157,c_1138]) ).
tcf(c_104006,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),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),X0),X1) ),
inference(superposition,[status(thm)],[c_91901,c_1138]) ).
tcf(c_104007,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_317,c_1138]) ).
tcf(c_104008,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_92805,c_1138]) ).
tcf(c_104009,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(superposition,[status(thm)],[c_92283,c_1138]) ).
tcf(c_104010,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_614,c_1138]) ).
tcf(c_104011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3),X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_1097,c_1138]) ).
tcf(c_104013,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_100509,c_1138]) ).
tcf(c_104021,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,v_n____),iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_91389,c_1138]) ).
tcf(c_104061,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),
inference(superposition,[status(thm)],[c_1458,c_1149]) ).
tcf(c_104062,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X2)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,X2) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1514,c_1149]) ).
tcf(c_104063,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1)) = c_Groups_Oplus__class_Oplus(iPr_def_10,X0,X1),
inference(superposition,[status(thm)],[c_90868,c_1149]) ).
tcf(c_104072,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),
inference(superposition,[status(thm)],[c_1455,c_1150]) ).
tcf(c_104073,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X2)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X1,X2) )
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(superposition,[status(thm)],[c_1511,c_1150]) ).
tcf(c_104074,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1)) = c_Groups_Ominus__class_Ominus(iPr_def_10,X0,X1),
inference(superposition,[status(thm)],[c_90848,c_1150]) ).
tcf(c_104078,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),X1),
inference(demodulation,[status(thm)],[c_90501,c_104072]) ).
tcf(c_104089,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X2)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X0),X1,X2) )
| ~ class_Groups_Oab__group__add(X0) ),
inference(superposition,[status(thm)],[c_1505,c_1151]) ).
tcf(c_104093,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_1214,c_103667]) ).
tcf(c_104094,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)),
inference(superposition,[status(thm)],[c_1099,c_103667]) ).
tcf(c_104096,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_1144,c_103667]) ).
tcf(c_104097,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91869,c_103667]) ).
tcf(c_104098,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_91389,c_103667]) ).
tcf(c_104099,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____)),
inference(superposition,[status(thm)],[c_91398,c_103667]) ).
tcf(c_104103,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0)),X0),
inference(superposition,[status(thm)],[c_103667,c_1118]) ).
tcf(c_104109,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,iPr_def_15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1099,c_104103]) ).
tcf(c_104111,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_1144,c_104103]) ).
tcf(c_104112,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),
inference(superposition,[status(thm)],[c_91869,c_104103]) ).
tcf(c_104113,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_n____),
inference(superposition,[status(thm)],[c_91389,c_104103]) ).
tcf(c_104114,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_91398,c_104103]) ).
tcf(c_104115,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0))),
inference(superposition,[status(thm)],[c_104103,c_49959]) ).
tcf(c_104116,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_104103,c_164]) ).
tcf(c_104119,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),X1),X0),
inference(superposition,[status(thm)],[c_104103,c_1118]) ).
tcf(c_104168,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_97571,c_731]) ).
tcf(c_104169,plain,
( ~ class_Rings_Olinordered__ring(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_97571,c_807]) ).
tcf(c_104170,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))
| ~ class_Rings_Olinordered__ring(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_97571,c_750]) ).
tcf(c_104174,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(forward_subsumption_resolution,[status(thm)],[c_104168,c_1360]) ).
tcf(c_104176,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(iPr_def_10),X0),c_Groups_Ozero__class_Ozero(iPr_def_10)))
| ~ class_Rings_Odvd(iPr_def_10) ),
inference(superposition,[status(thm)],[c_97575,c_736]) ).
tcf(c_104177,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(iPr_def_10),X0),c_Groups_Ozero__class_Ozero(iPr_def_10)))
| ~ class_Rings_Ocomm__semiring__1(iPr_def_10) ),
inference(superposition,[status(thm)],[c_97575,c_731]) ).
tcf(c_104178,plain,
( ~ class_Rings_Olinordered__ring(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_97575,c_807]) ).
tcf(c_104179,plain,
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10))
| ~ class_Rings_Olinordered__ring(iPr_def_10) ),
inference(superposition,[status(thm)],[c_97575,c_750]) ).
tcf(c_104180,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10)),c_Groups_Ozero__class_Ozero(iPr_def_10)))
| ~ class_Rings_Ocomm__semiring__1(iPr_def_10) ),
inference(superposition,[status(thm)],[c_97575,c_732]) ).
tcf(c_104186,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(iPr_def_11,X0),c_Groups_Ozero__class_Ozero(iPr_def_10)))
| ~ class_Rings_Odvd(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_104176,c_72167]) ).
tcf(c_104187,plain,
( hBOOL(hAPP(hAPP(iPr_def_11,c_Groups_Ozero__class_Ozero(iPr_def_10)),c_Groups_Ozero__class_Ozero(iPr_def_10)))
| ~ class_Rings_Ocomm__semiring__1(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_104180,c_72167]) ).
tcf(c_104192,plain,
( ~ class_Rings_Olinordered__ring(iPr_def_10)
| ~ class_Orderings_Olinorder(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_104179,c_300]) ).
tcf(c_104193,plain,
( ~ class_Rings_Olinordered__ring(iPr_def_10)
| ~ class_Orderings_Opreorder(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_104179,c_293]) ).
tcf(c_104212,plain,
hAPP(c_Polynomial_Ocoeff(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(superposition,[status(thm)],[c_1360,c_1225]) ).
tcf(c_104213,plain,
hAPP(c_Polynomial_Ocoeff(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_1408,c_1225]) ).
tcf(c_104214,plain,
hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1447,c_1225]) ).
tcf(c_104215,plain,
! [X0: $i] :
( ( hAPP(c_Polynomial_Ocoeff(tc_Polynomial_Opoly(X0),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(superposition,[status(thm)],[c_1501,c_1225]) ).
tcf(c_104216,plain,
hAPP(c_Polynomial_Ocoeff(iPr_def_10,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(iPr_def_10))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(iPr_def_10),
inference(superposition,[status(thm)],[c_90792,c_1225]) ).
tcf(c_104217,plain,
hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(iPr_def_10)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(light_normalisation,[status(thm)],[c_104214,c_72166]) ).
tcf(c_104226,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_93901,c_50530]) ).
tcf(c_104227,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_91901,c_50530]) ).
tcf(c_104228,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_49961,c_50530]) ).
tcf(c_104229,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_96089,c_50530]) ).
tcf(c_104230,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1)),
inference(superposition,[status(thm)],[c_344,c_50530]) ).
tcf(c_104234,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1))
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_50432,c_50530]) ).
tcf(c_104235,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1))
| ~ class_Orderings_Oorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_420,c_50530]) ).
tcf(c_104236,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_417,c_50530]) ).
tcf(c_104238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_92451,c_50530]) ).
tcf(c_104239,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_92408,c_50530]) ).
tcf(c_104240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_50489,c_50530]) ).
tcf(c_104241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_50325,c_50530]) ).
tcf(c_104242,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),X1)),
inference(superposition,[status(thm)],[c_651,c_50530]) ).
tcf(c_104243,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)),X2)),
inference(superposition,[status(thm)],[c_474,c_50530]) ).
tcf(c_104244,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_602,c_50530]) ).
tcf(c_104245,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),X1)),
inference(superposition,[status(thm)],[c_910,c_50530]) ).
tcf(c_104246,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X1)),
inference(superposition,[status(thm)],[c_911,c_50530]) ).
tcf(c_104247,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X1)) ),
inference(superposition,[status(thm)],[c_92531,c_50530]) ).
tcf(c_104248,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X1)) ),
inference(superposition,[status(thm)],[c_91905,c_50530]) ).
tcf(c_104249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X3)),X2)),
inference(superposition,[status(thm)],[c_92387,c_50530]) ).
tcf(c_104250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))),X3)),
inference(superposition,[status(thm)],[c_92431,c_50530]) ).
tcf(c_104251,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)),X2)),
inference(superposition,[status(thm)],[c_103643,c_50530]) ).
tcf(c_104253,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_1214,c_50530]) ).
tcf(c_104254,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_440,c_50530]) ).
tcf(c_104255,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_551,c_50530]) ).
tcf(c_104257,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_90483,c_50530]) ).
tcf(c_104263,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X1)),
inference(light_normalisation,[status(thm)],[c_104242,c_553]) ).
tcf(c_104344,plain,
! [X0: $i] : c_Polynomial_OpCons(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Polynomial_Omonom(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1384,c_210]) ).
tcf(c_104345,plain,
! [X0: $i] : c_Polynomial_OpCons(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) = c_Polynomial_Omonom(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1424,c_210]) ).
tcf(c_104346,plain,
! [X0: $i] : c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_1468,c_210]) ).
tcf(c_104347,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_OpCons(tc_Polynomial_Opoly(X0),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))) = c_Polynomial_Omonom(tc_Polynomial_Opoly(X0),X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_1525,c_210]) ).
tcf(c_104348,plain,
! [X0: $i] : c_Polynomial_OpCons(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) = c_Polynomial_Omonom(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_90973,c_210]) ).
tcf(c_104349,plain,
! [X0: $i] : c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(iPr_def_10)) = c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(light_normalisation,[status(thm)],[c_104346,c_72166]) ).
tcf(c_104367,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Odvd(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_97589,c_736]) ).
tcf(c_104368,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_97589,c_731]) ).
tcf(c_104374,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10)),c_Groups_Ozero__class_Ozero(iPr_def_10)))
| ~ class_Rings_Odvd(iPr_def_10) ),
inference(superposition,[status(thm)],[c_97593,c_736]) ).
tcf(c_104379,plain,
( hBOOL(hAPP(hAPP(iPr_def_11,c_Groups_Ozero__class_Ozero(iPr_def_10)),c_Groups_Ozero__class_Ozero(iPr_def_10)))
| ~ class_Rings_Odvd(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_104374,c_72167]) ).
tcf(c_104384,plain,
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = v_n____ ) ),
inference(superposition,[status(thm)],[c_1136,c_97645]) ).
tcf(c_104385,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = v_n____ ) ),
inference(superposition,[status(thm)],[c_256,c_97645]) ).
tcf(c_104408,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_97669,c_93809]) ).
tcf(c_104409,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_97669,c_92057]) ).
tcf(c_104416,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(superposition,[status(thm)],[c_97669,c_374]) ).
tcf(c_104417,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1)) ),
inference(superposition,[status(thm)],[c_97669,c_320]) ).
tcf(c_104419,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),X1)) ),
inference(superposition,[status(thm)],[c_97669,c_1137]) ).
tcf(c_104420,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_97669,c_449]) ).
tcf(c_104421,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0)) ),
inference(superposition,[status(thm)],[c_97669,c_100844]) ).
tcf(c_104430,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(light_normalisation,[status(thm)],[c_104420,c_553]) ).
tcf(c_104435,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X1)) ),
inference(light_normalisation,[status(thm)],[c_104419,c_553]) ).
tcf(c_104454,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_97670,c_93809]) ).
tcf(c_104455,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_97670,c_92057]) ).
tcf(c_104462,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(superposition,[status(thm)],[c_97670,c_374]) ).
tcf(c_104465,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)),X2)) ),
inference(superposition,[status(thm)],[c_97670,c_1137]) ).
tcf(c_104466,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))) ),
inference(superposition,[status(thm)],[c_97670,c_449]) ).
tcf(c_104468,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,v_n____)) ),
inference(superposition,[status(thm)],[c_97670,c_100844]) ).
tcf(c_104493,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(superposition,[status(thm)],[c_97709,c_164]) ).
tcf(c_104496,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_97709,c_300]) ).
tcf(c_104497,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_97709,c_293]) ).
tcf(c_104499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_97709,c_50530]) ).
tcf(c_104501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_97709,c_463]) ).
tcf(c_104502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_97709,c_1118]) ).
tcf(c_104504,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97709,c_603]) ).
tcf(c_104505,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97709,c_607]) ).
tcf(c_104506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_97709,c_1119]) ).
tcf(c_104523,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(superposition,[status(thm)],[c_97709,c_374]) ).
tcf(c_104524,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1)) ),
inference(superposition,[status(thm)],[c_97709,c_320]) ).
tcf(c_104526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),X1)) ),
inference(superposition,[status(thm)],[c_97709,c_1137]) ).
tcf(c_104527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_97709,c_449]) ).
tcf(c_104528,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0)) ),
inference(superposition,[status(thm)],[c_97709,c_100844]) ).
tcf(c_104535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(light_normalisation,[status(thm)],[c_104527,c_553]) ).
tcf(c_104549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X1)) ),
inference(light_normalisation,[status(thm)],[c_104526,c_553]) ).
tcf(c_104584,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_97710,c_49959]) ).
tcf(c_104585,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(superposition,[status(thm)],[c_97710,c_164]) ).
tcf(c_104587,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0)) ),
inference(superposition,[status(thm)],[c_97710,c_387]) ).
tcf(c_104588,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_97710,c_300]) ).
tcf(c_104589,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_97710,c_293]) ).
tcf(c_104591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_97710,c_50530]) ).
tcf(c_104593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_97710,c_463]) ).
tcf(c_104594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_97710,c_1118]) ).
tcf(c_104595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_97710,c_470]) ).
tcf(c_104596,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97710,c_603]) ).
tcf(c_104597,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1),X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97710,c_607]) ).
tcf(c_104598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_97710,c_1119]) ).
tcf(c_104615,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(superposition,[status(thm)],[c_97710,c_374]) ).
tcf(c_104618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)),X2)) ),
inference(superposition,[status(thm)],[c_97710,c_1137]) ).
tcf(c_104619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))) ),
inference(superposition,[status(thm)],[c_97710,c_449]) ).
tcf(c_104621,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,v_n____)) ),
inference(superposition,[status(thm)],[c_97710,c_100844]) ).
tcf(c_104698,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X1,X2)),c_Polynomial_Odegree(X0,X2))
| ( c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X1,X2)) = c_Polynomial_Odegree(X0,X2) )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(superposition,[status(thm)],[c_159,c_285]) ).
tcf(c_104705,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(X0,X2,X1)
| ( X1 = X2 )
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_421,c_285]) ).
tcf(c_104706,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
| ( X0 = X1 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97710,c_285]) ).
tcf(c_104707,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ( X0 = X1 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97709,c_285]) ).
tcf(c_104709,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X1,X2)),X2)
| ( c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X1,X2)) = X2 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_403,c_285]) ).
tcf(c_104710,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X2 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92451,c_285]) ).
tcf(c_104711,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X2 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92408,c_285]) ).
tcf(c_104712,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X2 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_50489,c_285]) ).
tcf(c_104716,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X1 )
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_602,c_285]) ).
tcf(c_104717,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X1 )
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(superposition,[status(thm)],[c_606,c_285]) ).
tcf(c_104723,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
| ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1 )
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_669,c_285]) ).
tcf(c_104724,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1) )
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_670,c_285]) ).
tcf(c_104727,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)) = X0 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_910,c_285]) ).
tcf(c_104734,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = X2 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_95505,c_285]) ).
tcf(c_104736,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0 )
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_1251,c_285]) ).
tcf(c_104774,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94737,c_285]) ).
tcf(c_104775,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94882,c_285]) ).
tcf(c_104782,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_100800,c_285]) ).
tcf(c_104784,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101217,c_285]) ).
tcf(c_104787,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = iPr_def_15 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101857,c_285]) ).
tcf(c_104788,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101860,c_285]) ).
tcf(c_104789,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101633,c_285]) ).
tcf(c_104790,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_103643,c_285]) ).
tcf(c_104792,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X1)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_103662,c_285]) ).
tcf(c_104794,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0)),X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0)) = X0 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_104103,c_285]) ).
tcf(c_104799,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ( X0 = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104707,c_1414]) ).
tcf(c_104803,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
| ( X0 = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104706,c_1414]) ).
tcf(c_104807,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104789,c_1414]) ).
tcf(c_104811,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104788,c_1414]) ).
tcf(c_104815,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = iPr_def_15 )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104787,c_1414]) ).
tcf(c_104819,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104784,c_1414]) ).
tcf(c_104823,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104734,c_1414]) ).
tcf(c_104827,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104712,c_1414]) ).
tcf(c_104831,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104711,c_1414]) ).
tcf(c_104835,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104710,c_1414]) ).
tcf(c_104839,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0)),X0)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0)) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104794,c_1414]) ).
tcf(c_104842,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)),X1)
| ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104792,c_1414]) ).
tcf(c_104845,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104790,c_1414]) ).
tcf(c_104848,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104782,c_1414]) ).
tcf(c_104863,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X1,X2)),X2)
| ( c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X1,X2)) = X2 )
| ~ class_Groups_Ozero(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104709,c_1414]) ).
tcf(c_104867,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104775,c_1414]) ).
tcf(c_104870,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104774,c_1414]) ).
tcf(c_104874,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X1,X2)),c_Polynomial_Odegree(X0,X2))
| ( c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X1,X2)) = c_Polynomial_Odegree(X0,X2) )
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104698,c_1414]) ).
tcf(c_104878,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104727,c_1414]) ).
tcf(c_104931,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_162,c_291]) ).
tcf(c_104933,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93901,c_291]) ).
tcf(c_104934,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91901,c_291]) ).
tcf(c_104935,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_49961,c_291]) ).
tcf(c_104938,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X2,X1)),c_Polynomial_Odegree(X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X2,X1)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(superposition,[status(thm)],[c_159,c_291]) ).
tcf(c_104939,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_384,c_291]) ).
tcf(c_104941,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X1)
| c_Orderings_Oord__class_Oless(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(superposition,[status(thm)],[c_301,c_291]) ).
tcf(c_104946,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97710,c_291]) ).
tcf(c_104947,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97709,c_291]) ).
tcf(c_104948,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Orderings_Opreorder(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_362,c_291]) ).
tcf(c_104949,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X2,X1)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X2,X1)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_403,c_291]) ).
tcf(c_104950,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92451,c_291]) ).
tcf(c_104951,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92408,c_291]) ).
tcf(c_104952,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_50489,c_291]) ).
tcf(c_104953,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_50325,c_291]) ).
tcf(c_104954,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_651,c_291]) ).
tcf(c_104955,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_474,c_291]) ).
tcf(c_104956,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_602,c_291]) ).
tcf(c_104957,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(superposition,[status(thm)],[c_606,c_291]) ).
tcf(c_104960,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ class_Orderings_Opreorder(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_661,c_291]) ).
tcf(c_104963,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_669,c_291]) ).
tcf(c_104964,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0))
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_670,c_291]) ).
tcf(c_104965,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Orderings_Opreorder(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_91782,c_291]) ).
tcf(c_104966,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1))
| c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__ring(X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(superposition,[status(thm)],[c_750,c_291]) ).
tcf(c_104967,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)),X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_910,c_291]) ).
tcf(c_104968,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0),X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_911,c_291]) ).
tcf(c_104972,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ class_Orderings_Opreorder(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_97045,c_291]) ).
tcf(c_104973,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1095,c_291]) ).
tcf(c_104974,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_95505,c_291]) ).
tcf(c_104976,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_1251,c_291]) ).
tcf(c_104977,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93902,c_291]) ).
tcf(c_104978,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93901,c_291]) ).
tcf(c_104979,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93899,c_291]) ).
tcf(c_104980,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_92438,c_291]) ).
tcf(c_104981,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91030,c_291]) ).
tcf(c_104984,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20)
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Opreorder(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_95200,c_291]) ).
tcf(c_104985,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20)
| ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_91132,c_291]) ).
tcf(c_104990,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92531,c_291]) ).
tcf(c_104992,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92307,c_291]) ).
tcf(c_104993,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X1)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92387,c_291]) ).
tcf(c_104994,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97717,c_291]) ).
tcf(c_104997,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X2)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92431,c_291]) ).
tcf(c_105006,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92879,c_291]) ).
tcf(c_105008,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92888,c_291]) ).
tcf(c_105014,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94737,c_291]) ).
tcf(c_105015,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_94882,c_291]) ).
tcf(c_105016,plain,
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Oone__class_Oone(iPr_def_10))
| c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),c_Groups_Ozero__class_Ozero(iPr_def_10))
| ~ class_Rings_Olinordered__ring(iPr_def_10)
| ~ class_Orderings_Opreorder(iPr_def_10) ),
inference(superposition,[status(thm)],[c_95189,c_291]) ).
tcf(c_105019,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_96296,c_291]) ).
tcf(c_105021,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 )
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97629,c_291]) ).
tcf(c_105022,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_100800,c_291]) ).
tcf(c_105024,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101217,c_291]) ).
tcf(c_105025,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_102263,c_291]) ).
tcf(c_105026,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101691,c_291]) ).
tcf(c_105027,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101857,c_291]) ).
tcf(c_105028,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101860,c_291]) ).
tcf(c_105029,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101633,c_291]) ).
tcf(c_105030,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X1)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_103643,c_291]) ).
tcf(c_105032,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_103662,c_291]) ).
tcf(c_105034,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0)))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_104103,c_291]) ).
tcf(c_105035,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104960,c_1367]) ).
tcf(c_105038,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104981,c_1413]) ).
tcf(c_105041,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104931,c_1413]) ).
tcf(c_105044,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104990,c_1413]) ).
tcf(c_105048,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104935,c_1413]) ).
tcf(c_105052,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104994,c_1413]) ).
tcf(c_105064,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104934,c_1413]) ).
tcf(c_105068,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104933,c_1413]) ).
tcf(c_105072,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104979,c_1413]) ).
tcf(c_105076,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104978,c_1413]) ).
tcf(c_105080,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104973,c_1413]) ).
tcf(c_105083,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104955,c_1413]) ).
tcf(c_105086,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104954,c_1413]) ).
tcf(c_105089,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105026,c_1413]) ).
tcf(c_105093,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105025,c_1413]) ).
tcf(c_105097,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = iPr_def_15 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105021,c_1413]) ).
tcf(c_105105,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104980,c_1413]) ).
tcf(c_105109,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104977,c_1413]) ).
tcf(c_105113,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104972,c_1367]) ).
tcf(c_105117,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104965,c_1367]) ).
tcf(c_105125,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104947,c_1413]) ).
tcf(c_105129,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104946,c_1413]) ).
tcf(c_105138,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105008,c_1413]) ).
tcf(c_105141,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105006,c_1413]) ).
tcf(c_105144,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104992,c_1413]) ).
tcf(c_105147,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105029,c_1413]) ).
tcf(c_105151,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105028,c_1413]) ).
tcf(c_105155,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105027,c_1413]) ).
tcf(c_105159,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105024,c_1413]) ).
tcf(c_105163,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105019,c_1413]) ).
tcf(c_105166,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104974,c_1413]) ).
tcf(c_105170,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104968,c_1413]) ).
tcf(c_105173,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104953,c_1413]) ).
tcf(c_105177,plain,
! [X0: $i,X1: $i,X2: $i] :
( 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,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104952,c_1413]) ).
tcf(c_105181,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104951,c_1413]) ).
tcf(c_105185,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104950,c_1413]) ).
tcf(c_105189,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105034,c_1413]) ).
tcf(c_105192,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105032,c_1413]) ).
tcf(c_105195,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105030,c_1413]) ).
tcf(c_105198,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105022,c_1413]) ).
tcf(c_105201,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104997,c_1413]) ).
tcf(c_105204,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104993,c_1413]) ).
tcf(c_105207,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104976,c_1367]) ).
tcf(c_105211,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104963,c_1367]) ).
tcf(c_105225,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X2,X1)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X2,X1)))
| ~ class_Groups_Ozero(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104949,c_1413]) ).
tcf(c_105229,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104939,c_1413]) ).
tcf(c_105233,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105015,c_1413]) ).
tcf(c_105236,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105014,c_1413]) ).
tcf(c_105243,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104964,c_1367]) ).
tcf(c_105247,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X2,X1)),c_Polynomial_Odegree(X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X2,X1)))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104938,c_1413]) ).
tcf(c_105251,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104967,c_1413]) ).
tcf(c_105357,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X1,X2)),c_Polynomial_Odegree(X0,X2))
| ( c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X1,X2)) = c_Polynomial_Odegree(X0,X2) )
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(superposition,[status(thm)],[c_159,c_294]) ).
tcf(c_105358,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X1 )
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_384,c_294]) ).
tcf(c_105360,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X1)
| c_Orderings_Oord__class_Oless(X0,X1,X2)
| ( X1 = X2 )
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_301,c_294]) ).
tcf(c_105367,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oone__class_Oone(X0) )
| ~ class_Orderings_Oorder(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_362,c_294]) ).
tcf(c_105368,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X1,X2)),X2)
| ( c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X1,X2)) = X2 )
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_403,c_294]) ).
tcf(c_105375,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X1 )
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_602,c_294]) ).
tcf(c_105376,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X1 )
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(superposition,[status(thm)],[c_606,c_294]) ).
tcf(c_105382,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
| ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1 )
| ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_669,c_294]) ).
tcf(c_105383,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1) )
| ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_670,c_294]) ).
tcf(c_105385,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Rings_Olinordered__ring(X0)
| ~ class_Orderings_Oorder(X0) ),
inference(superposition,[status(thm)],[c_750,c_294]) ).
tcf(c_105395,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0 )
| ~ class_Orderings_Oorder(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_1251,c_294]) ).
tcf(c_105399,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_92438,c_294]) ).
tcf(c_105403,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Oorder(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_95200,c_294]) ).
tcf(c_105404,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = iPr_def_20 )
| ~ class_Orderings_Oorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_91132,c_294]) ).
tcf(c_105435,plain,
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Oone__class_Oone(iPr_def_10))
| ( c_Groups_Ozero__class_Ozero(iPr_def_10) = c_Groups_Oone__class_Oone(iPr_def_10) )
| ~ class_Rings_Olinordered__ring(iPr_def_10)
| ~ class_Orderings_Oorder(iPr_def_10) ),
inference(superposition,[status(thm)],[c_95189,c_294]) ).
tcf(c_105444,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____) = iPr_def_15 )
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_102263,c_294]) ).
tcf(c_105446,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = iPr_def_15 )
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101857,c_294]) ).
tcf(c_105447,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101860,c_294]) ).
tcf(c_105454,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Orderings_Oorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105404,c_91065]) ).
tcf(c_105458,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Oorder(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105403,c_91065]) ).
tcf(c_105517,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_433,c_50323]) ).
tcf(c_105518,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_433,c_93809]) ).
tcf(c_105520,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_433,c_91603]) ).
tcf(c_105521,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_433,c_245]) ).
tcf(c_105522,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_433,c_240]) ).
tcf(c_105523,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_433,c_235]) ).
tcf(c_105524,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_433,c_295]) ).
tcf(c_105525,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_433,c_292]) ).
tcf(c_105526,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_433,c_374]) ).
tcf(c_105539,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ class_Orderings_Opreorder(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_105035,c_291]) ).
tcf(c_105544,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_105035,c_603]) ).
tcf(c_105545,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_105035,c_607]) ).
tcf(c_105560,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105545,c_1340]) ).
tcf(c_105563,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105544,c_1340]) ).
tcf(c_105566,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105539,c_1367]) ).
tcf(c_105585,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),c_Groups_Ozero__class_Ozero(tc_fun(X0,X1)),c_Groups_Oone__class_Oone(tc_fun(X0,X1)))
| ~ class_Orderings_Oord(X1)
| ~ class_Rings_Olinordered__semidom(tc_fun(X0,X1)) ),
inference(superposition,[status(thm)],[c_224,c_437]) ).
tcf(c_105586,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),c_Groups_Ozero__class_Ozero(tc_fun(X0,X1)),c_Groups_Oplus__class_Oplus(tc_fun(X0,X1),c_Groups_Oone__class_Oone(tc_fun(X0,X1)),c_Groups_Oone__class_Oone(tc_fun(X0,X1))))
| ~ class_Orderings_Oord(X1)
| ~ class_Rings_Olinordered__semidom(tc_fun(X0,X1)) ),
inference(superposition,[status(thm)],[c_226,c_437]) ).
tcf(c_105587,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,c_Groups_Oplus__class_Oplus(tc_fun(X0,X1),X2,c_Groups_Oone__class_Oone(tc_fun(X0,X1))))
| ~ class_Orderings_Oord(X1)
| ~ class_Rings_Olinordered__semidom(tc_fun(X0,X1)) ),
inference(superposition,[status(thm)],[c_227,c_437]) ).
tcf(c_105588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_fun(X0,X1),X3,X2)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X3)
| ( X2 = X3 )
| ~ class_Orderings_Oord(X1)
| ~ class_Orderings_Olinorder(tc_fun(X0,X1)) ),
inference(superposition,[status(thm)],[c_250,c_437]) ).
tcf(c_105589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_fun(X0,X1),X3,X2)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,X3)
| ( X2 = X3 )
| ~ class_Orderings_Oord(X1)
| ~ class_Rings_Olinordered__idom(tc_fun(X0,X1)) ),
inference(superposition,[status(thm)],[c_230,c_437]) ).
tcf(c_105590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_fun(X0,X1),X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X3,X2)
| ( X2 = X3 )
| ~ class_Orderings_Oord(X1)
| ~ class_Orderings_Olinorder(tc_fun(X0,X1)) ),
inference(superposition,[status(thm)],[c_250,c_437]) ).
tcf(c_105591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_fun(X0,X1),X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X3,X2)
| ( X2 = X3 )
| ~ class_Orderings_Oord(X1)
| ~ class_Rings_Olinordered__idom(tc_fun(X0,X1)) ),
inference(superposition,[status(thm)],[c_230,c_437]) ).
tcf(c_105592,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),X2,c_Groups_Ouminus__class_Ouminus(tc_fun(X0,X1),X2))
| ~ class_Orderings_Oord(X1)
| ~ class_Rings_Olinordered__idom(tc_fun(X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_fun(X0,X1),X2,c_Groups_Ozero__class_Ozero(tc_fun(X0,X1))) ),
inference(superposition,[status(thm)],[c_608,c_437]) ).
tcf(c_105593,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),c_Groups_Ouminus__class_Ouminus(tc_fun(X0,X1),X2),X2)
| ~ class_Orderings_Oord(X1)
| ~ class_Groups_Olinordered__ab__group__add(tc_fun(X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_fun(X0,X1),c_Groups_Ozero__class_Ozero(tc_fun(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_614,c_437]) ).
tcf(c_105677,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(superposition,[status(thm)],[c_1214,c_552]) ).
tcf(c_105678,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),
inference(superposition,[status(thm)],[c_440,c_552]) ).
tcf(c_105679,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
inference(superposition,[status(thm)],[c_551,c_552]) ).
tcf(c_105683,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),
inference(superposition,[status(thm)],[c_90483,c_552]) ).
tcf(c_105800,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)))),
inference(superposition,[status(thm)],[c_552,c_92168]) ).
tcf(c_105801,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))),
inference(superposition,[status(thm)],[c_552,c_91889]) ).
tcf(c_105802,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),X2) ),
inference(superposition,[status(thm)],[c_552,c_387]) ).
tcf(c_105803,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_552,c_384]) ).
tcf(c_105804,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),X2) ),
inference(superposition,[status(thm)],[c_552,c_320]) ).
tcf(c_105805,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))),
inference(superposition,[status(thm)],[c_552,c_1145]) ).
tcf(c_105806,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_552,c_101]) ).
tcf(c_105808,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(superposition,[status(thm)],[c_552,c_165]) ).
tcf(c_105809,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(superposition,[status(thm)],[c_552,c_129]) ).
tcf(c_105810,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))),
inference(superposition,[status(thm)],[c_552,c_331]) ).
tcf(c_105811,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)))),
inference(superposition,[status(thm)],[c_552,c_94661]) ).
tcf(c_105812,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2))) ),
inference(superposition,[status(thm)],[c_552,c_333]) ).
tcf(c_105813,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2))) ),
inference(superposition,[status(thm)],[c_552,c_334]) ).
tcf(c_105814,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(superposition,[status(thm)],[c_552,c_1214]) ).
tcf(c_105815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))) ),
inference(superposition,[status(thm)],[c_552,c_97710]) ).
tcf(c_105816,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))) ),
inference(superposition,[status(thm)],[c_552,c_97670]) ).
tcf(c_105817,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(superposition,[status(thm)],[c_552,c_103646]) ).
tcf(c_105818,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)))),
inference(superposition,[status(thm)],[c_552,c_94758]) ).
tcf(c_105819,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_552,c_91869]) ).
tcf(c_105820,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)))),
inference(superposition,[status(thm)],[c_552,c_491]) ).
tcf(c_105822,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(superposition,[status(thm)],[c_552,c_474]) ).
tcf(c_105823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))) ),
inference(superposition,[status(thm)],[c_552,c_97709]) ).
tcf(c_105824,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))) ),
inference(superposition,[status(thm)],[c_552,c_97669]) ).
tcf(c_105825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_552,c_50530]) ).
tcf(c_105826,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)),
inference(superposition,[status(thm)],[c_552,c_103646]) ).
tcf(c_105827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_552,c_1137]) ).
tcf(c_105830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
inference(superposition,[status(thm)],[c_552,c_470]) ).
tcf(c_105831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
inference(superposition,[status(thm)],[c_552,c_456]) ).
tcf(c_105832,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_552,c_443]) ).
tcf(c_105833,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_552,c_442]) ).
tcf(c_105834,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_552,c_92564]) ).
tcf(c_105835,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_552,c_92563]) ).
tcf(c_105836,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_552,c_92520]) ).
tcf(c_105837,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_552,c_92519]) ).
tcf(c_105838,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_552,c_92433]) ).
tcf(c_105839,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_552,c_92389]) ).
tcf(c_105841,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X1 ) ),
inference(superposition,[status(thm)],[c_552,c_444]) ).
tcf(c_105842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_552,c_464]) ).
tcf(c_105843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_552,c_463]) ).
tcf(c_105844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_552,c_449]) ).
tcf(c_105845,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_552,c_1144]) ).
tcf(c_105847,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) = X1,
inference(superposition,[status(thm)],[c_552,c_1067]) ).
tcf(c_105848,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),
inference(superposition,[status(thm)],[c_552,c_1066]) ).
tcf(c_105849,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(superposition,[status(thm)],[c_552,c_551]) ).
tcf(c_105851,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)),
inference(superposition,[status(thm)],[c_552,c_457]) ).
tcf(c_105857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_552,c_455]) ).
tcf(c_105858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)))),
inference(superposition,[status(thm)],[c_552,c_92431]) ).
tcf(c_105859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ) ),
inference(superposition,[status(thm)],[c_552,c_555]) ).
tcf(c_105860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_552,c_455]) ).
tcf(c_105861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_552,c_633]) ).
tcf(c_105863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = X3 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ) ),
inference(superposition,[status(thm)],[c_552,c_554]) ).
tcf(c_105864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))) ),
inference(superposition,[status(thm)],[c_552,c_470]) ).
tcf(c_105865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))) ),
inference(superposition,[status(thm)],[c_552,c_456]) ).
tcf(c_105866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_552,c_452]) ).
tcf(c_105868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))),
inference(superposition,[status(thm)],[c_552,c_552]) ).
tcf(c_105869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_552,c_1118]) ).
tcf(c_105870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_552,c_452]) ).
tcf(c_105871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,X1,X3)),
inference(superposition,[status(thm)],[c_552,c_92736]) ).
tcf(c_105873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_552,c_92451]) ).
tcf(c_105874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_552,c_92420]) ).
tcf(c_105875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_552,c_92408]) ).
tcf(c_105876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_552,c_92376]) ).
tcf(c_105877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_552,c_632]) ).
tcf(c_105878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_552,c_50489]) ).
tcf(c_105879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_552,c_50325]) ).
tcf(c_105885,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)))),
inference(superposition,[status(thm)],[c_552,c_94874]) ).
tcf(c_105886,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1))),
inference(superposition,[status(thm)],[c_552,c_94684]) ).
tcf(c_105892,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X2)))),
inference(superposition,[status(thm)],[c_552,c_100575]) ).
tcf(c_105893,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X2)))),
inference(superposition,[status(thm)],[c_552,c_94883]) ).
tcf(c_105894,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X2)))),
inference(superposition,[status(thm)],[c_552,c_94882]) ).
tcf(c_105895,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X2))),v_n____),
inference(superposition,[status(thm)],[c_552,c_93168]) ).
tcf(c_105896,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X2)))),
inference(superposition,[status(thm)],[c_552,c_94734]) ).
tcf(c_105897,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X2)))),
inference(superposition,[status(thm)],[c_552,c_92868]) ).
tcf(c_105934,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(light_normalisation,[status(thm)],[c_105817,c_553]) ).
tcf(c_106216,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)),
inference(superposition,[status(thm)],[c_551,c_553]) ).
tcf(c_106218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X3)),
inference(superposition,[status(thm)],[c_552,c_553]) ).
tcf(c_106221,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),
inference(superposition,[status(thm)],[c_90483,c_553]) ).
tcf(c_106223,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(superposition,[status(thm)],[c_553,c_440]) ).
tcf(c_106224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))) ),
inference(superposition,[status(thm)],[c_553,c_97710]) ).
tcf(c_106225,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))) ),
inference(superposition,[status(thm)],[c_553,c_97670]) ).
tcf(c_106226,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))),
inference(superposition,[status(thm)],[c_553,c_103646]) ).
tcf(c_106227,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)))),
inference(superposition,[status(thm)],[c_553,c_94758]) ).
tcf(c_106228,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_553,c_91869]) ).
tcf(c_106229,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)))),
inference(superposition,[status(thm)],[c_553,c_491]) ).
tcf(c_106232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(superposition,[status(thm)],[c_553,c_553]) ).
tcf(c_106233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_553,c_97709]) ).
tcf(c_106234,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_553,c_97669]) ).
tcf(c_106235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_553,c_50530]) ).
tcf(c_106236,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(superposition,[status(thm)],[c_553,c_103646]) ).
tcf(c_106237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_553,c_1137]) ).
tcf(c_106240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X3)) ),
inference(superposition,[status(thm)],[c_553,c_470]) ).
tcf(c_106241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X3)) ),
inference(superposition,[status(thm)],[c_553,c_456]) ).
tcf(c_106242,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_553,c_443]) ).
tcf(c_106243,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_553,c_442]) ).
tcf(c_106244,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_553,c_92564]) ).
tcf(c_106245,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_553,c_92563]) ).
tcf(c_106246,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_553,c_92520]) ).
tcf(c_106247,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_553,c_92519]) ).
tcf(c_106248,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_553,c_92433]) ).
tcf(c_106249,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_553,c_92389]) ).
tcf(c_106250,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))),
inference(superposition,[status(thm)],[c_553,c_94715]) ).
tcf(c_106251,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ) ),
inference(superposition,[status(thm)],[c_553,c_444]) ).
tcf(c_106252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_553,c_464]) ).
tcf(c_106253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_553,c_463]) ).
tcf(c_106254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_553,c_449]) ).
tcf(c_106255,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_553,c_1144]) ).
tcf(c_106256,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))),
inference(superposition,[status(thm)],[c_553,c_492]) ).
tcf(c_106257,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(superposition,[status(thm)],[c_553,c_1067]) ).
tcf(c_106258,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) = X2,
inference(superposition,[status(thm)],[c_553,c_1066]) ).
tcf(c_106260,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(superposition,[status(thm)],[c_553,c_458]) ).
tcf(c_106262,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(superposition,[status(thm)],[c_553,c_651]) ).
tcf(c_106264,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)))),
inference(superposition,[status(thm)],[c_553,c_94661]) ).
tcf(c_106265,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
inference(superposition,[status(thm)],[c_553,c_95861]) ).
tcf(c_106266,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_553,c_94346]) ).
tcf(c_106267,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_553,c_91886]) ).
tcf(c_106268,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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(superposition,[status(thm)],[c_553,c_91290]) ).
tcf(c_106269,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,X0,X1),
inference(superposition,[status(thm)],[c_553,c_91293]) ).
tcf(c_106270,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,X0,X1)),
inference(superposition,[status(thm)],[c_553,c_91292]) ).
tcf(c_106272,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_553,c_91294]) ).
tcf(c_106273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_553,c_455]) ).
tcf(c_106275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X3 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) ) ),
inference(superposition,[status(thm)],[c_553,c_555]) ).
tcf(c_106276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_553,c_455]) ).
tcf(c_106277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(superposition,[status(thm)],[c_553,c_633]) ).
tcf(c_106279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ) ),
inference(superposition,[status(thm)],[c_553,c_554]) ).
tcf(c_106280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))) ),
inference(superposition,[status(thm)],[c_553,c_470]) ).
tcf(c_106281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))) ),
inference(superposition,[status(thm)],[c_553,c_456]) ).
tcf(c_106282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_553,c_452]) ).
tcf(c_106283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))),
inference(superposition,[status(thm)],[c_553,c_92387]) ).
tcf(c_106284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))),
inference(superposition,[status(thm)],[c_553,c_552]) ).
tcf(c_106285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_553,c_1118]) ).
tcf(c_106286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_553,c_452]) ).
tcf(c_106288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,X1,X2)),
inference(superposition,[status(thm)],[c_553,c_92475]) ).
tcf(c_106289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_553,c_92451]) ).
tcf(c_106290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_553,c_92420]) ).
tcf(c_106291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_553,c_92408]) ).
tcf(c_106292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_553,c_92376]) ).
tcf(c_106293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(superposition,[status(thm)],[c_553,c_632]) ).
tcf(c_106294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_553,c_50489]) ).
tcf(c_106295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(superposition,[status(thm)],[c_553,c_50325]) ).
tcf(c_106299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3))),
inference(superposition,[status(thm)],[c_553,c_552]) ).
tcf(c_106301,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))))),
inference(superposition,[status(thm)],[c_553,c_103643]) ).
tcf(c_106302,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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(superposition,[status(thm)],[c_553,c_94656]) ).
tcf(c_106305,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)))),
inference(superposition,[status(thm)],[c_553,c_94879]) ).
tcf(c_106306,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15))),
inference(superposition,[status(thm)],[c_553,c_94663]) ).
tcf(c_106316,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X2)))),
inference(superposition,[status(thm)],[c_553,c_94734]) ).
tcf(c_106322,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,iPr_def_15)))),
inference(superposition,[status(thm)],[c_553,c_94729]) ).
tcf(c_106324,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,iPr_def_15)))),
inference(superposition,[status(thm)],[c_553,c_100576]) ).
tcf(c_106325,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,iPr_def_15)))),
inference(superposition,[status(thm)],[c_553,c_94738]) ).
tcf(c_106326,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,iPr_def_15)))),
inference(superposition,[status(thm)],[c_553,c_94737]) ).
tcf(c_106327,plain,
! [X0: $i,X1: $i,X2: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,iPr_def_15))),v_n____),
inference(superposition,[status(thm)],[c_553,c_93177]) ).
tcf(c_106328,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,iPr_def_15)))),
inference(superposition,[status(thm)],[c_553,c_94729]) ).
tcf(c_106329,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,iPr_def_15)))),
inference(superposition,[status(thm)],[c_553,c_92883]) ).
tcf(c_106330,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)))),
inference(superposition,[status(thm)],[c_553,c_94879]) ).
tcf(c_106331,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)))),
inference(superposition,[status(thm)],[c_553,c_94874]) ).
tcf(c_106332,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,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(superposition,[status(thm)],[c_553,c_94656]) ).
tcf(c_106333,plain,
! [X0: $i,X1: $i,X2: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
inference(superposition,[status(thm)],[c_553,c_95861]) ).
tcf(c_106334,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))))),
inference(superposition,[status(thm)],[c_553,c_103667]) ).
tcf(c_106335,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))))),
inference(superposition,[status(thm)],[c_553,c_103666]) ).
tcf(c_106390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(light_normalisation,[status(thm)],[c_106281,c_105849]) ).
tcf(c_106393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))) ),
inference(light_normalisation,[status(thm)],[c_106280,c_105849]) ).
tcf(c_106396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ) ),
inference(light_normalisation,[status(thm)],[c_106279,c_105849]) ).
tcf(c_106579,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
| ~ class_Groups_Ogroup__add(tc_Int_Oint)
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(superposition,[status(thm)],[c_700,c_561]) ).
tcf(c_106580,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = X2 )
| ~ class_Groups_Ogroup__add(tc_Int_Oint)
| ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) != c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2) ) ),
inference(superposition,[status(thm)],[c_12534,c_561]) ).
tcf(c_106581,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) = X0 )
| ~ class_Groups_Ogroup__add(tc_Int_Oint)
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) != X1 ) ),
inference(superposition,[status(thm)],[c_891,c_561]) ).
tcf(c_106582,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = X2 )
| ~ class_Groups_Ogroup__add(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) != c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2) ) ),
inference(superposition,[status(thm)],[c_16973,c_561]) ).
tcf(c_106583,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = X0 )
| ~ class_Groups_Ogroup__add(tc_Complex_Ocomplex)
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) != X1 ) ),
inference(superposition,[status(thm)],[c_45742,c_561]) ).
tcf(c_106584,plain,
! [X0: $i] :
( ( X0 = iPr_def_20 )
| ~ class_Groups_Ogroup__add(tc_Complex_Ocomplex)
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_90498,c_561]) ).
tcf(c_106585,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1) = X0 )
| ~ class_Groups_Ogroup__add(iPr_def_10)
| ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0) != X1 ) ),
inference(superposition,[status(thm)],[c_91673,c_561]) ).
tcf(c_106586,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(iPr_def_10) = X0 )
| ~ class_Groups_Ogroup__add(iPr_def_10)
| ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0) != c_Groups_Ozero__class_Ozero(iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_91692,c_561]) ).
tcf(c_106587,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X1) = X0 )
| ~ class_Groups_Ogroup__add(tc_HOL_Obool)
| ( c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0) != X1 ) ),
inference(superposition,[status(thm)],[c_91806,c_561]) ).
tcf(c_106588,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = X0 )
| ~ class_Groups_Ogroup__add(tc_Polynomial_Opoly(tc_Int_Oint))
| ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) ) ),
inference(superposition,[status(thm)],[c_97236,c_561]) ).
tcf(c_106589,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)) = X0 )
| ~ class_Groups_Ogroup__add(tc_Polynomial_Opoly(iPr_def_10))
| ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_97239,c_561]) ).
tcf(c_106591,plain,
! [X0: $i] :
( ( X0 = iPr_def_20 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) != iPr_def_20 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106584,c_1458]) ).
tcf(c_106597,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(iPr_def_10) = X0 )
| ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0) != c_Groups_Ozero__class_Ozero(iPr_def_10) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106586,c_90868]) ).
tcf(c_106600,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1) = X0 )
| ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0) != X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106585,c_90868]) ).
tcf(c_106603,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = X0 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) != X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106583,c_1458]) ).
tcf(c_106606,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) = X0 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) != X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106581,c_1373]) ).
tcf(c_106609,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106579,c_1373]) ).
tcf(c_106618,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = X2 )
| ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) != c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106580,c_1373]) ).
tcf(c_106621,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = X2 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) != c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106582,c_1458]) ).
tcf(c_106674,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(iPr_def_10)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_98697,c_159]) ).
tcf(c_106675,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(iPr_def_10)))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_98697,c_159]) ).
tcf(c_106676,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Groups_Oone__class_Oone(iPr_def_10)) = c_Groups_Ozero__class_Ozero(iPr_def_10) )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Groups_Oone__class_Oone(iPr_def_10)))),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Groups_Oone__class_Oone(iPr_def_10))))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Groups_Oone__class_Oone(iPr_def_10))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Groups_Oone__class_Oone(iPr_def_10)))) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Groups_Oone__class_Oone(iPr_def_10))) ) ),
inference(superposition,[status(thm)],[c_98697,c_100956]) ).
tcf(c_106678,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(iPr_def_10)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_subsumption_resolution,[status(thm)],[c_106674,c_1448]) ).
tcf(c_106685,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(iPr_def_10)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_98929,c_159]) ).
tcf(c_106686,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(iPr_def_10)) = c_Groups_Ozero__class_Ozero(iPr_def_10) )
| ( c_Groups_Ominus__class_Ominus(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(iPr_def_10)))),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Divides_Odiv__class_Omod(iPr_def_10,X1,c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(iPr_def_10))))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(iPr_def_10))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(iPr_def_10)))) = c_Divides_Odiv__class_Omod(iPr_def_10,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1),c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(iPr_def_10))) ) ),
inference(superposition,[status(thm)],[c_98929,c_100956]) ).
tcf(c_106687,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(iPr_def_10)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_subsumption_resolution,[status(thm)],[c_106685,c_1448]) ).
tcf(c_106700,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Olinorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20) ),
inference(superposition,[status(thm)],[c_99093,c_245]) ).
tcf(c_106701,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20) ),
inference(superposition,[status(thm)],[c_99093,c_240]) ).
tcf(c_106702,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Oorder(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20) ),
inference(superposition,[status(thm)],[c_99093,c_235]) ).
tcf(c_106724,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Olinorder(tc_Complex_Ocomplex)
| ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20) ),
inference(superposition,[status(thm)],[c_99561,c_240]) ).
tcf(c_106725,plain,
( ~ class_Rings_Olinordered__ring(tc_Complex_Ocomplex)
| ~ class_Orderings_Oorder(tc_Complex_Ocomplex)
| ~ class_Orderings_Olinorder(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),iPr_def_20) ),
inference(superposition,[status(thm)],[c_99561,c_235]) ).
tcf(c_106736,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_99673,c_92168]) ).
tcf(c_106737,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_99673,c_91889]) ).
tcf(c_106738,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_99673,c_387]) ).
tcf(c_106739,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(superposition,[status(thm)],[c_99673,c_384]) ).
tcf(c_106740,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_99673,c_320]) ).
tcf(c_106741,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_99673,c_1145]) ).
tcf(c_106744,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_99673,c_165]) ).
tcf(c_106745,plain,
sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_99673,c_129]) ).
tcf(c_106746,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_99673,c_331]) ).
tcf(c_106748,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(superposition,[status(thm)],[c_99673,c_333]) ).
tcf(c_106749,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(superposition,[status(thm)],[c_99673,c_334]) ).
tcf(c_106752,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_99673,c_103646]) ).
tcf(c_106754,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_99673,c_91869]) ).
tcf(c_106757,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(superposition,[status(thm)],[c_99673,c_553]) ).
tcf(c_106758,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(superposition,[status(thm)],[c_99673,c_97709]) ).
tcf(c_106759,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15) ),
inference(superposition,[status(thm)],[c_99673,c_97669]) ).
tcf(c_106760,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_99673,c_50530]) ).
tcf(c_106761,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_99673,c_103646]) ).
tcf(c_106762,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_99673,c_1137]) ).
tcf(c_106766,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(superposition,[status(thm)],[c_99673,c_456]) ).
tcf(c_106771,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_99673,c_92520]) ).
tcf(c_106776,plain,
sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_99673,c_444]) ).
tcf(c_106780,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_99673,c_1144]) ).
tcf(c_106781,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_99673,c_492]) ).
tcf(c_106782,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_99673,c_1067]) ).
tcf(c_106783,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_99673,c_1066]) ).
tcf(c_106787,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(superposition,[status(thm)],[c_99673,c_455]) ).
tcf(c_106789,plain,
! [X0: $i] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_99673,c_555]) ).
tcf(c_106790,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(superposition,[status(thm)],[c_99673,c_455]) ).
tcf(c_106793,plain,
! [X0: $i] :
( ( sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(superposition,[status(thm)],[c_99673,c_554]) ).
tcf(c_106794,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_99673,c_470]) ).
tcf(c_106795,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_99673,c_456]) ).
tcf(c_106796,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_99673,c_452]) ).
tcf(c_106798,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_99673,c_552]) ).
tcf(c_106799,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_99673,c_1118]) ).
tcf(c_106800,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_99673,c_452]) ).
tcf(c_106805,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(superposition,[status(thm)],[c_99673,c_92408]) ).
tcf(c_106808,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(superposition,[status(thm)],[c_99673,c_50489]) ).
tcf(c_106809,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[status(thm)],[c_99673,c_50325]) ).
tcf(c_106834,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_106759,c_337]) ).
tcf(c_106835,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_106758,c_337]) ).
tcf(c_106854,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,sK9(c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_subsumption_resolution,[status(thm)],[c_106790,c_458]) ).
tcf(c_106865,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(demodulation,[status(thm)],[c_99673,c_106776]) ).
tcf(c_106939,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),X0),X1) ) ),
inference(superposition,[status(thm)],[c_95904,c_90591]) ).
tcf(c_106940,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X2),X1),
inference(superposition,[status(thm)],[c_16698,c_90591]) ).
tcf(c_106941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X3),X2),
inference(superposition,[status(thm)],[c_17554,c_90591]) ).
tcf(c_106942,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(superposition,[status(thm)],[c_17690,c_90591]) ).
tcf(c_106943,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_17614,c_90591]) ).
tcf(c_106944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),X3),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) ) ),
inference(superposition,[status(thm)],[c_100594,c_90591]) ).
tcf(c_106945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),X3),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) ) ),
inference(superposition,[status(thm)],[c_100045,c_90591]) ).
tcf(c_106946,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[status(thm)],[c_17702,c_90591]) ).
tcf(c_106947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),X2)),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17708,c_90591]) ).
tcf(c_106948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2)),X3),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X0)) ) ),
inference(superposition,[status(thm)],[c_96740,c_90591]) ).
tcf(c_106949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),X3),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)) ) ),
inference(superposition,[status(thm)],[c_98303,c_90591]) ).
tcf(c_106950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1))) ) ),
inference(superposition,[status(thm)],[c_92641,c_90591]) ).
tcf(c_106951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = iPr_def_20 )
| ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X1))) ) ),
inference(superposition,[status(thm)],[c_92945,c_90591]) ).
tcf(c_106952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2))),X3),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),X2)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)) ) ),
inference(superposition,[status(thm)],[c_98712,c_90591]) ).
tcf(c_106953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2)),X3),X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X0))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X0)) ) ),
inference(superposition,[status(thm)],[c_97114,c_90591]) ).
tcf(c_106954,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),iPr_def_20) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,iPr_def_20)),
inference(superposition,[status(thm)],[c_90491,c_90591]) ).
tcf(c_106955,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20),X0),X1),
inference(superposition,[status(thm)],[c_90508,c_90591]) ).
tcf(c_106956,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_20 )
| ( c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),X1) ) ),
inference(superposition,[status(thm)],[c_95904,c_90591]) ).
tcf(c_106957,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),X1),
inference(superposition,[status(thm)],[c_16698,c_90591]) ).
tcf(c_106958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3)),X1),
inference(superposition,[status(thm)],[c_17554,c_90591]) ).
tcf(c_106959,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(superposition,[status(thm)],[c_17690,c_90591]) ).
tcf(c_106960,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_17614,c_90591]) ).
tcf(c_106961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X3) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3))) ) ),
inference(superposition,[status(thm)],[c_100594,c_90591]) ).
tcf(c_106962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X3) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X3)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3),X2)) ) ),
inference(superposition,[status(thm)],[c_100045,c_90591]) ).
tcf(c_106963,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17702,c_90591]) ).
tcf(c_106964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1)),X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),X2)),
inference(superposition,[status(thm)],[c_17708,c_90591]) ).
tcf(c_106965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X3)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) ) ),
inference(superposition,[status(thm)],[c_96740,c_90591]) ).
tcf(c_106966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),X3)) ) ),
inference(superposition,[status(thm)],[c_98303,c_90591]) ).
tcf(c_106967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2))),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2))) ) ),
inference(superposition,[status(thm)],[c_92641,c_90591]) ).
tcf(c_106968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = iPr_def_20 )
| ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X2))),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X4),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2))) ) ),
inference(superposition,[status(thm)],[c_92945,c_90591]) ).
tcf(c_106969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X3))),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X2)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),X3)) ) ),
inference(superposition,[status(thm)],[c_98712,c_90591]) ).
tcf(c_106970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = iPr_def_20 )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X3)),X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X1))) ) ),
inference(superposition,[status(thm)],[c_97114,c_90591]) ).
tcf(c_106971,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),iPr_def_20) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,iPr_def_20)),iPr_def_20),
inference(superposition,[status(thm)],[c_90491,c_90591]) ).
tcf(c_106972,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),iPr_def_20) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),iPr_def_20),X1),
inference(superposition,[status(thm)],[c_90508,c_90591]) ).
tcf(c_106973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),X2),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X5),X4)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X5),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X3))),X4),
inference(superposition,[status(thm)],[c_90591,c_16673]) ).
tcf(c_106974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X5),X1),X4)),X3)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X5,X1)),X3)),X4),
inference(superposition,[status(thm)],[c_90591,c_16673]) ).
tcf(c_106975,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X2),X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1),
inference(superposition,[status(thm)],[c_90591,c_95611]) ).
tcf(c_106976,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2),X0),X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)),
inference(superposition,[status(thm)],[c_90591,c_95602]) ).
tcf(c_106977,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),iPr_def_20) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_106971,c_90491,c_90498]) ).
tcf(c_106978,plain,
! [X0: $i,X1: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1)),
inference(light_normalisation,[status(thm)],[c_106955,c_16698,c_90498,c_95427]) ).
tcf(c_106979,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),iPr_def_20) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,iPr_def_20,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,iPr_def_20)),
inference(light_normalisation,[status(thm)],[c_106954,c_90498]) ).
tcf(c_106980,plain,
! [X0: $i,X1: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),
inference(light_normalisation,[status(thm)],[c_106960,c_17614]) ).
tcf(c_106985,plain,
! [X0: $i,X1: $i,X2: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),
inference(light_normalisation,[status(thm)],[c_106957,c_91358]) ).
tcf(c_106986,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X2),X1),
inference(light_normalisation,[status(thm)],[c_106940,c_45742]) ).
tcf(c_106987,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,X1))),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X2,X1))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(light_normalisation,[status(thm)],[c_106959,c_17690]) ).
tcf(c_106988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X3,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X3),X2),
inference(light_normalisation,[status(thm)],[c_106941,c_16973,c_91356]) ).
tcf(c_107083,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ class_Groups_Ogroup__add(tc_Int_Oint)
| ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(superposition,[status(thm)],[c_12534,c_574]) ).
tcf(c_107084,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ class_Groups_Ogroup__add(tc_Int_Oint)
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ),
inference(superposition,[status(thm)],[c_891,c_574]) ).
tcf(c_107085,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Groups_Ogroup__add(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_16973,c_574]) ).
tcf(c_107086,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Groups_Ogroup__add(tc_Complex_Ocomplex)
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0 ) ),
inference(superposition,[status(thm)],[c_45742,c_574]) ).
tcf(c_107088,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0) = c_Groups_Ozero__class_Ozero(iPr_def_10) )
| ~ class_Groups_Ogroup__add(iPr_def_10)
| ( c_Groups_Ozero__class_Ozero(iPr_def_10) != X0 ) ),
inference(superposition,[status(thm)],[c_91673,c_574]) ).
tcf(c_107090,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0) = c_Groups_Ozero__class_Ozero(tc_HOL_Obool) )
| ~ class_Groups_Ogroup__add(tc_HOL_Obool)
| ( c_Groups_Ozero__class_Ozero(tc_HOL_Obool) != X0 ) ),
inference(superposition,[status(thm)],[c_91806,c_574]) ).
tcf(c_107096,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0) = c_Groups_Ozero__class_Ozero(iPr_def_10) )
| ( c_Groups_Ozero__class_Ozero(iPr_def_10) != X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107088,c_90868]) ).
tcf(c_107099,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = iPr_def_20 )
| ~ class_Groups_Ogroup__add(tc_Complex_Ocomplex)
| ( X0 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_107086,c_72176]) ).
tcf(c_107100,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = iPr_def_20 )
| ( X0 != iPr_def_20 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107099,c_1458]) ).
tcf(c_107103,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107084,c_1373]) ).
tcf(c_107106,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107083,c_1373]) ).
tcf(c_107109,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = iPr_def_20 )
| ~ class_Groups_Ogroup__add(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_107085,c_72176]) ).
tcf(c_107110,plain,
! [X0: $i,X1: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = iPr_def_20 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) != iPr_def_20 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107109,c_1458]) ).
tcf(c_107135,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_162,c_577]) ).
tcf(c_107137,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93901,c_577]) ).
tcf(c_107138,plain,
! [X0: $i,X1: $i] :
( 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,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91901,c_577]) ).
tcf(c_107139,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_49961,c_577]) ).
tcf(c_107140,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X1)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_96089,c_577]) ).
tcf(c_107141,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0)))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_344,c_577]) ).
tcf(c_107142,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1)) ),
inference(superposition,[status(thm)],[c_384,c_577]) ).
tcf(c_107144,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2)
| c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_301,c_577]) ).
tcf(c_107145,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_50432,c_577]) ).
tcf(c_107146,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0) ),
inference(superposition,[status(thm)],[c_420,c_577]) ).
tcf(c_107147,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(superposition,[status(thm)],[c_417,c_577]) ).
tcf(c_107148,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_421,c_577]) ).
tcf(c_107149,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97710,c_577]) ).
tcf(c_107150,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97709,c_577]) ).
tcf(c_107151,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X2,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1)))))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Groups_Ozero(X0) ),
inference(superposition,[status(thm)],[c_403,c_577]) ).
tcf(c_107152,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_602,c_577]) ).
tcf(c_107153,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1))))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_606,c_577]) ).
tcf(c_107154,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_103045,c_577]) ).
tcf(c_107155,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_91783,c_577]) ).
tcf(c_107157,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_105035,c_577]) ).
tcf(c_107158,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_661,c_577]) ).
tcf(c_107159,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_660,c_577]) ).
tcf(c_107160,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(superposition,[status(thm)],[c_669,c_577]) ).
tcf(c_107161,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X1)))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1095,c_577]) ).
tcf(c_107162,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_95505,c_577]) ).
tcf(c_107163,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X0),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1)))
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(superposition,[status(thm)],[c_1234,c_577]) ).
tcf(c_107164,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93902,c_577]) ).
tcf(c_107165,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93901,c_577]) ).
tcf(c_107166,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93899,c_577]) ).
tcf(c_107167,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0)) ),
inference(superposition,[status(thm)],[c_92438,c_577]) ).
tcf(c_107168,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0)))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_91110,c_577]) ).
tcf(c_107169,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97717,c_577]) ).
tcf(c_107170,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),iPr_def_15)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92531,c_577]) ).
tcf(c_107171,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92511,c_577]) ).
tcf(c_107172,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_95466,c_577]) ).
tcf(c_107173,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101217,c_577]) ).
tcf(c_107174,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101860,c_577]) ).
tcf(c_107175,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101633,c_577]) ).
tcf(c_107176,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0)))))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_103662,c_577]) ).
tcf(c_107177,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0)))))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_104103,c_577]) ).
tcf(c_107178,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_700,c_577]) ).
tcf(c_107179,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)) ),
inference(superposition,[status(thm)],[c_12534,c_577]) ).
tcf(c_107180,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_891,c_577]) ).
tcf(c_107181,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))) ),
inference(superposition,[status(thm)],[c_16973,c_577]) ).
tcf(c_107182,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,X1) ),
inference(superposition,[status(thm)],[c_45742,c_577]) ).
tcf(c_107183,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,iPr_def_20) ),
inference(superposition,[status(thm)],[c_90498,c_577]) ).
tcf(c_107184,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless__eq(iPr_def_10,X0,X1) ),
inference(superposition,[status(thm)],[c_91673,c_577]) ).
tcf(c_107185,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless__eq(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_91692,c_577]) ).
tcf(c_107186,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X1),c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X0,X1) ),
inference(superposition,[status(thm)],[c_91806,c_577]) ).
tcf(c_107187,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Int_Oint),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_97236,c_577]) ).
tcf(c_107188,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(iPr_def_10))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(iPr_def_10),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_97239,c_577]) ).
tcf(c_107191,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_107159,c_891]) ).
tcf(c_107200,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,X0,X0)
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(light_normalisation,[status(thm)],[c_107168,c_91673]) ).
tcf(c_107230,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_subsumption_resolution,[status(thm)],[c_107172,c_1348]) ).
tcf(c_107237,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107158,c_1348]) ).
tcf(c_107240,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107157,c_1348]) ).
tcf(c_107261,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107180,c_1348]) ).
tcf(c_107264,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107178,c_1348]) ).
tcf(c_107292,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_107155,c_700]) ).
tcf(c_107293,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107292,c_1348]) ).
tcf(c_107296,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_107154,c_700]) ).
tcf(c_107297,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107296,c_1348]) ).
tcf(c_107318,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107160,c_1348]) ).
tcf(c_107330,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107179,c_1348]) ).
tcf(c_107444,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93901,c_579]) ).
tcf(c_107445,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91901,c_579]) ).
tcf(c_107446,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X1)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_49961,c_579]) ).
tcf(c_107448,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0)),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_344,c_579]) ).
tcf(c_107450,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_301,c_579]) ).
tcf(c_107451,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_50432,c_579]) ).
tcf(c_107452,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0) ),
inference(superposition,[status(thm)],[c_420,c_579]) ).
tcf(c_107453,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(superposition,[status(thm)],[c_417,c_579]) ).
tcf(c_107455,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X2),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1),X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97710,c_579]) ).
tcf(c_107456,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X2),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1)))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97709,c_579]) ).
tcf(c_107457,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X2)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92451,c_579]) ).
tcf(c_107458,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X2)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92408,c_579]) ).
tcf(c_107459,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X2)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_50489,c_579]) ).
tcf(c_107460,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),X2)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_50325,c_579]) ).
tcf(c_107461,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),X1)),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_651,c_579]) ).
tcf(c_107462,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1))),X1)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_474,c_579]) ).
tcf(c_107463,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1))),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_602,c_579]) ).
tcf(c_107464,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(superposition,[status(thm)],[c_606,c_579]) ).
tcf(c_107466,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_105035,c_579]) ).
tcf(c_107468,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_660,c_579]) ).
tcf(c_107469,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0)),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0)))),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_910,c_579]) ).
tcf(c_107470,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0)),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0))),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_911,c_579]) ).
tcf(c_107471,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_103045,c_579]) ).
tcf(c_107472,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_91750,c_579]) ).
tcf(c_107473,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X0),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),X1)),X1)
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(superposition,[status(thm)],[c_1234,c_579]) ).
tcf(c_107474,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) ),
inference(superposition,[status(thm)],[c_1251,c_579]) ).
tcf(c_107475,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0)),X0)
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ class_Rings_Olinordered__idom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_91110,c_579]) ).
tcf(c_107476,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_91175,c_579]) ).
tcf(c_107477,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_91377,c_579]) ).
tcf(c_107478,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92531,c_579]) ).
tcf(c_107479,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91905,c_579]) ).
tcf(c_107480,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1),X2))),X1)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92387,c_579]) ).
tcf(c_107481,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X2)))),X2)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_92431,c_579]) ).
tcf(c_107482,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_93019,c_579]) ).
tcf(c_107483,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_93191,c_579]) ).
tcf(c_107485,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101217,c_579]) ).
tcf(c_107486,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),v_n____)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_102263,c_579]) ).
tcf(c_107487,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),v_n____)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101691,c_579]) ).
tcf(c_107488,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101857,c_579]) ).
tcf(c_107489,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101860,c_579]) ).
tcf(c_107490,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101633,c_579]) ).
tcf(c_107491,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1),X0))),X1)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_103643,c_579]) ).
tcf(c_107492,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_700,c_579]) ).
tcf(c_107493,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_12534,c_579]) ).
tcf(c_107495,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2) ),
inference(superposition,[status(thm)],[c_16973,c_579]) ).
tcf(c_107497,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),iPr_def_20)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,X0) ),
inference(superposition,[status(thm)],[c_90498,c_579]) ).
tcf(c_107499,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),c_Groups_Ozero__class_Ozero(iPr_def_10))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_91692,c_579]) ).
tcf(c_107501,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),X0) ),
inference(superposition,[status(thm)],[c_97236,c_579]) ).
tcf(c_107502,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)))
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(iPr_def_10))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_97239,c_579]) ).
tcf(c_107503,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))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_107483,c_700]) ).
tcf(c_107549,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_107477,c_1348]) ).
tcf(c_107550,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_107476,c_1348]) ).
tcf(c_107551,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107466,c_1348]) ).
tcf(c_107560,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),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),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107492,c_1348]) ).
tcf(c_107575,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107472,c_1348]) ).
tcf(c_107578,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107471,c_1348]) ).
tcf(c_107612,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107474,c_1348]) ).
tcf(c_107621,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107493,c_1348]) ).
tcf(c_107738,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_93901,c_581]) ).
tcf(c_107739,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_91901,c_581]) ).
tcf(c_107740,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_49961,c_581]) ).
tcf(c_107741,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X0),c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_96089,c_581]) ).
tcf(c_107744,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_301,c_581]) ).
tcf(c_107745,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_50432,c_581]) ).
tcf(c_107746,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0) ),
inference(superposition,[status(thm)],[c_420,c_581]) ).
tcf(c_107747,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(superposition,[status(thm)],[c_417,c_581]) ).
tcf(c_107748,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_421,c_581]) ).
tcf(c_107749,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1),X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97710,c_581]) ).
tcf(c_107750,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,X1)))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_97709,c_581]) ).
tcf(c_107751,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_602,c_581]) ).
tcf(c_107752,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_606,c_581]) ).
tcf(c_107754,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_105035,c_581]) ).
tcf(c_107755,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_661,c_581]) ).
tcf(c_107759,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101217,c_581]) ).
tcf(c_107760,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101860,c_581]) ).
tcf(c_107761,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101633,c_581]) ).
tcf(c_107762,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(superposition,[status(thm)],[c_700,c_581]) ).
tcf(c_107763,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) ),
inference(superposition,[status(thm)],[c_12534,c_581]) ).
tcf(c_107764,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(superposition,[status(thm)],[c_891,c_581]) ).
tcf(c_107765,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)) ),
inference(superposition,[status(thm)],[c_16973,c_581]) ).
tcf(c_107766,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) ),
inference(superposition,[status(thm)],[c_45742,c_581]) ).
tcf(c_107767,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,iPr_def_20)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
inference(superposition,[status(thm)],[c_90498,c_581]) ).
tcf(c_107768,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,X1,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless__eq(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1)) ),
inference(superposition,[status(thm)],[c_91673,c_581]) ).
tcf(c_107769,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(iPr_def_10))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_91692,c_581]) ).
tcf(c_107770,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X1,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X0,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X1)) ),
inference(superposition,[status(thm)],[c_91806,c_581]) ).
tcf(c_107771,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Int_Oint),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),X0)) ),
inference(superposition,[status(thm)],[c_97236,c_581]) ).
tcf(c_107772,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(iPr_def_10),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)))
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(iPr_def_10))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),X0)) ),
inference(superposition,[status(thm)],[c_97239,c_581]) ).
tcf(c_107773,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_700,c_581]) ).
tcf(c_107774,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)) ),
inference(superposition,[status(thm)],[c_12534,c_581]) ).
tcf(c_107775,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) ),
inference(superposition,[status(thm)],[c_891,c_581]) ).
tcf(c_107776,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))) ),
inference(superposition,[status(thm)],[c_16973,c_581]) ).
tcf(c_107777,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1) ),
inference(superposition,[status(thm)],[c_45742,c_581]) ).
tcf(c_107778,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),iPr_def_20) ),
inference(superposition,[status(thm)],[c_90498,c_581]) ).
tcf(c_107779,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1),X0)
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_91673,c_581]) ).
tcf(c_107780,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0)
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless__eq(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_91692,c_581]) ).
tcf(c_107781,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X1),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0),X1) ),
inference(superposition,[status(thm)],[c_91806,c_581]) ).
tcf(c_107782,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_97236,c_581]) ).
tcf(c_107783,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(iPr_def_10))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_97239,c_581]) ).
tcf(c_107814,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107755,c_1348]) ).
tcf(c_107817,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107754,c_1348]) ).
tcf(c_107838,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107775,c_1348]) ).
tcf(c_107841,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107773,c_1348]) ).
tcf(c_107856,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107764,c_1348]) ).
tcf(c_107859,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,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_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107762,c_1348]) ).
tcf(c_107890,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107774,c_1348]) ).
tcf(c_107899,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107763,c_1348]) ).
tcf(c_108016,plain,
~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat),
inference(superposition,[status(thm)],[c_107135,c_91292]) ).
tcf(c_108032,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
inference(superposition,[status(thm)],[c_12534,c_582]) ).
tcf(c_108034,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) ),
inference(superposition,[status(thm)],[c_16973,c_582]) ).
tcf(c_108043,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_12534,c_582]) ).
tcf(c_108045,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2) ),
inference(superposition,[status(thm)],[c_16973,c_582]) ).
tcf(c_108054,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = c_Groups_Ouminus__class_Ouminus(X0,X2) )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_582,c_294]) ).
tcf(c_108055,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),c_Groups_Ouminus__class_Ouminus(X0,X1))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_582,c_291]) ).
tcf(c_108056,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = c_Groups_Ouminus__class_Ouminus(X0,X2) )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_582,c_285]) ).
tcf(c_108057,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) ),
inference(superposition,[status(thm)],[c_582,c_300]) ).
tcf(c_108058,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) ),
inference(superposition,[status(thm)],[c_582,c_293]) ).
tcf(c_108059,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X2)))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_582,c_577]) ).
tcf(c_108060,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)),X2)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_582,c_579]) ).
tcf(c_108062,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_582,c_603]) ).
tcf(c_108063,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_582,c_607]) ).
tcf(c_108064,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) )
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(superposition,[status(thm)],[c_582,c_672]) ).
tcf(c_108065,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(superposition,[status(thm)],[c_582,c_671]) ).
tcf(c_108066,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) )
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_582,c_662]) ).
tcf(c_108089,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108065,c_1348]) ).
tcf(c_108093,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108043,c_1348]) ).
tcf(c_108096,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108032,c_1348]) ).
tcf(c_108099,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108066,c_1348]) ).
tcf(c_108103,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108064,c_1348]) ).
tcf(c_108145,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2)
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X2 )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_250,c_584]) ).
tcf(c_108146,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X2))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X2)
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X2 )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Rings_Olinordered__idom(X0) ),
inference(superposition,[status(thm)],[c_230,c_584]) ).
tcf(c_108154,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_608,c_584]) ).
tcf(c_108155,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1))))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_614,c_584]) ).
tcf(c_108156,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_91757,c_584]) ).
tcf(c_108157,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X1 )
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_697,c_584]) ).
tcf(c_108161,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_95465,c_584]) ).
tcf(c_108162,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_96923,c_584]) ).
tcf(c_108163,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Ominus__class_Ominus(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),c_Groups_Oone__class_Oone(iPr_def_10))))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_96963,c_584]) ).
tcf(c_108164,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_700,c_584]) ).
tcf(c_108165,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)) ),
inference(superposition,[status(thm)],[c_12534,c_584]) ).
tcf(c_108166,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_891,c_584]) ).
tcf(c_108167,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))) ),
inference(superposition,[status(thm)],[c_16973,c_584]) ).
tcf(c_108168,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,X1) ),
inference(superposition,[status(thm)],[c_45742,c_584]) ).
tcf(c_108169,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,iPr_def_20) ),
inference(superposition,[status(thm)],[c_90498,c_584]) ).
tcf(c_108170,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,X0,X1) ),
inference(superposition,[status(thm)],[c_91673,c_584]) ).
tcf(c_108171,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_91692,c_584]) ).
tcf(c_108172,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X1),c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,X0,X1) ),
inference(superposition,[status(thm)],[c_91806,c_584]) ).
tcf(c_108173,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(tc_Int_Oint),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_97236,c_584]) ).
tcf(c_108174,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(iPr_def_10))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(iPr_def_10),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_97239,c_584]) ).
tcf(c_108178,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_subsumption_resolution,[status(thm)],[c_108161,c_1348]) ).
tcf(c_108191,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108166,c_1348]) ).
tcf(c_108194,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108164,c_1348]) ).
tcf(c_108197,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_108156,c_700]) ).
tcf(c_108198,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108197,c_1348]) ).
tcf(c_108211,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108157,c_1348]) ).
tcf(c_108221,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108165,c_1348]) ).
tcf(c_108265,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Oplus__class_Oplus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Oone__class_Oone(X0))),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(superposition,[status(thm)],[c_227,c_586]) ).
tcf(c_108268,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ouminus__class_Ouminus(X0,X1))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),X1)
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X2 )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_250,c_586]) ).
tcf(c_108269,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ouminus__class_Ouminus(X0,X1))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),X1)
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = X2 )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Rings_Olinordered__idom(X0) ),
inference(superposition,[status(thm)],[c_230,c_586]) ).
tcf(c_108277,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1))),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_608,c_586]) ).
tcf(c_108278,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(superposition,[status(thm)],[c_614,c_586]) ).
tcf(c_108279,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X1 )
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_697,c_586]) ).
tcf(c_108281,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) ),
inference(superposition,[status(thm)],[c_665,c_586]) ).
tcf(c_108282,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_695,c_586]) ).
tcf(c_108284,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_91757,c_586]) ).
tcf(c_108286,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_91378,c_586]) ).
tcf(c_108293,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_93018,c_586]) ).
tcf(c_108294,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_93182,c_586]) ).
tcf(c_108296,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,iPr_def_20),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_94038,c_586]) ).
tcf(c_108297,plain,
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10)),c_Groups_Oone__class_Oone(iPr_def_10))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94092,c_586]) ).
tcf(c_108298,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm)],[c_94256,c_586]) ).
tcf(c_108299,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,c_Groups_Oplus__class_Oplus(iPr_def_10,c_Groups_Oone__class_Oone(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0))),X0)
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94279,c_586]) ).
tcf(c_108316,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_700,c_586]) ).
tcf(c_108317,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_12534,c_586]) ).
tcf(c_108319,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),X2) ),
inference(superposition,[status(thm)],[c_16973,c_586]) ).
tcf(c_108321,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),iPr_def_20)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,X0) ),
inference(superposition,[status(thm)],[c_90498,c_586]) ).
tcf(c_108323,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),c_Groups_Ozero__class_Ozero(iPr_def_10))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_91692,c_586]) ).
tcf(c_108325,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),X0) ),
inference(superposition,[status(thm)],[c_97236,c_586]) ).
tcf(c_108326,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)))
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(iPr_def_10))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_97239,c_586]) ).
tcf(c_108327,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))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(light_normalisation,[status(thm)],[c_108294,c_700]) ).
tcf(c_108328,plain,
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ class_Rings_Olinordered__semidom(tc_Complex_Ocomplex) ),
inference(light_normalisation,[status(thm)],[c_108296,c_90498]) ).
tcf(c_108336,plain,
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Oone__class_Oone(iPr_def_10))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ class_Rings_Olinordered__semidom(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_108297,c_91692]) ).
tcf(c_108340,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_108286,c_1348]) ).
tcf(c_108341,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_108282,c_1348]) ).
tcf(c_108346,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108284,c_1348]) ).
tcf(c_108362,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108281,c_1348]) ).
tcf(c_108365,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108279,c_1348]) ).
tcf(c_108375,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108317,c_1348]) ).
tcf(c_108414,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
inference(superposition,[status(thm)],[c_12534,c_587]) ).
tcf(c_108415,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(superposition,[status(thm)],[c_891,c_587]) ).
tcf(c_108416,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) ),
inference(superposition,[status(thm)],[c_16973,c_587]) ).
tcf(c_108417,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) ),
inference(superposition,[status(thm)],[c_45742,c_587]) ).
tcf(c_108419,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,X1,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,X0,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1)) ),
inference(superposition,[status(thm)],[c_91673,c_587]) ).
tcf(c_108421,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_HOL_Obool,X1,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,X0,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X1)) ),
inference(superposition,[status(thm)],[c_91806,c_587]) ).
tcf(c_108425,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_12534,c_587]) ).
tcf(c_108426,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) ),
inference(superposition,[status(thm)],[c_891,c_587]) ).
tcf(c_108427,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2) ),
inference(superposition,[status(thm)],[c_16973,c_587]) ).
tcf(c_108428,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1) ),
inference(superposition,[status(thm)],[c_45742,c_587]) ).
tcf(c_108430,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X1),X0)
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_91673,c_587]) ).
tcf(c_108432,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X1),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0),X1) ),
inference(superposition,[status(thm)],[c_91806,c_587]) ).
tcf(c_108439,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) ),
inference(superposition,[status(thm)],[c_587,c_245]) ).
tcf(c_108440,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) ),
inference(superposition,[status(thm)],[c_587,c_240]) ).
tcf(c_108441,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2)) ),
inference(superposition,[status(thm)],[c_587,c_235]) ).
tcf(c_108442,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_587,c_295]) ).
tcf(c_108443,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_587,c_292]) ).
tcf(c_108448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X1),c_Groups_Ouminus__class_Ouminus(tc_fun(X0,X1),X3),c_Groups_Ouminus__class_Ouminus(tc_fun(X0,X1),X2))
| ~ class_Orderings_Oord(X1)
| ~ class_Groups_Oordered__ab__group__add(tc_fun(X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_fun(X0,X1),X2,X3) ),
inference(superposition,[status(thm)],[c_587,c_437]) ).
tcf(c_108449,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X2)))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_587,c_584]) ).
tcf(c_108450,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)),X2)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_587,c_586]) ).
tcf(c_108451,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_587,c_609]) ).
tcf(c_108452,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_587,c_615]) ).
tcf(c_108453,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(superposition,[status(thm)],[c_587,c_663]) ).
tcf(c_108457,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108453,c_1348]) ).
tcf(c_108475,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108426,c_1348]) ).
tcf(c_108487,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108415,c_1348]) ).
tcf(c_108518,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108425,c_1348]) ).
tcf(c_108521,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108414,c_1348]) ).
tcf(c_108557,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15) ),
inference(light_normalisation,[status(thm)],[c_99839,c_100506]) ).
tcf(c_108564,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0)) = v_n____ )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_1136,c_108557]) ).
tcf(c_108565,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____)
| ( X0 = v_n____ )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_256,c_108557]) ).
tcf(c_108567,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____),iPr_def_15),
inference(superposition,[status(thm)],[c_331,c_108557]) ).
tcf(c_108568,plain,
( ~ class_Rings_Olinordered__semidom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15) ),
inference(superposition,[status(thm)],[c_227,c_108557]) ).
tcf(c_108571,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____)
| ( X0 = v_n____ )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_250,c_108557]) ).
tcf(c_108572,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____)
| ( X0 = v_n____ )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_230,c_108557]) ).
tcf(c_108573,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),iPr_def_15) ),
inference(superposition,[status(thm)],[c_334,c_108557]) ).
tcf(c_108574,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_633,c_108557]) ).
tcf(c_108575,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,v_n____)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_92420,c_108557]) ).
tcf(c_108576,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_92376,c_108557]) ).
tcf(c_108577,plain,
! [X0: $i,X1: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_632,c_108557]) ).
tcf(c_108578,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0)),iPr_def_15),
inference(superposition,[status(thm)],[c_492,c_108557]) ).
tcf(c_108579,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,v_n____)),iPr_def_15),
inference(superposition,[status(thm)],[c_491,c_108557]) ).
tcf(c_108580,plain,
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),iPr_def_15) ),
inference(superposition,[status(thm)],[c_608,c_108557]) ).
tcf(c_108582,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),iPr_def_15),
inference(superposition,[status(thm)],[c_91294,c_108557]) ).
tcf(c_108585,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,v_n____),iPr_def_15) ),
inference(superposition,[status(thm)],[c_97710,c_108557]) ).
tcf(c_108586,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,v_n____),iPr_def_15) ),
inference(superposition,[status(thm)],[c_97670,c_108557]) ).
tcf(c_108587,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0),iPr_def_15) ),
inference(superposition,[status(thm)],[c_97709,c_108557]) ).
tcf(c_108588,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0),iPr_def_15) ),
inference(superposition,[status(thm)],[c_97669,c_108557]) ).
tcf(c_108589,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,v_n____)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,iPr_def_15) ),
inference(superposition,[status(thm)],[c_100509,c_108557]) ).
tcf(c_108590,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____)),iPr_def_15),
inference(superposition,[status(thm)],[c_92168,c_108557]) ).
tcf(c_108591,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_92433,c_108557]) ).
tcf(c_108592,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_92389,c_108557]) ).
tcf(c_108593,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0),iPr_def_15),
inference(superposition,[status(thm)],[c_98277,c_108557]) ).
tcf(c_108594,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15),iPr_def_15),
inference(superposition,[status(thm)],[c_98253,c_108557]) ).
tcf(c_108595,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),iPr_def_15),iPr_def_15),iPr_def_15),
inference(superposition,[status(thm)],[c_100571,c_108557]) ).
tcf(c_108596,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),iPr_def_15),
inference(superposition,[status(thm)],[c_94656,c_108557]) ).
tcf(c_108597,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),iPr_def_15),
inference(superposition,[status(thm)],[c_94661,c_108557]) ).
tcf(c_108598,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,iPr_def_15),iPr_def_15),
inference(superposition,[status(thm)],[c_94663,c_108557]) ).
tcf(c_108599,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,v_n____),iPr_def_15),
inference(superposition,[status(thm)],[c_94684,c_108557]) ).
tcf(c_108600,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X0)),iPr_def_15),
inference(superposition,[status(thm)],[c_94715,c_108557]) ).
tcf(c_108601,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,iPr_def_15)),iPr_def_15),
inference(superposition,[status(thm)],[c_94729,c_108557]) ).
tcf(c_108602,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X0)),iPr_def_15),
inference(superposition,[status(thm)],[c_94734,c_108557]) ).
tcf(c_108603,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,v_n____)),iPr_def_15),
inference(superposition,[status(thm)],[c_94758,c_108557]) ).
tcf(c_108604,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,v_n____)),iPr_def_15),
inference(superposition,[status(thm)],[c_94874,c_108557]) ).
tcf(c_108605,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,iPr_def_15)),iPr_def_15),
inference(superposition,[status(thm)],[c_94879,c_108557]) ).
tcf(c_108606,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),iPr_def_15),
inference(superposition,[status(thm)],[c_95861,c_108557]) ).
tcf(c_108607,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,X1)),iPr_def_15),
inference(superposition,[status(thm)],[c_100575,c_108557]) ).
tcf(c_108608,plain,
! [X0: $i,X1: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,iPr_def_15)),iPr_def_15),
inference(superposition,[status(thm)],[c_100576,c_108557]) ).
tcf(c_108609,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0)),iPr_def_15),
inference(superposition,[status(thm)],[c_103666,c_108557]) ).
tcf(c_108630,plain,
( ~ class_Rings_Olinordered__semidom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,iPr_def_15) ),
inference(light_normalisation,[status(thm)],[c_108568,c_90483]) ).
tcf(c_108687,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_552,c_100568]) ).
tcf(c_108689,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_553,c_100568]) ).
tcf(c_108697,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_100568,c_235]) ).
tcf(c_108701,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_100568,c_108557]) ).
tcf(c_108702,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_100568,c_100844]) ).
tcf(c_108740,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_552,c_100832]) ).
tcf(c_108742,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,iPr_def_15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_553,c_100832]) ).
tcf(c_108750,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_100832,c_235]) ).
tcf(c_108754,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_100832,c_108557]) ).
tcf(c_108755,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_100832,c_100844]) ).
tcf(c_108769,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_1214,c_100862]) ).
tcf(c_108770,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____) ),
inference(superposition,[status(thm)],[c_440,c_100862]) ).
tcf(c_108773,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_552,c_100862]) ).
tcf(c_108775,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))) ),
inference(superposition,[status(thm)],[c_553,c_100862]) ).
tcf(c_108776,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____) ),
inference(superposition,[status(thm)],[c_90483,c_100862]) ).
tcf(c_108779,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,v_n____)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_100862,c_291]) ).
tcf(c_108780,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,v_n____)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = iPr_def_15 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_100862,c_285]) ).
tcf(c_108781,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,v_n____)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_100862,c_300]) ).
tcf(c_108782,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,v_n____)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_100862,c_293]) ).
tcf(c_108783,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X0),X1) ),
inference(superposition,[status(thm)],[c_100862,c_1118]) ).
tcf(c_108784,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,v_n____)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_100862,c_100811]) ).
tcf(c_108785,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(superposition,[status(thm)],[c_100862,c_92394]) ).
tcf(c_108800,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,v_n____)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = iPr_def_15 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108780,c_1414]) ).
tcf(c_108804,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,v_n____)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),iPr_def_15) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108779,c_1413]) ).
tcf(c_108820,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_108769,c_49959]) ).
tcf(c_108821,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_108769,c_164]) ).
tcf(c_108823,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_108769,c_291]) ).
tcf(c_108824,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____)
| ( X0 = iPr_def_15 )
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_108769,c_285]) ).
tcf(c_108825,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_108769,c_300]) ).
tcf(c_108826,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_108769,c_293]) ).
tcf(c_108827,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,iPr_def_15,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_108769,c_1118]) ).
tcf(c_108829,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),v_n____)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_108769,c_603]) ).
tcf(c_108831,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_108769,c_100811]) ).
tcf(c_108832,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____) ),
inference(superposition,[status(thm)],[c_108769,c_92394]) ).
tcf(c_108838,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_108769,c_291]) ).
tcf(c_108840,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0) ),
inference(superposition,[status(thm)],[c_108769,c_300]) ).
tcf(c_108841,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,X0) ),
inference(superposition,[status(thm)],[c_108769,c_293]) ).
tcf(c_108842,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X1)) ),
inference(superposition,[status(thm)],[c_108769,c_50530]) ).
tcf(c_108846,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_108769,c_607]) ).
tcf(c_108847,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,X1)) ),
inference(superposition,[status(thm)],[c_108769,c_1119]) ).
tcf(c_108852,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,v_n____) ),
inference(superposition,[status(thm)],[c_108769,c_92394]) ).
tcf(c_108867,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),v_n____)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108829,c_92941]) ).
tcf(c_108872,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108838,c_1413]) ).
tcf(c_108876,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____)
| ( X0 = iPr_def_15 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108824,c_1414]) ).
tcf(c_108880,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108823,c_1413]) ).
tcf(c_108907,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X1)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = c_Groups_Ouminus__class_Ouminus(X0,X2) )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_250,c_588]) ).
tcf(c_108908,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X2,X1)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X2),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = c_Groups_Ouminus__class_Ouminus(X0,X2) )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Rings_Olinordered__idom(X0) ),
inference(superposition,[status(thm)],[c_230,c_588]) ).
tcf(c_108909,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X2)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = c_Groups_Ouminus__class_Ouminus(X0,X2) )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_250,c_588]) ).
tcf(c_108910,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,X2)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ouminus__class_Ouminus(X0,X2))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = c_Groups_Ouminus__class_Ouminus(X0,X2) )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Rings_Olinordered__idom(X0) ),
inference(superposition,[status(thm)],[c_230,c_588]) ).
tcf(c_108912,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_608,c_588]) ).
tcf(c_108913,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Groups_Olinordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_614,c_588]) ).
tcf(c_108914,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) )
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_697,c_588]) ).
tcf(c_108915,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) )
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_697,c_588]) ).
tcf(c_108916,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(superposition,[status(thm)],[c_700,c_588]) ).
tcf(c_108917,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) ),
inference(superposition,[status(thm)],[c_12534,c_588]) ).
tcf(c_108919,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)) ),
inference(superposition,[status(thm)],[c_16973,c_588]) ).
tcf(c_108921,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,X0,iPr_def_20)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
inference(superposition,[status(thm)],[c_90498,c_588]) ).
tcf(c_108923,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,X0,c_Groups_Ozero__class_Ozero(iPr_def_10))
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_91692,c_588]) ).
tcf(c_108925,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(tc_Int_Oint),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),X0)) ),
inference(superposition,[status(thm)],[c_97236,c_588]) ).
tcf(c_108926,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(iPr_def_10),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)))
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(iPr_def_10))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),X0)) ),
inference(superposition,[status(thm)],[c_97239,c_588]) ).
tcf(c_108927,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_700,c_588]) ).
tcf(c_108928,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)) ),
inference(superposition,[status(thm)],[c_12534,c_588]) ).
tcf(c_108930,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2))) ),
inference(superposition,[status(thm)],[c_16973,c_588]) ).
tcf(c_108932,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,iPr_def_20,X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),iPr_def_20) ),
inference(superposition,[status(thm)],[c_90498,c_588]) ).
tcf(c_108934,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ozero__class_Ozero(iPr_def_10),X0)
| ~ class_Groups_Oordered__ab__group__add(iPr_def_10)
| ~ c_Orderings_Oord__class_Oless(iPr_def_10,c_Groups_Ouminus__class_Ouminus(iPr_def_10,X0),c_Groups_Ozero__class_Ozero(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_91692,c_588]) ).
tcf(c_108936,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) ),
inference(superposition,[status(thm)],[c_97236,c_588]) ).
tcf(c_108937,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10)),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(iPr_def_10))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(iPr_def_10),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(iPr_def_10),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_97239,c_588]) ).
tcf(c_108951,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108916,c_1348]) ).
tcf(c_108968,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108928,c_1348]) ).
tcf(c_108977,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108917,c_1348]) ).
tcf(c_108980,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108915,c_1348]) ).
tcf(c_108984,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108914,c_1348]) ).
tcf(c_109054,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_72176,c_600]) ).
tcf(c_109056,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_12534,c_600]) ).
tcf(c_109058,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_16973,c_600]) ).
tcf(c_109059,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_45742,c_600]) ).
tcf(c_109060,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),iPr_def_20)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_90498,c_600]) ).
tcf(c_109063,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0),c_Groups_Ozero__class_Ozero(tc_HOL_Obool)) ),
inference(superposition,[status(thm)],[c_91806,c_600]) ).
tcf(c_109067,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_600,c_294]) ).
tcf(c_109068,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_600,c_291]) ).
tcf(c_109069,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_600,c_285]) ).
tcf(c_109070,plain,
! [X0: $i,X1: $i] :
( ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_600,c_300]) ).
tcf(c_109071,plain,
! [X0: $i,X1: $i] :
( ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_600,c_293]) ).
tcf(c_109072,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0)))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0)) ),
inference(superposition,[status(thm)],[c_600,c_577]) ).
tcf(c_109074,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_600,c_672]) ).
tcf(c_109075,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(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,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_600,c_671]) ).
tcf(c_109076,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_600,c_662]) ).
tcf(c_109095,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ 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,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109075,c_1348]) ).
tcf(c_109099,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109056,c_1348]) ).
tcf(c_109102,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109076,c_1348]) ).
tcf(c_109106,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109074,c_1348]) ).
tcf(c_109125,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),iPr_def_20) ),
inference(light_normalisation,[status(thm)],[c_109058,c_72176]) ).
tcf(c_109159,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_301,c_601]) ).
tcf(c_109160,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_421,c_601]) ).
tcf(c_109168,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_105035,c_601]) ).
tcf(c_109169,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_661,c_601]) ).
tcf(c_109170,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
inference(superposition,[status(thm)],[c_72176,c_601]) ).
tcf(c_109172,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)) ),
inference(superposition,[status(thm)],[c_12534,c_601]) ).
tcf(c_109174,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) ),
inference(superposition,[status(thm)],[c_16973,c_601]) ).
tcf(c_109175,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) ),
inference(superposition,[status(thm)],[c_45742,c_601]) ).
tcf(c_109176,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),iPr_def_20) ),
inference(superposition,[status(thm)],[c_90498,c_601]) ).
tcf(c_109179,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0),c_Groups_Ozero__class_Ozero(tc_HOL_Obool))
| ~ class_Groups_Oordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),X0) ),
inference(superposition,[status(thm)],[c_91806,c_601]) ).
tcf(c_109184,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109169,c_1348]) ).
tcf(c_109187,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109168,c_1348]) ).
tcf(c_109202,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,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_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109172,c_1348]) ).
tcf(c_109205,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),iPr_def_20)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))) ),
inference(light_normalisation,[status(thm)],[c_109174,c_72176]) ).
tcf(c_109232,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ 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,X0,X1)) ),
inference(superposition,[status(thm)],[c_12534,c_604]) ).
tcf(c_109234,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) ),
inference(superposition,[status(thm)],[c_16973,c_604]) ).
tcf(c_109235,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
inference(superposition,[status(thm)],[c_45742,c_604]) ).
tcf(c_109239,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X0,c_Groups_Ozero__class_Ozero(tc_HOL_Obool))
| ~ class_Groups_Oordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) ),
inference(superposition,[status(thm)],[c_91806,c_604]) ).
tcf(c_109242,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),iPr_def_20)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) ),
inference(superposition,[status(thm)],[c_72176,c_604]) ).
tcf(c_109245,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(superposition,[status(thm)],[c_604,c_294]) ).
tcf(c_109246,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(superposition,[status(thm)],[c_604,c_291]) ).
tcf(c_109247,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),c_Groups_Ozero__class_Ozero(X0))
| ( c_Groups_Ouminus__class_Ouminus(X0,X1) = c_Groups_Ozero__class_Ozero(X0) )
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(superposition,[status(thm)],[c_604,c_285]) ).
tcf(c_109248,plain,
! [X0: $i,X1: $i] :
( ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_604,c_300]) ).
tcf(c_109249,plain,
! [X0: $i,X1: $i] :
( ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1)) ),
inference(superposition,[status(thm)],[c_604,c_293]) ).
tcf(c_109250,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0)),X1)
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(superposition,[status(thm)],[c_604,c_579]) ).
tcf(c_109252,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(superposition,[status(thm)],[c_604,c_672]) ).
tcf(c_109253,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(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__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(superposition,[status(thm)],[c_604,c_671]) ).
tcf(c_109254,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_604,c_662]) ).
tcf(c_109255,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_604,c_97283]) ).
tcf(c_109256,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(superposition,[status(thm)],[c_604,c_94504]) ).
tcf(c_109258,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109256,c_1348]) ).
tcf(c_109261,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109255,c_1348]) ).
tcf(c_109279,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,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__eq(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109253,c_1348]) ).
tcf(c_109283,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),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_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109232,c_1348]) ).
tcf(c_109286,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = 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),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109254,c_1348]) ).
tcf(c_109290,plain,
! [X0: $i] :
( ( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) = 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),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109252,c_1348]) ).
tcf(c_109309,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),iPr_def_20)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) ),
inference(light_normalisation,[status(thm)],[c_109234,c_72176]) ).
tcf(c_109357,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_n____)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,iPr_def_15,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,iPr_def_15)) = X0 ) ),
inference(superposition,[status(thm)],[c_1136,c_108820]) ).
tcf(c_109364,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,iPr_def_15) ),
inference(superposition,[status(thm)],[c_96459,c_108820]) ).
tcf(c_109365,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____) ),
inference(superposition,[status(thm)],[c_93100,c_108820]) ).
tcf(c_109366,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____) ),
inference(superposition,[status(thm)],[c_92157,c_108820]) ).
tcf(c_109369,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,iPr_def_15) ),
inference(superposition,[status(thm)],[c_92805,c_108820]) ).
tcf(c_109372,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),v_n____)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_1097,c_108820]) ).
tcf(c_109375,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,v_n____) ),
inference(superposition,[status(thm)],[c_100509,c_108820]) ).
tcf(c_109376,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v_n____ ) ),
inference(superposition,[status(thm)],[c_98061,c_108820]) ).
tcf(c_109377,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____) ),
inference(superposition,[status(thm)],[c_97717,c_108820]) ).
tcf(c_109380,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),v_n____) ),
inference(superposition,[status(thm)],[c_95503,c_108820]) ).
tcf(c_109381,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,X0),v_n____),
inference(superposition,[status(thm)],[c_94342,c_108820]) ).
tcf(c_109382,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_n____)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101214,c_108820]) ).
tcf(c_109383,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),v_n____)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101854,c_108820]) ).
tcf(c_109384,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),v_n____)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101638,c_108820]) ).
tcf(c_109385,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_n____)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101863,c_108820]) ).
tcf(c_109386,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),v_n____)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_101631,c_108820]) ).
tcf(c_109415,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15)) ),
inference(superposition,[status(thm)],[c_108867,c_49959]) ).
tcf(c_109417,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_108867,c_291]) ).
tcf(c_109418,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),v_n____)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15) = v_n____ )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_108867,c_285]) ).
tcf(c_109419,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15)) ),
inference(superposition,[status(thm)],[c_108867,c_300]) ).
tcf(c_109420,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15)) ),
inference(superposition,[status(thm)],[c_108867,c_293]) ).
tcf(c_109426,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),v_n____)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15) = v_n____ )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109418,c_1414]) ).
tcf(c_109430,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109417,c_1413]) ).
tcf(c_109450,plain,
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____)) ),
inference(superposition,[status(thm)],[c_109383,c_49959]) ).
tcf(c_109451,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),v_n____)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____) = v_n____ )
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_109383,c_294]) ).
tcf(c_109452,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_109383,c_291]) ).
tcf(c_109453,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),v_n____)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____) = v_n____ )
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_109383,c_285]) ).
tcf(c_109455,plain,
( ~ class_Rings_Olinordered__idom(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____)) ),
inference(superposition,[status(thm)],[c_109383,c_293]) ).
tcf(c_109457,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_109383,c_607]) ).
tcf(c_109461,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),v_n____)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____) = v_n____ )
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109453,c_1414]) ).
tcf(c_109465,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| ~ class_Rings_Olinordered__idom(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109452,c_1413]) ).
tcf(c_109474,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____)) ),
inference(superposition,[status(thm)],[c_109384,c_49959]) ).
tcf(c_109476,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_109384,c_291]) ).
tcf(c_109477,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),v_n____)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____) = v_n____ )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_109384,c_285]) ).
tcf(c_109478,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____)) ),
inference(superposition,[status(thm)],[c_109384,c_300]) ).
tcf(c_109479,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____)) ),
inference(superposition,[status(thm)],[c_109384,c_293]) ).
tcf(c_109481,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_n____)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_109384,c_607]) ).
tcf(c_109486,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),v_n____)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____) = v_n____ )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109477,c_1414]) ).
tcf(c_109490,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____),v_n____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,v_n____))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109476,c_1413]) ).
tcf(c_109498,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_n____,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15))) = v_n____ )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_1136,c_109415]) ).
tcf(c_109505,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_100509,c_109415]) ).
tcf(c_109514,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15)) ),
inference(superposition,[status(thm)],[c_109505,c_50323]) ).
tcf(c_109517,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_109505,c_91603]) ).
tcf(c_109518,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15)) ),
inference(superposition,[status(thm)],[c_109505,c_245]) ).
tcf(c_109519,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15)) ),
inference(superposition,[status(thm)],[c_109505,c_240]) ).
tcf(c_109520,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Oorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15)) ),
inference(superposition,[status(thm)],[c_109505,c_235]) ).
tcf(c_109539,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_109517,c_291]) ).
tcf(c_109540,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),iPr_def_15)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15) = iPr_def_15 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| ~ class_Orderings_Olinorder(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_109517,c_285]) ).
tcf(c_109544,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),iPr_def_15)
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(superposition,[status(thm)],[c_109517,c_607]) ).
tcf(c_109545,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),iPr_def_15)
| ( c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15) = iPr_def_15 )
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109540,c_1414]) ).
tcf(c_109549,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15),iPr_def_15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,iPr_def_15,c_Groups_Ouminus__class_Ouminus(tc_Nat_Onat,iPr_def_15))
| ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109539,c_1413]) ).
tcf(c_109553,plain,
! [X0: $i,X1: $i,X2: $i] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X2) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0),X2),
inference(demodulation,[status(thm)],[c_90594,c_104061,c_94258]) ).
tcf(c_109566,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_301,c_605]) ).
tcf(c_109567,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ouminus__class_Ouminus(X0,X1))
| ~ class_Groups_Oordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(superposition,[status(thm)],[c_421,c_605]) ).
tcf(c_109573,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_105035,c_605]) ).
tcf(c_109574,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
inference(superposition,[status(thm)],[c_661,c_605]) ).
tcf(c_109580,plain,
! [X0: $i,X1: $i] :
( 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,X0,X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(superposition,[status(thm)],[c_12534,c_605]) ).
tcf(c_109582,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_16973,c_605]) ).
tcf(c_109583,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(superposition,[status(thm)],[c_45742,c_605]) ).
tcf(c_109587,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0))
| ~ class_Groups_Oordered__ab__group__add(tc_HOL_Obool)
| ~ c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X0,c_Groups_Ozero__class_Ozero(tc_HOL_Obool)) ),
inference(superposition,[status(thm)],[c_91806,c_605]) ).
tcf(c_109590,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),iPr_def_20) ),
inference(superposition,[status(thm)],[c_72176,c_605]) ).
tcf(c_109592,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109574,c_1348]) ).
tcf(c_109595,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109573,c_1348]) ).
tcf(c_109610,plain,
! [X0: $i,X1: $i] :
( 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,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109580,c_1348]) ).
tcf(c_109613,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,iPr_def_20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1))
| ~ class_Groups_Oordered__ab__group__add(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),iPr_def_20) ),
inference(light_normalisation,[status(thm)],[c_109582,c_72176]) ).
fof(f2425,definition,
! [X3,X0,X2,X1,X4] :
( sP0(X3,X0,X2,X1,X4)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) )
& X3 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f2426,definition,
! [X4,X1,X2,X0,X3] :
( ~ sP1(X4,X1,X2,X0,X3)
| ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
<=> sP0(X3,X0,X2,X1,X4) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f2427,plain,
! [X0,X1,X2,X3,X4] :
( ~ class_Fields_Ofield(X4)
| sP1(X4,X1,X2,X0,X3) ),
inference(definition_folding,[],[f2103,f2426,f2425]) ).
fof(f2695,plain,
! [X3,X0,X2,X1,X4] :
( ( ~ sP0(X3,X0,X2,X1,X4)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) )
& X3 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) ) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X1 )
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) != X3
| sP0(X3,X0,X2,X1,X4) ) ),
inference(nnf_transformation,[],[f2425]) ).
fof(f2696,plain,
! [X3,X0,X2,X1,X4] :
( ( ~ sP0(X3,X0,X2,X1,X4)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
| X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) )
& X3 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) ) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X1 )
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) != X3
| sP0(X3,X0,X2,X1,X4) ) ),
inference(flattening,[],[f2695]) ).
fof(f2697,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ sP0(X0,X1,X2,X3,X4)
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X1),c_Polynomial_Odegree(X4,X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X3 )
& c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1) = X0 ) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X1),c_Polynomial_Odegree(X4,X2))
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X3 )
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1) != X0
| sP0(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f2696]) ).
fof(f3797,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP0(X0,X1,X2,X3,X4)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X1),c_Polynomial_Odegree(X4,X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1 ),
inference(cnf_transformation,[],[f2697]) ).
fof(f3799,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP0(X0,X1,X2,X3,X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1) = X0 ),
inference(cnf_transformation,[],[f2697]) ).
fof(f3801,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X1),c_Polynomial_Odegree(X4,X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1) != X0
| sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f2697]) ).
fof(f3802,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1) != X0
| sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f2697]) ).
fof(f3803,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X3
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1) != X0
| sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f2697]) ).
fof(f3804,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X1),c_Polynomial_Odegree(X4,X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X3
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1) != X0
| sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f2697]) ).
fof(f3805,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X3
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1) != X0
| sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f2697]) ).
fof(f4650,plain,
! [X2,X3,X1,X4] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X3
| sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1),X1,X2,X3,X4) ),
inference(equality_resolution,[],[f3805]) ).
fof(f4651,plain,
! [X2,X1,X4] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X1
| sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X2),X1),X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) ),
inference(equality_resolution,[],[f4650]) ).
fof(f4652,plain,
! [X2,X4] : sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),
inference(equality_resolution,[],[f4651]) ).
fof(f4653,plain,
! [X2,X3,X1,X4] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X1),c_Polynomial_Odegree(X4,X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X3
| sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1),X1,X2,X3,X4) ),
inference(equality_resolution,[],[f3804]) ).
fof(f4654,plain,
! [X2,X1,X4] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X1),c_Polynomial_Odegree(X4,X2))
| sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X2),X1),X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) ),
inference(equality_resolution,[],[f4653]) ).
fof(f4655,plain,
! [X2,X3,X1,X4] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X3
| sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1),X1,X2,X3,X4) ),
inference(equality_resolution,[],[f3803]) ).
fof(f4656,plain,
! [X2,X1,X4] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
| sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X2),X1),X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) ),
inference(equality_resolution,[],[f4655]) ).
fof(f4657,plain,
! [X1,X4] : sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X1),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),
inference(equality_resolution,[],[f4656]) ).
fof(f4658,plain,
! [X2,X3,X1,X4] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1),X1,X2,X3,X4) ),
inference(equality_resolution,[],[f3802]) ).
fof(f4659,plain,
! [X2,X3,X4] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X2,X3,X4) ),
inference(equality_resolution,[],[f4658]) ).
fof(f4660,plain,
! [X2,X3,X1,X4] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X1),c_Polynomial_Odegree(X4,X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1),X1,X2,X3,X4) ),
inference(equality_resolution,[],[f3801]) ).
tcf(c_1014,plain,
! [X0: $i,X1: $i] : sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),
inference(cnf_transformation,[],[f4652]) ).
tcf(c_1015,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X2),X1),X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2)) ),
inference(cnf_transformation,[],[f4654]) ).
tcf(c_1016,plain,
! [X0: $i,X1: $i] : sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),
inference(cnf_transformation,[],[f4657]) ).
tcf(c_1017,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X2),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X2,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 ) ),
inference(cnf_transformation,[],[f4659]) ).
tcf(c_1018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X3),X2),X1),X1,X2,X3,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2)) ),
inference(cnf_transformation,[],[f4660]) ).
tcf(c_1019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1) = X0 )
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3799]) ).
tcf(c_1021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X1),c_Polynomial_Odegree(X4,X2))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1 )
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3797]) ).
tcf(c_2908,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X2),X1),X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2)) ),
inference(prop_impl_just,[status(thm)],[c_1015]) ).
tcf(c_3240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X3),X2),X1) = X0 )
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(prop_impl_just,[status(thm)],[c_1019]) ).
tcf(c_3802,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X2),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X2,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_1017]) ).
tcf(c_21137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X8,X2),c_Polynomial_Odegree(X8,X4))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) = X4 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) = X2 )
| ~ class_Fields_Ofield(X9)
| ~ c_Polynomial_Opdivmod__rel(X9,X1,X5,X7,X3)
| ( X8 != X9 )
| ( X6 != X7 )
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1021,c_16822]) ).
tcf(c_21138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X4),c_Polynomial_Odegree(X0,X2))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X4 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Fields_Ofield(X0)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4) ),
inference(unflattening,[status(thm)],[c_21137]) ).
tcf(c_21155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X6),X4),X2) = X0 )
| ~ class_Fields_Ofield(X9)
| ~ c_Polynomial_Opdivmod__rel(X9,X1,X5,X7,X3)
| ( X8 != X9 )
| ( X6 != X7 )
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_3240,c_16822]) ).
tcf(c_21156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X3),X2),X4) = X1 )
| ~ class_Fields_Ofield(X0)
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4) ),
inference(unflattening,[status(thm)],[c_21155]) ).
tcf(c_21167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_Polynomial_Opdivmod__rel(X6,X2,X4,X5,X3)
| ~ class_Fields_Ofield(X6)
| ( X1 != X4 )
| ( X0 != X6 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != X5 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != X3 )
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_16810,c_1014]) ).
tcf(c_21168,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Fields_Ofield(X0) ),
inference(unflattening,[status(thm)],[c_21167]) ).
tcf(c_21180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( c_Polynomial_Opdivmod__rel(X7,X3,X5,X6,X4)
| ~ class_Fields_Ofield(X7)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X2),c_Polynomial_Odegree(X0,X1))
| ( X2 != X4 )
| ( X1 != X5 )
| ( X0 != X7 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != X6 )
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1),X2) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_16810,c_2908]) ).
tcf(c_21181,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X2),X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1)
| ~ class_Fields_Ofield(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2)) ),
inference(unflattening,[status(thm)],[c_21180]) ).
tcf(c_21196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_Polynomial_Opdivmod__rel(X6,X2,X4,X5,X3)
| ~ class_Fields_Ofield(X6)
| ( X1 != X3 )
| ( X0 != X6 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != X5 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != X4 )
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_16810,c_1016]) ).
tcf(c_21197,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1)
| ~ class_Fields_Ofield(X0) ),
inference(unflattening,[status(thm)],[c_21196]) ).
tcf(c_21209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( c_Polynomial_Opdivmod__rel(X7,X3,X5,X6,X4)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Fields_Ofield(X7)
| ( X2 != X5 )
| ( X1 != X6 )
| ( X0 != X7 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != X4 )
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_16810,c_3802]) ).
tcf(c_21210,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X2),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ~ class_Fields_Ofield(X0) ),
inference(unflattening,[status(thm)],[c_21209]) ).
tcf(c_21225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( c_Polynomial_Opdivmod__rel(X8,X4,X6,X7,X5)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Fields_Ofield(X8)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X3),c_Polynomial_Odegree(X0,X2))
| ( X3 != X5 )
| ( X2 != X6 )
| ( X1 != X7 )
| ( X0 != X8 )
| ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),X2),X3) != X4 ) ),
inference(resolution_lifted,[status(thm)],[c_16810,c_1018]) ).
tcf(c_21226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X3),X2),X1),X2,X3,X1)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ class_Fields_Ofield(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2)) ),
inference(unflattening,[status(thm)],[c_21225]) ).
tcf(c_22413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X3),X2),X1),X2,X3,X1)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_21226,c_1466]) ).
tcf(c_22414,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),X1),X0),X1,X2,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,X0),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1)) ),
inference(unflattening,[status(thm)],[c_22413]) ).
tcf(c_22425,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X2),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1 )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_21210,c_1466]) ).
tcf(c_22426,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 ) ),
inference(unflattening,[status(thm)],[c_22425]) ).
tcf(c_22434,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_21197,c_1466]) ).
tcf(c_22435,plain,
! [X0: $i] : c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),
inference(unflattening,[status(thm)],[c_22434]) ).
tcf(c_22440,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X2),X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X1),c_Polynomial_Odegree(X0,X2))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_21181,c_1466]) ).
tcf(c_22441,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X1),X0),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,X0),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1)) ),
inference(unflattening,[status(thm)],[c_22440]) ).
tcf(c_22449,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(X0,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_21168,c_1466]) ).
tcf(c_22450,plain,
! [X0: $i] : c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(unflattening,[status(thm)],[c_22449]) ).
tcf(c_22455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X3),X2),X4) = X1 )
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_21156,c_1466]) ).
tcf(c_22456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),X1),X3) = X0 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,X1,X2,X3) ),
inference(unflattening,[status(thm)],[c_22455]) ).
tcf(c_22464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X0,X4),c_Polynomial_Odegree(X0,X2))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X4 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 )
| ~ c_Polynomial_Opdivmod__rel(X0,X1,X2,X3,X4)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_21138,c_1466]) ).
tcf(c_22465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,X3),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X3 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,X1,X2,X3) ),
inference(unflattening,[status(thm)],[c_22464]) ).
tcf(c_51518,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X1),X0),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,X0),c_Polynomial_Odegree(tc_Complex_Ocomplex,X1)) ),
inference(prop_impl_just,[status(thm)],[c_22441]) ).
tcf(c_51526,plain,
! [X0: $i,X1: $i] :
( c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_22426]) ).
tcf(c_51532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),X1),X3) = X0 )
| ~ c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_22456]) ).
tcf(c_109647,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_109613,c_109610,c_109595,c_109592,c_109590,c_109587,c_109583,c_109582,c_109580,c_109573,c_109574,c_109566,c_109567,c_109553,c_109549,c_109545,c_109544,c_109540,c_109539,c_109520,c_109519,c_109518,c_109517,c_109514,c_109505,c_109498,c_109490,c_109486,c_109481,c_109479,c_109478,c_109477,c_109476,c_109474,c_109465,c_109461,c_109457,c_109455,c_109453,c_109452,c_109451,c_109450,c_109430,c_109426,c_109420,c_109419,c_109418,c_109417,c_109415,c_109386,c_109385,c_109384,c_109383,c_109382,c_109381,c_109380,c_109377,c_109376,c_109375,c_109372,c_109369,c_109366,c_109365,c_109364,c_109357,c_109309,c_109290,c_109286,c_109283,c_109279,c_109261,c_109258,c_109256,c_109255,c_109254,c_109253,c_109252,c_109250,c_109249,c_109248,c_109247,c_109246,c_109245,c_109242,c_109239,c_109235,c_109234,c_109232,c_109205,c_109202,c_109187,c_109184,c_109179,c_109176,c_109175,c_109174,c_109172,c_109170,c_109168,c_109169,c_109159,c_109160,c_109125,c_109106,c_109102,c_109099,c_109095,c_109076,c_109075,c_109074,c_109072,c_109071,c_109070,c_109069,c_109068,c_109067,c_109063,c_109060,c_109059,c_109058,c_109056,c_109054,c_108984,c_108980,c_108977,c_108968,c_108937,c_108936,c_108934,c_108932,c_108930,c_108928,c_108926,c_108925,c_108923,c_108921,c_108919,c_108917,c_108915,c_108914,c_108913,c_108912,c_108910,c_108909,c_108908,c_108907,c_108880,c_108876,c_108872,c_108867,c_108852,c_108847,c_108846,c_108842,c_108841,c_108840,c_108838,c_108832,c_108831,c_108829,c_108827,c_108826,c_108825,c_108824,c_108823,c_108821,c_108820,c_108804,c_108800,c_108785,c_108784,c_108783,c_108782,c_108781,c_108780,c_108779,c_108776,c_108775,c_108773,c_108770,c_108769,c_108755,c_108754,c_108750,c_108742,c_108740,c_108702,c_108701,c_108697,c_108689,c_108687,c_108630,c_108609,c_108608,c_108607,c_108606,c_108605,c_108604,c_108603,c_108602,c_108601,c_108600,c_108599,c_108598,c_108597,c_108596,c_108595,c_108594,c_108593,c_108592,c_108591,c_108590,c_108589,c_108588,c_108587,c_108586,c_108585,c_108582,c_108580,c_108579,c_108578,c_108577,c_108576,c_108575,c_108574,c_108573,c_108572,c_108571,c_108568,c_108567,c_108565,c_108564,c_108557,c_108521,c_108518,c_108457,c_108453,c_108452,c_108451,c_108450,c_108449,c_108448,c_108443,c_108442,c_108441,c_108440,c_108439,c_108432,c_108430,c_108428,c_108427,c_108426,c_108425,c_108421,c_108419,c_108417,c_108416,c_108415,c_108414,c_108375,c_108365,c_108362,c_108346,c_108341,c_108340,c_108336,c_108328,c_108327,c_108326,c_108325,c_108323,c_108321,c_108319,c_108317,c_108299,c_108298,c_108297,c_108296,c_108294,c_108293,c_108286,c_108284,c_108282,c_108281,c_108279,c_108278,c_108277,c_108269,c_108268,c_108265,c_108221,c_108211,c_108198,c_108197,c_108178,c_108174,c_108173,c_108172,c_108171,c_108170,c_108169,c_108168,c_108167,c_108166,c_108165,c_108163,c_108162,c_108161,c_108157,c_108156,c_108155,c_108154,c_108146,c_108145,c_108103,c_108099,c_108096,c_108093,c_108089,c_108066,c_108065,c_108064,c_108063,c_108062,c_108060,c_108059,c_108058,c_108057,c_108056,c_108055,c_108054,c_108045,c_108043,c_108034,c_108032,c_108016,c_107899,c_107890,c_107817,c_107814,c_107783,c_107782,c_107781,c_107780,c_107779,c_107778,c_107777,c_107776,c_107775,c_107774,c_107773,c_107772,c_107771,c_107770,c_107769,c_107768,c_107767,c_107766,c_107765,c_107764,c_107763,c_107762,c_107761,c_107760,c_107759,c_107754,c_107755,c_107752,c_107751,c_107750,c_107749,c_107747,c_107746,c_107745,c_107744,c_107748,c_107740,c_107739,c_107738,c_107741,c_107621,c_107612,c_107578,c_107575,c_107551,c_107550,c_107549,c_107503,c_107502,c_107501,c_107499,c_107497,c_107495,c_107493,c_107491,c_107490,c_107489,c_107488,c_107487,c_107486,c_107485,c_107483,c_107482,c_107481,c_107480,c_107479,c_107478,c_107477,c_107476,c_107475,c_107474,c_107473,c_107472,c_107471,c_107470,c_107469,c_107468,c_107466,c_107464,c_107463,c_107462,c_107461,c_107460,c_107459,c_107458,c_107457,c_107456,c_107455,c_107453,c_107452,c_107451,c_107450,c_107448,c_107446,c_107445,c_107444,c_107330,c_107318,c_107297,c_107296,c_107293,c_107292,c_107240,c_107237,c_107230,c_107200,c_107191,c_107188,c_107187,c_107186,c_107185,c_107184,c_107183,c_107182,c_107181,c_107180,c_107179,c_107177,c_107176,c_107175,c_107174,c_107173,c_107172,c_107171,c_107170,c_107169,c_107168,c_107167,c_107166,c_107165,c_107164,c_107163,c_107162,c_107161,c_107160,c_107159,c_107157,c_107158,c_107155,c_107154,c_107153,c_107152,c_107151,c_107150,c_107149,c_107147,c_107146,c_107145,c_107144,c_107148,c_107142,c_107141,c_107139,c_107138,c_107137,c_107140,c_107135,c_107110,c_107109,c_107106,c_107103,c_107100,c_107099,c_107096,c_107090,c_107088,c_107086,c_107085,c_107084,c_107083,c_106988,c_106987,c_106986,c_106985,c_106980,c_106979,c_106978,c_106977,c_106976,c_106975,c_106974,c_106973,c_106972,c_106971,c_106970,c_106969,c_106968,c_106967,c_106966,c_106965,c_106964,c_106963,c_106962,c_106961,c_106960,c_106959,c_106958,c_106957,c_106956,c_106955,c_106954,c_106953,c_106952,c_106951,c_106950,c_106949,c_106948,c_106947,c_106946,c_106945,c_106944,c_106943,c_106942,c_106941,c_106940,c_106939,c_106854,c_106835,c_106834,c_106809,c_106808,c_106805,c_106800,c_106799,c_106796,c_106795,c_106794,c_106798,c_106790,c_106787,c_106783,c_106782,c_106781,c_106780,c_106776,c_106771,c_106766,c_106793,c_106789,c_106762,c_106761,c_106760,c_106759,c_106758,c_106757,c_106754,c_106752,c_106749,c_106748,c_106746,c_106745,c_106744,c_106741,c_106740,c_106739,c_106738,c_106737,c_106736,c_106725,c_106724,c_106702,c_106701,c_106700,c_106687,c_106686,c_106685,c_106678,c_106676,c_106675,c_106674,c_106621,c_106618,c_106606,c_106603,c_106600,c_106597,c_106591,c_106589,c_106588,c_106587,c_106586,c_106585,c_106584,c_106583,c_106582,c_106581,c_106580,c_106579,c_106396,c_106393,c_106390,c_106335,c_106334,c_106333,c_106332,c_106331,c_106330,c_106328,c_106329,c_106322,c_106327,c_106326,c_106325,c_106324,c_106316,c_106306,c_106305,c_106302,c_106301,c_106295,c_106294,c_106293,c_106292,c_106291,c_106290,c_106289,c_106288,c_106286,c_106285,c_106283,c_106282,c_106281,c_106280,c_106284,c_106277,c_106276,c_106273,c_106272,c_106270,c_106269,c_106268,c_106267,c_106266,c_106265,c_106264,c_106262,c_106260,c_106258,c_106257,c_106256,c_106255,c_106254,c_106253,c_106252,c_106251,c_106250,c_106249,c_106248,c_106247,c_106246,c_106245,c_106244,c_106243,c_106242,c_106241,c_106240,c_106279,c_106275,c_106237,c_106236,c_106235,c_106234,c_106233,c_106229,c_106228,c_106227,c_106226,c_106225,c_106224,c_106221,c_106232,c_106218,c_106216,c_106299,c_106223,c_108927,c_105934,c_105897,c_105896,c_105895,c_105894,c_105893,c_105892,c_105886,c_105885,c_105879,c_105878,c_105877,c_105876,c_105875,c_105874,c_105873,c_105871,c_105870,c_105869,c_105866,c_105865,c_105864,c_105861,c_105860,c_105858,c_105857,c_105851,c_105848,c_105847,c_105845,c_105844,c_105843,c_105842,c_105841,c_105839,c_105838,c_105837,c_105836,c_105835,c_105834,c_105833,c_105832,c_105831,c_105830,c_105863,c_105859,c_105827,c_105826,c_105825,c_105824,c_105823,c_105822,c_105820,c_105819,c_105818,c_105817,c_105816,c_105815,c_105813,c_105812,c_105811,c_105810,c_105809,c_105808,c_105806,c_105805,c_105804,c_105803,c_105802,c_105801,c_105800,c_105683,c_105868,c_105679,c_105678,c_105677,c_105849,c_105814,c_105593,c_105592,c_105591,c_105590,c_105589,c_105588,c_105587,c_105586,c_105585,c_108316,c_105566,c_105563,c_105560,c_105545,c_105544,c_105539,c_108916,c_105526,c_105525,c_105524,c_105523,c_105522,c_105521,c_105520,c_105518,c_105517,c_108164,c_107492,c_105458,c_105454,c_105447,c_105446,c_105444,c_105435,c_105404,c_105403,c_105399,c_105395,c_105385,c_105383,c_105382,c_105376,c_105375,c_105368,c_105367,c_105360,c_105358,c_105357,c_107178,c_105251,c_105247,c_105243,c_105236,c_105233,c_105229,c_105225,c_105211,c_105207,c_105204,c_105201,c_105198,c_105195,c_105192,c_105189,c_105185,c_105181,c_105177,c_105173,c_105170,c_105166,c_105163,c_105159,c_105155,c_105151,c_105147,c_105144,c_105141,c_105138,c_105129,c_105125,c_105117,c_105113,c_105109,c_105105,c_105097,c_105093,c_105089,c_105086,c_105083,c_105080,c_105076,c_105072,c_105068,c_105064,c_105052,c_105048,c_105044,c_105041,c_105038,c_105034,c_105032,c_105030,c_105029,c_105028,c_105027,c_105026,c_105025,c_105024,c_105022,c_105021,c_105019,c_105016,c_105015,c_105014,c_105008,c_105006,c_104997,c_104994,c_104993,c_104992,c_104990,c_104985,c_104984,c_104981,c_104980,c_104979,c_104978,c_104977,c_104976,c_104974,c_104973,c_104972,c_104968,c_104967,c_104966,c_104965,c_104964,c_104963,c_104960,c_104957,c_104956,c_104955,c_104954,c_104953,c_104952,c_104951,c_104950,c_104949,c_104948,c_104947,c_104946,c_104941,c_104939,c_104938,c_104935,c_104934,c_104933,c_104931,c_104878,c_104874,c_104870,c_104867,c_104863,c_104848,c_104845,c_104842,c_104839,c_104835,c_104831,c_104827,c_104823,c_104819,c_104815,c_104811,c_104807,c_104803,c_104799,c_104794,c_104792,c_104790,c_104789,c_104788,c_104787,c_104784,c_104782,c_104775,c_104774,c_104736,c_104734,c_104727,c_104724,c_104723,c_104717,c_104716,c_104712,c_104711,c_104710,c_104709,c_104707,c_104706,c_104705,c_104698,c_104621,c_104619,c_104618,c_104615,c_104598,c_104597,c_104596,c_104594,c_104593,c_104595,c_104591,c_104589,c_104588,c_104587,c_104585,c_104584,c_104549,c_104528,c_104527,c_104526,c_104524,c_104523,c_104506,c_104505,c_104504,c_104502,c_104501,c_104535,c_104499,c_104497,c_104496,c_104493,c_104468,c_104466,c_104465,c_104462,c_104455,c_104454,c_104435,c_104430,c_104421,c_104420,c_104419,c_104417,c_104416,c_104409,c_104408,c_104385,c_104384,c_104379,c_104374,c_104368,c_104367,c_104349,c_104348,c_104347,c_104346,c_104345,c_104344,c_104263,c_104257,c_104255,c_104254,c_104253,c_104251,c_104250,c_104249,c_104248,c_104247,c_104246,c_104245,c_104244,c_104243,c_104242,c_104241,c_104240,c_104239,c_104238,c_104236,c_104235,c_104234,c_104230,c_104228,c_104227,c_104226,c_104229,c_104217,c_104216,c_104215,c_104214,c_104213,c_104212,c_104193,c_104192,c_104187,c_104186,c_104180,c_104179,c_104178,c_104177,c_104176,c_104174,c_104170,c_104169,c_104168,c_104119,c_104116,c_104115,c_104114,c_104113,c_10411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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW287+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 % Computer : n016.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Thu Sep 24 22:02:43 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.46 Running first-order theorem proving
% 0.14/0.46 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.48
% 0.14/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.48
% 0.14/0.48 % Detected problem language: tptp
% 0.14/0.49 % Proving...
% 53.21/11.68 % SZS status Started for theBenchmark.p
% 53.21/11.68 ERROR - "ProverProcess:heur/409474:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 53.21/11.68 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 53.21/11.68 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 4 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution false --res_forward_subs subset_subsumption --res_forward_subs_resolution true --res_lit_sel pos_max --res_lit_sel_side num_var --res_ordering kbo_pred --res_passive_queue_type priority_queues --res_passive_queues "[[-num_lits];[-conj_symb;-num_symb;+num_symb]]" --res_passive_queues_freq "[15;3]" --res_prop_simpl_given false --res_prop_simpl_new true --res_sim_input true --res_time_limit 202.80 --res_to_prop_solver passive --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_0zc8afpk/2wlgstg4 2>> /export/starexec/sandbox2/tmp/iprover_out_0zc8afpk/2wlgstg4_error
% 53.21/11.68 ERROR - "ProverProcess:heur/469571:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 53.21/11.68 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 53.21/11.68 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 6 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3.0 --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 32 --inst_dismatching false --inst_eager_unprocessed_to_passive false --inst_eq_res_simp false --inst_learning_factor 10 --inst_learning_loop_flag true --inst_learning_start 256 --inst_lit_activity_flag true --inst_lit_sel "[+sign;-ground;-non_prol_conj_symb;-num_var]" --inst_lit_sel_side num_lit --inst_orphan_elimination true --inst_passive_queue_type list --inst_passive_queues "[[-ground;-epr]]" --inst_passive_queues_freq "[2]" --inst_prop_sim_given false --inst_prop_sim_new false --inst_restr_to_given true --inst_sel_renew solver --inst_solver_calls_frac 0.6939020527068606 --inst_solver_per_active 8 --inst_sos_flag false --inst_start_prop_sim_after_learn 9 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 2048 --prop_solver_per_cl 128 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[DemodLightNormLoopTriv;ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 640 --sup_share_score_frac 0.1 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_0zc8afpk/hstpw1o_ 2>> /export/starexec/sandbox2/tmp/iprover_out_0zc8afpk/hstpw1o__error
% 53.21/11.68 ERROR - "ProverProcess:heur/381325:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 53.21/11.68 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 53.21/11.68 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 1 --comb_sup_mult 3 --conj_cone_tolerance 3. --demod_completeness_check full --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[Demod;DemodLoopTriv;LightNorm;ACNormalisation]" --sup_full_triv "[]" --sup_fun_splitting true --sup_immed_bw_immed "[]" --sup_immed_bw_main "[SubsumptionRes;UnitSubsAndRes]" --sup_immed_fw_immed "[Subsumption;UnitSubsAndRes;Demod;DemodLoopTriv;LightNorm;DemodLightNormLoopTriv]" --sup_immed_fw_main "[Subsumption;SubsumptionRes;LightNorm;DemodLightNormLoopTriv]" --sup_immed_triv "[PropSubs]" --sup_indices_passive "[UnitSubsumption;NonunitSubsumption;FwDemod]" --sup_input_bw "[UnitSubsAndRes]" --sup_input_fw "[]" --sup_input_triv "[PropSubs]" --sup_iter_deepening 0 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_symb;-max_atom_input_occur];[+horn];[+bc_imp_inh;+ground;-conj_dist]]" --sup_passive_queues_freq "[3;1;25]" --sup_prop_simpl_given true --sup_prop_simpl_new false --sup_restarts_mult 8 --sup_score sim_d_gen --sup_share_max_num_cl 40 --sup_share_score_frac 0.1 --sup_smt_interval 10000 --sup_symb_ordering arity_random --sup_to_prop_solver active --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_0zc8afpk/xvsgrl4b 2>> /export/starexec/sandbox2/tmp/iprover_out_0zc8afpk/xvsgrl4b_error
% 53.21/11.68 ERROR - "ProverProcess:heur/346297:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 53.21/11.68 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 53.21/11.68 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode time_based --comb_sup_deep_mult 6 --comb_sup_mult 32 --conj_cone_tolerance 2.7380125131254 --demod_completeness_check full --demod_use_ground true --eq_ax_congr_red false --extra_neg_conj none --inst_activity_threshold 16 --inst_dismatching false --inst_eager_unprocessed_to_passive false --inst_eq_res_simp true --inst_learning_factor 6 --inst_learning_loop_flag true --inst_learning_start 1024 --inst_lit_activity_flag true --inst_lit_sel "[+depth;+sign;+num_symb;-split;-eq]" --inst_lit_sel_side cnt --inst_orphan_elimination true --inst_passive_queue_type list --inst_passive_queues "[[-num_lits];[-max_atom_input_occur;-ground]]" --inst_passive_queues_freq "[8;50]" --inst_prop_sim_given false --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 0.21724605765256222 --inst_solver_per_active 256 --inst_sos_flag true --inst_sos_phase true --inst_sos_sth_lit_sel "[-depth;+non_prol_conj_symb;-split;-ground;+num_var]" --inst_start_prop_sim_after_learn 8 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd false --prep_def_merge_prop_impl true --prep_def_merge_tr_cl true --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim false --prep_sem_filter none --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten false --prep_upred true --preprocessing_flag true --prolific_symb_bound 2048 --prop_solver_per_cl 32 --pure_diseq_elim false --resolution_flag false --schedule none --share_sel_clauses false --smt_ac_axioms full --smt_preprocessing true --splitting_cvd true --splitting_cvd_svl false --splitting_grd true --splitting_mode full --splitting_nvd 128 --stats_out none --sub_typing true --subs_bck_mult 0 --sup_full_bw "[Demod]" --sup_full_fw "[Subsumption;SubsumptionRes;UnitSubsAndRes;DemodLoopTriv;DemodLightNormLoopTriv;ACJoinability;ACNormalisation]" --sup_full_triv "[PropSubs;Unflattening]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes;Demod;ACJoinability]" --sup_immed_fw_main "[SubsumptionRes;DemodLoopTriv;DemodLightNormLoopTriv;ACJoinability;ACNormalisation]" --sup_immed_triv "[]" --sup_indices_passive "[UnitSubsumption;NonunitSubsumption;Subsumption;FwDemod;BwDemod;LightNorm]" --sup_input_bw "[]" --sup_input_fw "[]" --sup_input_triv "[PropSubs;Unflattening]" --sup_iter_deepening 4 --sup_passive_queue_type queue --sup_passive_queues "[[+num_symb]]" --sup_passive_queues_freq "[5]" --sup_prop_simpl_given true --sup_prop_simpl_new false --sup_restarts_mult 4 --sup_smt_interval 10000 --sup_symb_ordering arity_random --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.4432297345384799 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_0zc8afpk/jviq7zpb 2>> /export/starexec/sandbox2/tmp/iprover_out_0zc8afpk/jviq7zpb_error
% 53.21/11.68 ERROR - "ProverProcess:heur/397442:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 53.21/11.68 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 53.21/11.68 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 64 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 4 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp true --inst_learning_factor 8 --inst_learning_loop_flag true --inst_learning_start 2 --inst_lit_activity_flag false --inst_lit_sel "[-split]" --inst_lit_sel_side num_lit --inst_orphan_elimination false --inst_passive_queue_type priority_queues --inst_passive_queues "[[+conj_symb]]" --inst_passive_queues_freq "[50]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 0.8199321230744955 --inst_solver_per_active 4 --inst_sos_flag false --inst_start_prop_sim_after_learn 7 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_0zc8afpk/5jqd66t2 2>> /export/starexec/sandbox2/tmp/iprover_out_0zc8afpk/5jqd66t2_error
% 53.21/11.68 ERROR - "ProverProcess:heur/421498:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 53.21/11.68 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 53.21/11.68 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 8 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 512 --inst_dismatching true --inst_eager_unprocessed_to_passive false --inst_eq_res_simp true --inst_learning_factor 8 --inst_learning_loop_flag true --inst_learning_start 128 --inst_lit_activity_flag false --inst_lit_sel "[+sign;+prop]" --inst_lit_sel_side none --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[+num_symb;-age;-age];[+num_symb;+conj_non_prolific_symb]]" --inst_passive_queues_freq "[512;10]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew model --inst_solver_calls_frac 0.006221608720445637 --inst_solver_per_active 32768 --inst_sos_flag true --inst_sos_phase false --inst_sos_sth_lit_sel "[+non_prol_conj_symb;+sign;-depth;-prop]" --inst_start_prop_sim_after_learn 9 --inst_subs_given true --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_0zc8afpk/gfvydtcz 2>> /export/starexec/sandbox2/tmp/iprover_out_0zc8afpk/gfvydtcz_error
% 53.21/11.68 % SZS status Theorem for theBenchmark.p
% 53.21/11.68
% 53.21/11.68 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 53.21/11.68
% 53.21/11.68 % ------ iProver source info
% 53.21/11.68
% 53.21/11.68 % git: date: 2026-07-19 20:42:38 +0200
% 53.21/11.68 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 53.21/11.68 % git: non_committed_changes: false
% 53.21/11.68
% 53.21/11.68 % ------ Parsing...
% 53.21/11.68 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 53.21/11.68
% 53.21/11.68 % ------ Preprocessing... sup_sim: 52 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 13 sf_s rm: 15 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 15 0s sf_e pe_s pe_e %
% 53.21/11.68
% 53.21/11.68 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 53.21/11.68
% 53.21/11.68 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 53.21/11.68 % ------ Proving...
% 53.21/11.68 % ------ Problem Properties
% 53.21/11.68
% 53.21/11.68 %
% 53.21/11.68 % clauses 1145
% 53.21/11.68 % conjectures 2
% 53.21/11.68 % EPR 169
% 53.21/11.68 % Horn 981
% 53.21/11.68 % unary 270
% 53.21/11.68 % binary 420
% 53.21/11.68 % lits 2701
% 53.21/11.68 % lits eq 681
% 53.21/11.68 % fd_pure 0
% 53.21/11.68 % fd_pseudo 0
% 53.21/11.68 % fd_cond 70
% 53.21/11.68 % fd_pseudo_cond 99
% 53.21/11.68 % AC symbols 0
% 53.21/11.68
% 53.21/11.68 % ------ Schedule dynamic 5 is on
% 53.21/11.68
% 53.21/11.68 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 53.21/11.68
% 53.21/11.68
% 53.21/11.68 % ------
% 53.21/11.68 % Current options:
% 53.21/11.68 % ------
% 53.21/11.68
% 53.21/11.68
% 53.21/11.68 %
% 53.21/11.68
% 53.21/11.68 % ------ Proving...
% 53.21/11.68 %
% 53.21/11.68
% 53.21/11.68 % SZS status Theorem for theBenchmark.p
% 53.21/11.68
% 53.21/11.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 80.26/11.85
% 80.26/11.85
%------------------------------------------------------------------------------