%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG373-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 : Thu Sep 24 11:49:17 AM UTC 2026
% Result : Unsatisfiable 18.07s 2.80s
% Output : CNFRefutation 7.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 261
% Syntax : Number of formulae : 900 ( 175 unt; 160 def)
% Number of atoms : 2138 ( 260 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2225 ( 987 ~;1078 |; 0 &)
% ( 160 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 185 ( 183 usr; 161 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 868 ( 868 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [T_a,V_v,V_w] :
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a)
| c_lessequals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ class_Int_Onumber(T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [T_a,V_w,V_v] :
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a)
| ~ class_Int_Onumber(T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [T_a,V_x,V_y] :
( V_x = V_y
| c_Int_Onumber__class_Onumber__of(V_x,T_a) != c_Int_Onumber__class_Onumber__of(V_y,T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Int_Oring__char__0(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T_a,V_x] :
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_x,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) = c_Int_Onumber__class_Onumber__of(V_x,T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [T_a,V_x,V_y] :
( V_x = V_y
| c_RealVector_Oof__real(V_x,T_a) != c_RealVector_Oof__real(V_y,T_a)
| ~ class_RealVector_Oreal__algebra__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [T_a,V_x] :
( V_x = c_HOL_Ozero__class_Ozero(T_a)
| c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [T_a] :
( c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__algebra__1(T_a)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_x,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [T_a,V_x,V_y] :
( c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [V_z,V_w] : c_HOL_Otimes__class_Otimes(V_z,V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,V_z,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [T_a,V_a] :
( c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,axiom,
! [T_a,V_a,V_c,V_b] :
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [T_a,V_a,V_c,V_b] :
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [T_a,V_c,V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,axiom,
! [T_a,V_a] :
( c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [T_a,V_a] :
( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f105,axiom,
! [T_a,V_a] :
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f112,axiom,
! [T_a,V_a] :
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a
| ~ class_OrderedGroup_Oordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f124,axiom,
! [V_x,V_y,V_z] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f132,axiom,
! [T_a,V_a] :
( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_a,T_a)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f154,axiom,
! [T_a,V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f155,axiom,
! [T_a,V_b,V_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f158,axiom,
! [T_a,V_a,V_c,V_b] :
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Omult__mono(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f160,axiom,
! [T_a,V_a,V_c,V_b] :
( ~ c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f164,axiom,
! [T_a,V_a,V_b] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f176,axiom,
! [V_z1,V_z2,V_z3] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_z1,V_z2,tc_RealDef_Oreal),V_z3,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_z1,c_HOL_Otimes__class_Otimes(V_z2,V_z3,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f188,axiom,
! [V_p,V_r] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(V_p,V_r),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f219,axiom,
! [T_a,V_a] :
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f220,axiom,
! [T_a,V_a] :
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f232,axiom,
! [V_r] :
( c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f233,axiom,
! [T_a,V_a] :
( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f246,axiom,
! [V_x] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
| V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f247,axiom,
! [T_a,V_a] :
( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f262,axiom,
! [T_a,V_a,V_x] :
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a)
| ~ class_RealVector_Oreal__vector(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f267,axiom,
! [V_u,V_x] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_u,V_u,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f268,axiom,
! [V_x] : c_lessequals(c_Complex_ORe(V_x),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f270,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f275,axiom,
! [T_a,V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f277,axiom,
! [V_w,V_z] :
( c_lessequals(V_z,V_w,tc_RealDef_Oreal)
| c_lessequals(V_w,V_z,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f278,axiom,
! [T_a,V_y,V_x] :
( c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f287,axiom,
! [V_w] : c_lessequals(V_w,V_w,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f288,axiom,
! [V_i,V_k,V_j] :
( ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| c_lessequals(V_i,V_k,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f289,axiom,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f291,axiom,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f292,axiom,
! [V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f295,axiom,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f296,axiom,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f300,axiom,
! [V_x] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f307,axiom,
! [V_x,V_y] :
( ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f318,axiom,
! [V_z,V_w] :
( ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal)
| ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal)
| V_z = V_w ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f323,axiom,
! [T_a,V_a,V_b] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f324,axiom,
! [T_a,V_b,V_a] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f326,axiom,
! [T_a,V_x,V_z,V_y] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f327,axiom,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f328,axiom,
! [T_a,V_x,V_y] :
( c_lessequals(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f335,axiom,
! [T_a,V_b] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f340,axiom,
! [T_a,V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f349,negated_conjecture,
! [V_xb] : c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(V_xb),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f350,negated_conjecture,
! [V_xb] : c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(V_xb),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(V_xb),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f351,negated_conjecture,
! [V_xb] : ~ c_HOL_Oord__class_Oless(v_x(V_xb),V_xb,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f366,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f367,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f368,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f370,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f371,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f378,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f380,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f382,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f383,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f385,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f387,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f391,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f392,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f393,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f395,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f396,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f399,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f400,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f401,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f403,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f405,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f407,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f413,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f416,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f417,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f419,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f420,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f421,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f423,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f426,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f427,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f431,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f432,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f433,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f434,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f435,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f436,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f444,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f445,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f449,axiom,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f454,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f502,plain,
! [X0,X1,X2] :
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X0),c_Int_Onumber__class_Onumber__of(X1,X0),X0)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X0),c_Int_Onumber__class_Onumber__of(X2,X0),X0)
| ~ class_Int_Onumber(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f503,plain,
! [X0,X1,X2] :
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X0),c_Int_Onumber__class_Onumber__of(X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X0),c_Int_Onumber__class_Onumber__of(X2,X0),X0)
| ~ class_Int_Onumber(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f504,plain,
! [V_x,V_y] :
( V_x = V_y
| ! [T_a] :
( c_Int_Onumber__class_Onumber__of(V_x,T_a) != c_Int_Onumber__class_Onumber__of(V_y,T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Int_Oring__char__0(T_a) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f505,plain,
! [X0,X1,X2] :
( X1 = X2
| c_Int_Onumber__class_Onumber__of(X1,X0) != c_Int_Onumber__class_Onumber__of(X2,X0)
| ~ class_Int_Onumber__ring(X0)
| ~ class_Int_Oring__char__0(X0) ),
inference(cnf_transformation,[status(thm)],[f504]) ).
fof(f506,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X1,X0),X0) = c_Int_Onumber__class_Onumber__of(X1,X0)
| ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f507,plain,
! [V_x,V_y] :
( V_x = V_y
| ! [T_a] :
( c_RealVector_Oof__real(V_x,T_a) != c_RealVector_Oof__real(V_y,T_a)
| ~ class_RealVector_Oreal__algebra__1(T_a) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f508,plain,
! [X0,X1,X2] :
( X1 = X2
| c_RealVector_Oof__real(X1,X0) != c_RealVector_Oof__real(X2,X0)
| ~ class_RealVector_Oreal__algebra__1(X0) ),
inference(cnf_transformation,[status(thm)],[f507]) ).
fof(f509,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| c_RealVector_Onorm__class_Onorm(X1,X0) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f524,plain,
! [X0] :
( c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_RealVector_Oreal__algebra__1(X0)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f568,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X1,X0),X0)
| ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f573,plain,
! [T_a] :
( ! [V_x,V_y] : c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f574,plain,
! [X0,X1,X2] :
( c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f573]) ).
fof(f575,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f583,plain,
! [T_a] :
( ! [V_a] : c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(miniscoping,[status(thm)],[f56]) ).
fof(f584,plain,
! [X0,X1] :
( c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[status(thm)],[f583]) ).
fof(f594,plain,
! [T_a,V_c] :
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ! [V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ) ),
inference(miniscoping,[status(thm)],[f62]) ).
fof(f595,plain,
! [X0,X1,X2,X3] :
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ),
inference(cnf_transformation,[status(thm)],[f594]) ).
fof(f598,plain,
! [T_a,V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ! [V_c] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f599,plain,
! [X0,X1,X2,X3] :
( ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) ),
inference(cnf_transformation,[status(thm)],[f598]) ).
fof(f602,plain,
! [T_a,V_c] :
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ! [V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f603,plain,
! [X0,X1,X2,X3] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ),
inference(cnf_transformation,[status(thm)],[f602]) ).
fof(f651,plain,
! [T_a] :
( ! [V_a] : c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
inference(miniscoping,[status(thm)],[f94]) ).
fof(f652,plain,
! [X0,X1] :
( c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f651]) ).
fof(f656,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ouminus__class_Ouminus(X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f665,plain,
! [T_a] :
( ! [V_a] : c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
inference(miniscoping,[status(thm)],[f105]) ).
fof(f666,plain,
! [X0,X1] :
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Oabs__class_Oabs(X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f665]) ).
fof(f679,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1
| ~ class_OrderedGroup_Oordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f699,plain,
! [V_z] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal)
| ! [V_x,V_y] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ),
inference(miniscoping,[status(thm)],[f124]) ).
fof(f700,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f699]) ).
fof(f710,plain,
! [T_a] :
( ! [V_a] : c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_a,T_a)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(miniscoping,[status(thm)],[f132]) ).
fof(f711,plain,
! [X0,X1] :
( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,X0)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[status(thm)],[f710]) ).
fof(f738,plain,
! [T_a,V_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ! [V_b] :
( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ) ),
inference(miniscoping,[status(thm)],[f154]) ).
fof(f739,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) ),
inference(cnf_transformation,[status(thm)],[f738]) ).
fof(f740,plain,
! [T_a,V_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ! [V_b] :
( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ) ),
inference(miniscoping,[status(thm)],[f155]) ).
fof(f741,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) ),
inference(cnf_transformation,[status(thm)],[f740]) ).
fof(f746,plain,
! [T_a,V_a,V_b] :
( ~ c_lessequals(V_a,V_b,T_a)
| ! [V_c] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Omult__mono(T_a) ) ),
inference(miniscoping,[status(thm)],[f158]) ).
fof(f747,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0)
| ~ class_Ring__and__Field_Omult__mono(X0) ),
inference(cnf_transformation,[status(thm)],[f746]) ).
fof(f750,plain,
! [T_a,V_a,V_b] :
( ~ c_lessequals(V_b,V_a,T_a)
| ! [V_c] :
( ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ) ),
inference(miniscoping,[status(thm)],[f160]) ).
fof(f751,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0)
| ~ class_Ring__and__Field_Opordered__ring(X0) ),
inference(cnf_transformation,[status(thm)],[f750]) ).
fof(f758,plain,
! [T_a,V_a] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ! [V_b] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ) ),
inference(miniscoping,[status(thm)],[f164]) ).
fof(f759,plain,
! [X0,X1,X2] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Opordered__ring(X0) ),
inference(cnf_transformation,[status(thm)],[f758]) ).
fof(f782,plain,
! [X0,X1,X2] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f803,plain,
! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f860,plain,
! [T_a] :
( ! [V_a] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f219]) ).
fof(f861,plain,
! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f860]) ).
fof(f862,plain,
! [T_a] :
( ! [V_a] : c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f220]) ).
fof(f863,plain,
! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f862]) ).
fof(f886,plain,
! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
inference(cnf_transformation,[status(thm)],[f232]) ).
fof(f887,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f905,plain,
! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f906,plain,
! [T_a] :
( ! [V_a] : c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
inference(miniscoping,[status(thm)],[f247]) ).
fof(f907,plain,
! [X0,X1] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f906]) ).
fof(f926,plain,
! [T_a] :
( ! [V_a,V_x] : c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a)
| ~ class_RealVector_Oreal__vector(T_a) ),
inference(miniscoping,[status(thm)],[f262]) ).
fof(f927,plain,
! [X0,X1,X2] :
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),X0)
| ~ class_RealVector_Oreal__vector(X0) ),
inference(cnf_transformation,[status(thm)],[f926]) ).
fof(f934,plain,
! [X0,X1] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f935,plain,
! [X0] : c_lessequals(c_Complex_ORe(X0),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f268]) ).
fof(f938,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f270]) ).
fof(f945,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f275]) ).
fof(f947,plain,
! [X0,X1] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f277]) ).
fof(f948,plain,
! [X0,X1,X2] :
( c_lessequals(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f963,plain,
! [X0] : c_lessequals(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f964,plain,
! [V_i,V_j] :
( ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal)
| ! [V_k] :
( ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| c_lessequals(V_i,V_k,tc_RealDef_Oreal) ) ),
inference(miniscoping,[status(thm)],[f288]) ).
fof(f965,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X0,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f964]) ).
fof(f966,plain,
! [T_a] :
( ! [V_x] : c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(miniscoping,[status(thm)],[f289]) ).
fof(f967,plain,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f966]) ).
fof(f970,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(thm)],[f291]) ).
fof(f971,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f292]) ).
fof(f974,plain,
! [T_a] :
( ! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(miniscoping,[status(thm)],[f295]) ).
fof(f975,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(thm)],[f974]) ).
fof(f976,plain,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f296]) ).
fof(f983,plain,
! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f300]) ).
fof(f992,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f307]) ).
fof(f1005,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f1012,plain,
! [X0,X1,X2] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f323]) ).
fof(f1013,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X2,X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f324]) ).
fof(f1016,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ! [V_z] :
( ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ) ),
inference(miniscoping,[status(thm)],[f326]) ).
fof(f1017,plain,
! [X0,X1,X2,X3] :
( ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(thm)],[f1016]) ).
fof(f1018,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(thm)],[f327]) ).
fof(f1019,plain,
! [X0,X1,X2] :
( c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f1026,plain,
! [T_a] :
( ! [V_b] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
inference(miniscoping,[status(thm)],[f335]) ).
fof(f1027,plain,
! [X0,X1] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1
| ~ class_OrderedGroup_Ogroup__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1026]) ).
fof(f1036,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f340]) ).
fof(f1046,plain,
! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f349]) ).
fof(f1047,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f350]) ).
fof(f1048,plain,
! [X0] : ~ c_HOL_Oord__class_Oless(v_x(X0),X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f351]) ).
fof(f1063,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f366]) ).
fof(f1064,plain,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f367]) ).
fof(f1065,plain,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f368]) ).
fof(f1067,plain,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f370]) ).
fof(f1068,plain,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f1075,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f378]) ).
fof(f1077,plain,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f380]) ).
fof(f1079,plain,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f382]) ).
fof(f1080,plain,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f383]) ).
fof(f1082,plain,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f385]) ).
fof(f1084,plain,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f387]) ).
fof(f1088,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f391]) ).
fof(f1089,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f1090,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f393]) ).
fof(f1092,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f395]) ).
fof(f1093,plain,
class_Int_Onumber(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f396]) ).
fof(f1096,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f1097,plain,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f400]) ).
fof(f1098,plain,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f401]) ).
fof(f1100,plain,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f1102,plain,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f405]) ).
fof(f1104,plain,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f407]) ).
fof(f1110,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f413]) ).
fof(f1113,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f1114,plain,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f1116,plain,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f1117,plain,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f1118,plain,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f421]) ).
fof(f1120,plain,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f423]) ).
fof(f1123,plain,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f426]) ).
fof(f1124,plain,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f427]) ).
fof(f1128,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f1129,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f1130,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f1131,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f1132,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f1133,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f1141,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f444]) ).
fof(f1142,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f445]) ).
fof(f1146,plain,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f449]) ).
fof(f1151,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f454]) ).
fof(f1186,definition,
( sQ1_spl
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1196,plain,
! [X0] :
( ~ c_lessequals(v_x(X0),X0,tc_RealDef_Oreal)
| v_x(X0) = X0 ),
inference(resolution,[status(thm)],[f992,f1048]) ).
fof(f1199,plain,
! [X0] :
( c_lessequals(X0,v_x(X0),tc_RealDef_Oreal)
| v_x(X0) = X0 ),
inference(resolution,[status(thm)],[f1196,f947]) ).
fof(f1204,plain,
( ~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_r = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1005,f938]) ).
fof(f1205,plain,
! [X0] :
( ~ c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f1005,f1046]) ).
fof(f1210,definition,
( sQ2_spl
<=> v_r = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1211,plain,
( ~ sQ2_spl
| v_r = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1210]) ).
fof(f1212,plain,
( sQ2_spl
| v_r != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1210]) ).
fof(f1213,definition,
( sQ3_spl
<=> c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1215,plain,
( sQ3_spl
| ~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1213]) ).
fof(f1216,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1204,f1210,f1213]) ).
fof(f1235,plain,
! [X0,X1] :
( v_r = c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f965,f1205]) ).
fof(f1236,plain,
! [X0,X1] :
( v_x(X1) = X1
| ~ c_lessequals(v_x(X1),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f965,f1196]) ).
fof(f1237,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X2,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f965,f1005]) ).
fof(f1239,plain,
! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(paramodulation,[status(thm)],[f1047,f983]) ).
fof(f1241,plain,
! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[status(thm)],[f1047,f1239]) ).
fof(f1264,plain,
! [X0] :
( v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1235,f983]) ).
fof(f1265,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X0,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1235,f965]) ).
fof(f1267,plain,
! [X0,X1] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1235,f947]) ).
fof(f1277,definition,
! [X0] :
( sQ4_spl
<=> X0 = v_r ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1278,plain,
! [X0] :
( ~ sQ4_spl
| X0 = v_r ),
inference(component_clause,[status(thm)],[f1277]) ).
fof(f1280,definition,
! [X1] :
( sQ5_spl
<=> X1 = X1 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1284,plain,
! [X0] :
( sQ3_spl
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1215,f965]) ).
fof(f1300,definition,
! [X0] :
( sQ6_spl
<=> ( v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1326,definition,
! [X0] :
( sQ7_spl
<=> X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1327,plain,
! [X0] :
( ~ sQ7_spl
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1326]) ).
fof(f1374,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),tc_Int_Oint)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(X1,tc_Int_Oint),tc_Int_Oint)
| ~ class_Int_Onumber(tc_Int_Oint) ),
inference(resolution,[status(thm)],[f1089,f502]) ).
fof(f1375,definition,
( sQ8_spl
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1377,plain,
( sQ8_spl
| ~ class_Int_Onumber(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f1375]) ).
fof(f1378,definition,
! [X0,X1] :
( sQ9_spl
<=> ( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),tc_Int_Oint)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(X1,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1381,plain,
( sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1374,f1375,f1378]) ).
fof(f1382,plain,
! [X0,X1] :
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(X1,tc_Int_Oint),tc_Int_Oint)
| ~ class_Int_Onumber(tc_Int_Oint) ),
inference(resolution,[status(thm)],[f503,f1089]) ).
fof(f1383,definition,
! [X0,X1] :
( sQ10_spl
<=> ( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(X1,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1386,plain,
( sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1382,f1375,f1383]) ).
fof(f1387,plain,
! [X0,X1] :
( X1 = X1
| ~ class_Int_Onumber__ring(X0)
| ~ class_Int_Oring__char__0(X0) ),
inference(equality_resolution,[status(thm)],[f505]) ).
fof(f1388,definition,
! [X0] :
( sQ11_spl
<=> ( ~ class_Int_Onumber__ring(X0)
| ~ class_Int_Oring__char__0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f1389,plain,
! [X0] :
( ~ sQ11_spl
| ~ class_Int_Onumber__ring(X0)
| ~ class_Int_Oring__char__0(X0) ),
inference(component_clause,[status(thm)],[f1388]) ).
fof(f1391,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f1387,f1388,f1280]) ).
fof(f1392,plain,
! [X0] :
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
inference(resolution,[status(thm)],[f506,f1092]) ).
fof(f1393,definition,
( sQ12_spl
<=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f1395,plain,
( sQ12_spl
| ~ class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f1393]) ).
fof(f1396,definition,
! [X0] :
( sQ13_spl
<=> ( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f1399,plain,
( sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1392,f1393,f1396]) ).
fof(f1400,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1395,f1079]) ).
fof(f1401,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f1400]) ).
fof(f1417,plain,
! [X0,X1] :
( ~ c_lessequals(v_r,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f1264,f965]) ).
fof(f1422,definition,
( sQ14_spl
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f1423,plain,
( ~ sQ14_spl
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1422]) ).
fof(f1424,plain,
( sQ14_spl
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1422]) ).
fof(f1443,definition,
( sQ17_spl
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f1457,definition,
( sQ20_spl
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1470,plain,
! [X0] :
( ~ sQ14_spl
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1423,f934]) ).
fof(f1472,plain,
! [X0] :
( ~ sQ14_spl
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1423,f934]) ).
fof(f1475,plain,
( ~ sQ14_spl
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1423,f1470]) ).
fof(f1491,definition,
! [X0] :
( sQ23_spl
<=> ~ class_RealVector_Oreal__algebra__1(X0) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1492,plain,
! [X0] :
( ~ sQ23_spl
| ~ class_RealVector_Oreal__algebra__1(X0) ),
inference(component_clause,[status(thm)],[f1491]) ).
fof(f1518,plain,
! [X0,X1,X2] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex),X2,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X2,tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1265,f947]) ).
fof(f1520,definition,
! [X0] :
( sQ24_spl
<=> ( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f1521,plain,
! [X0] :
( ~ sQ24_spl
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1520]) ).
fof(f1524,plain,
! [X0,X1] :
( ~ sQ2_spl
| X1 = c_HOL_Ozero__class_Ozero(X0)
| c_RealVector_Onorm__class_Onorm(X1,X0) != v_r
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(backward_demodulation,[status(thm)],[f1211,f509]) ).
fof(f1576,plain,
! [X0,X1] :
( v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1267,f1235]) ).
fof(f1578,definition,
! [X1,X2] :
( sQ25_spl
<=> ( ~ c_lessequals(X2,c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(v_r,X2,tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f1582,plain,
sQ6_spl,
inference(split_clause,[status(thm)],[f1576,f1300]) ).
fof(f1606,definition,
( sQ27_spl
<=> v_r = c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f1607,plain,
( ~ sQ27_spl
| v_r = c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1606]) ).
fof(f1637,plain,
! [X0,X1] :
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Int_Onumber(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1129,f503]) ).
fof(f1638,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Int_Onumber(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1129,f502]) ).
fof(f1639,definition,
( sQ29_spl
<=> class_Int_Onumber(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f1641,plain,
( sQ29_spl
| ~ class_Int_Onumber(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1639]) ).
fof(f1642,definition,
! [X0,X1] :
( sQ30_spl
<=> ( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1645,plain,
( sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f1637,f1639,f1642]) ).
fof(f1646,definition,
! [X0,X1] :
( sQ31_spl
<=> ( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1649,plain,
( sQ31_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f1638,f1639,f1646]) ).
fof(f1650,plain,
! [X0] :
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1132,f506]) ).
fof(f1651,definition,
( sQ32_spl
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1653,plain,
( sQ32_spl
| ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1651]) ).
fof(f1654,definition,
! [X0] :
( sQ33_spl
<=> ( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f1657,plain,
( sQ33_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f1650,f1651,f1654]) ).
fof(f1658,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1653,f1116]) ).
fof(f1659,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f1658]) ).
fof(f1732,plain,
( c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f524,f1141]) ).
fof(f1733,plain,
( c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f524,f1113]) ).
fof(f1734,definition,
( sQ36_spl
<=> class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f1736,plain,
( sQ36_spl
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f1734]) ).
fof(f1737,definition,
( sQ37_spl
<=> c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f1738,plain,
( ~ sQ37_spl
| c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f1737]) ).
fof(f1740,plain,
( sQ37_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f1732,f1734,f1737]) ).
fof(f1741,definition,
( sQ38_spl
<=> class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f1743,plain,
( sQ38_spl
| ~ class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1741]) ).
fof(f1744,definition,
( sQ39_spl
<=> c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f1745,plain,
( ~ sQ39_spl
| c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1744]) ).
fof(f1747,plain,
( sQ39_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f1733,f1741,f1744]) ).
fof(f1748,plain,
( sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1743,f1118]) ).
fof(f1749,plain,
sQ38_spl,
inference(contradiction_clause,[status(thm)],[f1748]) ).
fof(f1750,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1736,f1142]) ).
fof(f1751,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f1750]) ).
fof(f1777,plain,
( ~ sQ14_spl
| sQ3_spl
| ~ c_lessequals(v_r,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1284,f1475]) ).
fof(f1785,plain,
( ~ sQ14_spl
| sQ3_spl
| ~ c_HOL_Oord__class_Oless(v_r,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1777,f971]) ).
fof(f1786,plain,
( ~ sQ14_spl
| sQ3_spl
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1777,f947]) ).
fof(f1787,plain,
( ~ sQ14_spl
| sQ3_spl
| ~ c_lessequals(v_r,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_r = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1785,f992]) ).
fof(f1788,definition,
( sQ40_spl
<=> v_r = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1789,plain,
( ~ sQ40_spl
| v_r = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1788]) ).
fof(f1791,definition,
( sQ41_spl
<=> c_lessequals(v_r,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1794,plain,
( ~ sQ14_spl
| sQ3_spl
| ~ sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1787,f1788,f1791,f1213,f1422]) ).
fof(f1796,plain,
( ~ sQ14_spl
| sQ3_spl
| ~ sQ40_spl
| ~ c_lessequals(v_r,v_r,tc_RealDef_Oreal) ),
inference(backward_demodulation,[status(thm)],[f1789,f1777]) ).
fof(f1798,plain,
( ~ sQ14_spl
| sQ3_spl
| ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1796,f963]) ).
fof(f1799,plain,
( ~ sQ14_spl
| sQ3_spl
| ~ sQ40_spl ),
inference(contradiction_clause,[status(thm)],[f1798]) ).
fof(f1817,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1377,f1093]) ).
fof(f1818,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f1817]) ).
fof(f1819,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1641,f1133]) ).
fof(f1820,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f1819]) ).
fof(f1822,plain,
! [X0] : c_lessequals(X0,X0,tc_Int_Oint),
inference(resolution,[status(thm)],[f967,f1090]) ).
fof(f1825,plain,
! [X0] :
( ~ c_lessequals(X0,X0,tc_RealDef_Oreal)
| X0 = X0
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f975,f992]) ).
fof(f1826,definition,
( sQ44_spl
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1828,plain,
( sQ44_spl
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1826]) ).
fof(f1829,definition,
! [X0] :
( sQ45_spl
<=> ( ~ c_lessequals(X0,X0,tc_RealDef_Oreal)
| X0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f1832,plain,
( sQ45_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f1825,f1826,f1829]) ).
fof(f1833,plain,
( sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1828,f1128]) ).
fof(f1834,plain,
sQ44_spl,
inference(contradiction_clause,[status(thm)],[f1833]) ).
fof(f1859,plain,
! [X0,X1] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_lessequals(v_r,X1,tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f1417,f947]) ).
fof(f1861,definition,
! [X0] :
( sQ46_spl
<=> ( ~ c_lessequals(v_r,c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1898,definition,
( sQ49_spl
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1900,plain,
( sQ49_spl
| ~ class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1898]) ).
fof(f1903,definition,
( sQ50_spl
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1905,plain,
( sQ50_spl
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1903]) ).
fof(f1926,plain,
! [X0,X1] :
( ~ c_lessequals(v_r,c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f1859,f1417]) ).
fof(f1933,plain,
sQ46_spl,
inference(split_clause,[status(thm)],[f1926,f1861]) ).
fof(f1961,plain,
! [X0] :
( sQ3_spl
| ~ sQ14_spl
| ~ c_lessequals(v_r,c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1472,f1284]) ).
fof(f2022,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(X3,c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X2),tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_xa(X2),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1518,f1265]) ).
fof(f2028,plain,
sQ25_spl,
inference(split_clause,[status(thm)],[f2022,f1578]) ).
fof(f2166,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1237,f938]) ).
fof(f2170,plain,
! [X0] :
( ~ sQ14_spl
| sQ3_spl
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = v_r
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1237,f1786]) ).
fof(f2190,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X2,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1237,f971]) ).
fof(f2193,definition,
( sQ53_spl
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f2195,plain,
( sQ53_spl
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f2193]) ).
fof(f2197,plain,
( sQ2_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f2166,f1520,f1210]) ).
fof(f2202,definition,
! [X0] :
( sQ55_spl
<=> ( ~ c_lessequals(v_r,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f2205,plain,
( ~ sQ14_spl
| sQ3_spl
| sQ40_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f2170,f2202,f1788,f1213,f1422]) ).
fof(f2247,plain,
! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f652,f1097]) ).
fof(f2256,plain,
! [X0] :
( v_x(X0) = X0
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(v_x(X0),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f2247,f1236]) ).
fof(f2259,plain,
! [X0] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
inference(resolution,[status(thm)],[f2247,f1005]) ).
fof(f2267,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ2_spl
| ~ c_lessequals(X0,v_r,tc_RealDef_Oreal)
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f1211,f1521]) ).
fof(f2276,plain,
( ~ sQ24_spl
| ~ sQ2_spl
| ~ c_lessequals(v_r,v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f2267,f963]) ).
fof(f2286,plain,
( ~ sQ24_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2276,f963]) ).
fof(f2287,plain,
( ~ sQ24_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f2286]) ).
fof(f2315,plain,
( sQ3_spl
| ~ sQ2_spl
| ~ c_lessequals(v_r,v_r,tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f1211,f1215]) ).
fof(f2316,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2315,f963]) ).
fof(f2317,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f2316]) ).
fof(f2345,plain,
! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0,
inference(resolution,[status(thm)],[f1027,f1124]) ).
fof(f2346,plain,
! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint) = X0,
inference(resolution,[status(thm)],[f1027,f1084]) ).
fof(f2354,plain,
! [X0] : c_lessequals(v_x(X0),c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(backward_demodulation,[status(thm)],[f2345,f1241]) ).
fof(f2377,plain,
! [X0] :
( v_x(X0) = X0
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f2354,f1236]) ).
fof(f2450,plain,
! [X0] :
( c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_x(X0) = X0 ),
inference(resolution,[status(thm)],[f2377,f947]) ).
fof(f2473,plain,
! [X0] :
( X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) != X0 ),
inference(resolution,[status(thm)],[f679,f1104]) ).
fof(f2495,plain,
! [X0] :
( ~ sQ39_spl
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X0,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1745,f508]) ).
fof(f2497,definition,
! [X0] :
( sQ62_spl
<=> ( X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X0,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f2500,plain,
( ~ sQ39_spl
| sQ62_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f2495,f1741,f2497,f1744]) ).
fof(f2502,plain,
! [X0] :
( ~ sQ37_spl
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f1738,f508]) ).
fof(f2504,definition,
! [X0] :
( sQ63_spl
<=> ( X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f2505,plain,
! [X0] :
( ~ sQ63_spl
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f2504]) ).
fof(f2507,plain,
( ~ sQ37_spl
| sQ63_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f2502,f1734,f2504,f1737]) ).
fof(f2609,definition,
( sQ64_spl
<=> c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f2624,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Int_Oint),
inference(resolution,[status(thm)],[f574,f1075]) ).
fof(f2633,plain,
! [X0] :
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f568,f992]) ).
fof(f2634,definition,
( sQ65_spl
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f2636,plain,
( sQ65_spl
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f2634]) ).
fof(f2637,definition,
! [X0] :
( sQ66_spl
<=> ( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f2640,plain,
( sQ66_spl
| ~ sQ65_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f2633,f1651,f2634,f2637]) ).
fof(f2641,plain,
( sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2636,f1132]) ).
fof(f2642,plain,
sQ65_spl,
inference(contradiction_clause,[status(thm)],[f2641]) ).
fof(f2700,plain,
! [X0] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f584,f1141]) ).
fof(f2715,plain,
! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f861,f1110]) ).
fof(f2719,plain,
! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f863,f1110]) ).
fof(f2839,plain,
! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f907,f1097]) ).
fof(f2842,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f945,f1130]) ).
fof(f2843,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_Int_Oint) ),
inference(resolution,[status(thm)],[f945,f1090]) ).
fof(f2845,plain,
! [X0,X1] : ~ c_HOL_Oord__class_Oless(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f2842,f803]) ).
fof(f2853,plain,
! [X0,X1] :
( c_lessequals(X1,X0,tc_Int_Oint)
| c_lessequals(X0,X1,tc_Int_Oint) ),
inference(resolution,[status(thm)],[f948,f1089]) ).
fof(f2964,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_Int_Oint)
| c_lessequals(X0,X1,tc_Int_Oint) ),
inference(resolution,[status(thm)],[f970,f1088]) ).
fof(f3000,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1018,f1128]) ).
fof(f3001,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_Int_Oint)
| ~ c_lessequals(X0,X1,tc_Int_Oint) ),
inference(resolution,[status(thm)],[f1018,f1088]) ).
fof(f3002,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f595,f992]) ).
fof(f3003,definition,
( sQ73_spl
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f3005,plain,
( sQ73_spl
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f3003]) ).
fof(f3006,definition,
! [X0,X1,X2] :
( sQ74_spl
<=> ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f3009,plain,
( sQ74_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f3002,f3003,f3006]) ).
fof(f3010,plain,
( sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3005,f1100]) ).
fof(f3011,plain,
sQ73_spl,
inference(contradiction_clause,[status(thm)],[f3010]) ).
fof(f3015,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f599,f905]) ).
fof(f3016,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X1,X2),X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f599,f803]) ).
fof(f3017,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X0,X2,tc_RealDef_Oreal)
| X0 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f599,f992]) ).
fof(f3018,definition,
( sQ75_spl
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f3020,plain,
( sQ75_spl
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f3018]) ).
fof(f3021,definition,
! [X0,X1] :
( sQ76_spl
<=> ( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f3024,plain,
( sQ76_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f3015,f3018,f3021]) ).
fof(f3025,definition,
! [X0,X1,X2] :
( sQ77_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X1,X2),X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f3028,plain,
( sQ77_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f3016,f3018,f3025]) ).
fof(f3029,definition,
! [X0,X1,X2] :
( sQ78_spl
<=> ( ~ c_lessequals(X0,X2,tc_RealDef_Oreal)
| X0 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f3032,plain,
( sQ78_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f3017,f3018,f3029]) ).
fof(f3033,plain,
( sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3020,f1096]) ).
fof(f3034,plain,
sQ75_spl,
inference(contradiction_clause,[status(thm)],[f3033]) ).
fof(f3099,plain,
! [X0,X1] : ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f3000,f803]) ).
fof(f3103,plain,
! [X0,X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f3099,f947]) ).
fof(f3108,plain,
! [X0,X1] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1019,f1129]) ).
fof(f3116,plain,
! [X0] :
( v_x(X0) = X0
| c_HOL_Oord__class_Oless(X0,c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3108,f2377]) ).
fof(f3120,plain,
! [X0] :
( v_x(X0) = X0
| c_HOL_Oord__class_Oless(X0,c_HOL_Oabs__class_Oabs(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3108,f2256]) ).
fof(f3122,plain,
! [X0] :
( c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0
| c_HOL_Oord__class_Oless(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3108,f2259]) ).
fof(f3125,plain,
( sQ3_spl
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3108,f1215]) ).
fof(f3127,plain,
! [X0] :
( v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3108,f1205]) ).
fof(f3138,plain,
! [X0] :
( v_x(X0) = X0
| c_HOL_Oord__class_Oless(X0,v_x(X0),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3108,f1196]) ).
fof(f3141,plain,
! [X0] :
( ~ sQ24_spl
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3108,f1521]) ).
fof(f3166,plain,
! [X0] :
( sQ3_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_r,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3125,f599]) ).
fof(f3168,definition,
! [X0] :
( sQ82_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_r,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f3171,plain,
( sQ3_spl
| sQ82_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f3166,f3018,f3168,f1213]) ).
fof(f3194,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_x(X0),X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| v_x(X0) = X0 ),
inference(resolution,[status(thm)],[f3138,f599]) ).
fof(f3235,definition,
! [X0,X1] :
( sQ93_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_x(X0),X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_x(X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f3238,plain,
( ~ sQ75_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f3194,f3235,f3018]) ).
fof(f3476,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f603,f992]) ).
fof(f3477,definition,
! [X0,X1,X2] :
( sQ138_spl
<=> ( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f3480,plain,
( sQ138_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f3476,f3003,f3477]) ).
fof(f3506,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| v_x(X0) = X0 ),
inference(resolution,[status(thm)],[f3116,f599]) ).
fof(f3544,definition,
! [X0,X1] :
( sQ148_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_x(X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f3547,plain,
( ~ sQ75_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f3506,f3544,f3018]) ).
fof(f3574,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(v_x(X0),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| v_x(X0) = X0 ),
inference(resolution,[status(thm)],[f3120,f599]) ).
fof(f3612,definition,
! [X0,X1] :
( sQ159_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(v_x(X0),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_x(X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f3615,plain,
( ~ sQ75_spl
| sQ159_spl ),
inference(split_clause,[status(thm)],[f3574,f3612,f3018]) ).
fof(f3620,plain,
( ~ sQ24_spl
| v_x(v_r) = v_r
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3141,f2450]) ).
fof(f3625,plain,
( ~ sQ24_spl
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3141,f2247]) ).
fof(f3633,plain,
( ~ sQ24_spl
| v_x(v_r) = v_r
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x(v_r),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3141,f1199]) ).
fof(f3634,plain,
! [X0] :
( ~ sQ24_spl
| c_HOL_Oord__class_Oless(X0,v_r,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3141,f3108]) ).
fof(f3636,plain,
! [X0] :
( ~ sQ24_spl
| ~ c_HOL_Oord__class_Oless(v_r,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3141,f971]) ).
fof(f3637,plain,
! [X0] :
( ~ sQ24_spl
| c_lessequals(X0,v_r,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3141,f947]) ).
fof(f3639,definition,
( sQ161_spl
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f3640,plain,
( ~ sQ161_spl
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f3639]) ).
fof(f3642,definition,
( sQ162_spl
<=> v_x(v_r) = v_r ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f3643,plain,
( ~ sQ162_spl
| v_x(v_r) = v_r ),
inference(component_clause,[status(thm)],[f3642]) ).
fof(f3645,plain,
( ~ sQ24_spl
| sQ162_spl
| sQ161_spl ),
inference(split_clause,[status(thm)],[f3620,f3639,f3642,f1520]) ).
fof(f3669,definition,
( sQ169_spl
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x(v_r),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f3670,plain,
( ~ sQ169_spl
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x(v_r),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f3669]) ).
fof(f3671,plain,
( sQ169_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x(v_r),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f3669]) ).
fof(f3672,plain,
( ~ sQ24_spl
| sQ162_spl
| sQ169_spl ),
inference(split_clause,[status(thm)],[f3633,f3669,f3642,f1520]) ).
fof(f3745,definition,
( sQ175_spl
<=> v_x(v_r) = c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f3746,plain,
( ~ sQ175_spl
| v_x(v_r) = c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f3745]) ).
fof(f3747,plain,
( sQ175_spl
| v_x(v_r) != c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f3745]) ).
fof(f3908,plain,
( ~ sQ175_spl
| ~ sQ162_spl
| v_r = c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f3643,f3746]) ).
fof(f3909,plain,
( ~ sQ175_spl
| ~ sQ162_spl
| v_r = c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f3643,f3908]) ).
fof(f3910,plain,
( ~ sQ175_spl
| ~ sQ162_spl
| v_r = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3909,f2473]) ).
fof(f3915,plain,
( ~ sQ175_spl
| ~ sQ162_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f3910,f1210,f3642,f3745]) ).
fof(f4204,plain,
( ~ sQ169_spl
| ~ c_HOL_Oord__class_Oless(v_x(v_r),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3670,f2842]) ).
fof(f4412,plain,
( sQ2_spl
| c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) != v_r ),
inference(resolution,[status(thm)],[f2473,f1212]) ).
fof(f4519,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2195,f963]) ).
fof(f4520,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f4519]) ).
fof(f4521,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1905,f1129]) ).
fof(f4522,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f4521]) ).
fof(f4523,plain,
( sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1900,f1130]) ).
fof(f4524,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f4523]) ).
fof(f4525,plain,
( ~ sQ27_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1607,f4412]) ).
fof(f4526,plain,
( ~ sQ27_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f4525]) ).
fof(f4637,plain,
( ~ sQ24_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3625,f2842]) ).
fof(f4638,plain,
! [X0] :
( ~ sQ24_spl
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3625,f2190]) ).
fof(f4640,plain,
! [X0] :
( ~ sQ24_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3625,f599]) ).
fof(f4641,definition,
! [X0] :
( sQ268_spl
<=> ( ~ c_lessequals(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f4644,definition,
( sQ269_spl
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f4645,plain,
( ~ sQ269_spl
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f4644]) ).
fof(f4647,plain,
( ~ sQ24_spl
| sQ269_spl
| sQ268_spl ),
inference(split_clause,[status(thm)],[f4638,f4641,f4644,f1520]) ).
fof(f4648,definition,
! [X0] :
( sQ270_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f4651,plain,
( ~ sQ24_spl
| sQ270_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f4640,f3018,f4648,f1520]) ).
fof(f4652,plain,
( ~ sQ24_spl
| ~ sQ269_spl
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(backward_demodulation,[status(thm)],[f4645,f3625]) ).
fof(f4659,plain,
( ~ sQ24_spl
| ~ sQ269_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4652,f976]) ).
fof(f4660,plain,
( ~ sQ24_spl
| ~ sQ269_spl ),
inference(contradiction_clause,[status(thm)],[f4659]) ).
fof(f4879,plain,
( ~ sQ24_spl
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f4637,f992]) ).
fof(f4880,definition,
( sQ279_spl
<=> c_lessequals(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f4883,plain,
( ~ sQ24_spl
| ~ sQ279_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f4879,f4644,f4880,f1520]) ).
fof(f5137,plain,
! [X0] :
( ~ sQ24_spl
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3634,f3000]) ).
fof(f5142,plain,
! [X0,X1] :
( ~ sQ24_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3634,f599]) ).
fof(f5146,definition,
( sQ290_spl
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f5153,definition,
! [X0,X1] :
( sQ292_spl
<=> ( ~ c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f5154,plain,
! [X0,X1] :
( ~ sQ292_spl
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5153]) ).
fof(f5168,definition,
! [X0,X1] :
( sQ295_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,v_r,tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f5171,plain,
( ~ sQ24_spl
| ~ sQ75_spl
| sQ295_spl ),
inference(split_clause,[status(thm)],[f5142,f5168,f3018,f1520]) ).
fof(f5182,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_r,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f3127,f599]) ).
fof(f5184,definition,
! [X0,X1] :
( sQ296_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_r,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f5187,plain,
( ~ sQ75_spl
| sQ296_spl ),
inference(split_clause,[status(thm)],[f5182,f5184,f3018]) ).
fof(f5213,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
inference(resolution,[status(thm)],[f3122,f599]) ).
fof(f5228,definition,
! [X0,X1] :
( sQ300_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f5231,plain,
( ~ sQ75_spl
| sQ300_spl ),
inference(split_clause,[status(thm)],[f5213,f5228,f3018]) ).
fof(f5244,definition,
( sQ302_spl
<=> c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f5261,plain,
! [X0] :
( ~ sQ24_spl
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3637,f2842]) ).
fof(f5265,plain,
! [X0,X1] :
( ~ sQ24_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| c_lessequals(X0,v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3637,f599]) ).
fof(f5282,definition,
! [X0,X1] :
( sQ305_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,v_r,tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f5285,plain,
( ~ sQ24_spl
| ~ sQ75_spl
| sQ305_spl ),
inference(split_clause,[status(thm)],[f5265,f5282,f3018,f1520]) ).
fof(f5305,definition,
( sQ307_spl
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f5306,plain,
( ~ sQ307_spl
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5305]) ).
fof(f5307,plain,
( sQ307_spl
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5305]) ).
fof(f5576,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f2719,f700]) ).
fof(f5579,definition,
! [X0] :
( sQ318_spl
<=> c_lessequals(X0,X0,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f5590,definition,
! [X0,X1] :
( sQ321_spl
<=> ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition]) ).
fof(f5591,plain,
! [X0,X1] :
( ~ sQ321_spl
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5590]) ).
fof(f5593,plain,
( ~ sQ20_spl
| sQ321_spl ),
inference(split_clause,[status(thm)],[f5576,f5590,f1457]) ).
fof(f5626,plain,
! [X0] : c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f666,f1097]) ).
fof(f5718,plain,
( sQ14_spl
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f2715,f1424]) ).
fof(f5719,plain,
( sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5718]) ).
fof(f5720,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f5719]) ).
fof(f5852,plain,
( ~ sQ37_spl
| ~ sQ63_spl
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f1738,f2505]) ).
fof(f5853,definition,
( sQ330_spl
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f5855,plain,
( sQ330_spl
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f5853]) ).
fof(f5856,plain,
( ~ sQ37_spl
| ~ sQ63_spl
| sQ17_spl
| ~ sQ330_spl ),
inference(split_clause,[status(thm)],[f5852,f5853,f1443,f2504,f1737]) ).
fof(f5904,plain,
( ~ sQ24_spl
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f5137,f963]) ).
fof(f5953,plain,
( ~ sQ24_spl
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f5261,f3637]) ).
fof(f5956,plain,
( ~ sQ24_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f5953,f1186,f1520]) ).
fof(f5962,plain,
( ~ sQ161_spl
| ~ sQ307_spl
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(backward_demodulation,[status(thm)],[f5306,f3640]) ).
fof(f5967,plain,
( ~ sQ307_spl
| v_x(v_r) = v_r
| c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f5306,f3116]) ).
fof(f5984,plain,
( ~ sQ161_spl
| ~ sQ307_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5962,f976]) ).
fof(f5985,plain,
( ~ sQ161_spl
| ~ sQ307_spl ),
inference(contradiction_clause,[status(thm)],[f5984]) ).
fof(f5986,plain,
( sQ307_spl
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f5307,f2473]) ).
fof(f5987,plain,
( sQ307_spl
| v_x(v_r) != c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f2345,f5986]) ).
fof(f6101,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f656,f1098]) ).
fof(f6102,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint)
| ~ class_Orderings_Olinorder(tc_Int_Oint) ),
inference(resolution,[status(thm)],[f656,f1065]) ).
fof(f6103,definition,
! [X0] :
( sQ336_spl
<=> ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f6106,plain,
( sQ336_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f6101,f1903,f6103]) ).
fof(f6107,definition,
( sQ337_spl
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f6109,plain,
( sQ337_spl
| ~ class_Orderings_Olinorder(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f6107]) ).
fof(f6110,definition,
! [X0] :
( sQ338_spl
<=> ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f6113,plain,
( sQ338_spl
| ~ sQ337_spl ),
inference(split_clause,[status(thm)],[f6102,f6107,f6110]) ).
fof(f6114,plain,
( sQ337_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6109,f1089]) ).
fof(f6115,plain,
sQ337_spl,
inference(contradiction_clause,[status(thm)],[f6114]) ).
fof(f6134,plain,
! [X0] :
( sQ3_spl
| ~ sQ14_spl
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1961,f3108]) ).
fof(f6354,plain,
! [X0] : c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f711,f1141]) ).
fof(f6358,plain,
! [X0] : c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f1047,f6354]) ).
fof(f6362,plain,
! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(paramodulation,[status(thm)],[f6354,f2839]) ).
fof(f6373,plain,
! [X0] : c_HOL_Oabs__class_Oabs(v_x(X0),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f5626,f6358]) ).
fof(f6374,plain,
! [X0] : c_HOL_Oabs__class_Oabs(v_x(X0),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),
inference(forward_demodulation,[status(thm)],[f1047,f6373]) ).
fof(f6378,plain,
! [X0] :
( v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f6362,f1235]) ).
fof(f6389,definition,
! [X1] :
( sQ350_spl
<=> v_r = c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f6390,plain,
! [X0] :
( ~ sQ350_spl
| v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f6389]) ).
fof(f6394,plain,
( sQ350_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6378,f1213,f6389]) ).
fof(f6471,plain,
! [X0,X1] :
( sQ3_spl
| ~ sQ14_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_r,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f6134,f599]) ).
fof(f6475,definition,
! [X0,X1] :
( sQ351_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_r,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f6478,plain,
( sQ3_spl
| ~ sQ14_spl
| sQ351_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f6471,f3018,f6475,f1422,f1213]) ).
fof(f6753,plain,
! [X0,X1] : c_HOL_Oabs__class_Oabs(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal) = v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),
inference(resolution,[status(thm)],[f886,f2845]) ).
fof(f6760,plain,
! [X0] :
( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f886,f568]) ).
fof(f6767,plain,
( ~ sQ24_spl
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r ),
inference(resolution,[status(thm)],[f886,f3636]) ).
fof(f6768,plain,
( ~ sQ169_spl
| c_HOL_Oabs__class_Oabs(v_x(v_r),tc_RealDef_Oreal) = v_x(v_r) ),
inference(resolution,[status(thm)],[f886,f4204]) ).
fof(f6777,plain,
c_HOL_Oabs__class_Oabs(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_RealDef_Oreal) = v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(resolution,[status(thm)],[f886,f1048]) ).
fof(f6781,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
inference(resolution,[status(thm)],[f886,f603]) ).
fof(f6782,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
inference(resolution,[status(thm)],[f886,f595]) ).
fof(f6791,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
inference(resolution,[status(thm)],[f886,f599]) ).
fof(f6794,plain,
( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f886,f975]) ).
fof(f6811,definition,
! [X0] :
( sQ359_spl
<=> ( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(X0,tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f6814,plain,
( ~ sQ65_spl
| ~ sQ32_spl
| sQ359_spl ),
inference(split_clause,[status(thm)],[f6760,f6811,f1651,f2634]) ).
fof(f6824,plain,
( ~ sQ24_spl
| sQ20_spl
| sQ302_spl ),
inference(split_clause,[status(thm)],[f6767,f5244,f1457,f1520]) ).
fof(f6825,plain,
( ~ sQ169_spl
| c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal) = v_x(v_r) ),
inference(forward_demodulation,[status(thm)],[f6374,f6768]) ).
fof(f6826,plain,
( ~ sQ169_spl
| sQ175_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6825,f3747]) ).
fof(f6827,plain,
( ~ sQ169_spl
| sQ175_spl ),
inference(contradiction_clause,[status(thm)],[f6826]) ).
fof(f6841,plain,
c_HOL_Ouminus__class_Ouminus(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_RealDef_Oreal) = v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(forward_demodulation,[status(thm)],[f6374,f6777]) ).
fof(f6844,definition,
! [X0,X1,X2] :
( sQ364_spl
<=> ( ~ c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f6847,plain,
( ~ sQ73_spl
| sQ364_spl ),
inference(split_clause,[status(thm)],[f6781,f6844,f3003]) ).
fof(f6848,definition,
! [X0,X1,X2] :
( sQ365_spl
<=> ( ~ c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f6851,plain,
( ~ sQ73_spl
| sQ365_spl ),
inference(split_clause,[status(thm)],[f6782,f6848,f3003]) ).
fof(f6855,definition,
! [X0,X1] :
( sQ366_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f6858,plain,
( ~ sQ75_spl
| sQ366_spl ),
inference(split_clause,[status(thm)],[f6791,f6855,f3018]) ).
fof(f6861,plain,
( ~ sQ44_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f6794,f2609,f1826]) ).
fof(f6862,plain,
! [X0,X1] :
( ~ sQ321_spl
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f2719,f5591]) ).
fof(f6863,plain,
! [X0,X1] :
( ~ sQ321_spl
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(forward_subsumption_resolution,[status(thm)],[f6862,f963]) ).
fof(f6868,plain,
! [X0,X1] :
( ~ sQ292_spl
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f2719,f5154]) ).
fof(f6869,plain,
! [X0,X1] :
( ~ sQ292_spl
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f2719,f6868]) ).
fof(f6870,plain,
! [X0,X1] :
( ~ sQ292_spl
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(forward_subsumption_resolution,[status(thm)],[f6869,f976]) ).
fof(f6897,plain,
( sQ2_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1212,f1327]) ).
fof(f6943,plain,
( sQ2_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f6897]) ).
fof(f6948,plain,
( sQ330_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5855]) ).
fof(f6949,plain,
sQ330_spl,
inference(contradiction_clause,[status(thm)],[f6948]) ).
fof(f6956,plain,
( sQ307_spl
| ~ sQ175_spl ),
inference(split_clause,[status(thm)],[f5987,f3745,f5305]) ).
fof(f6974,definition,
( sQ371_spl
<=> c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f6975,plain,
( ~ sQ371_spl
| c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f6974]) ).
fof(f6977,plain,
( ~ sQ307_spl
| sQ162_spl
| sQ371_spl ),
inference(split_clause,[status(thm)],[f5967,f6974,f3642,f5305]) ).
fof(f7039,plain,
( ~ sQ321_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3099,f6863]) ).
fof(f7080,plain,
~ sQ321_spl,
inference(contradiction_clause,[status(thm)],[f7039]) ).
fof(f7092,plain,
( ~ sQ292_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f803,f6870]) ).
fof(f7097,plain,
~ sQ292_spl,
inference(contradiction_clause,[status(thm)],[f7092]) ).
fof(f7179,plain,
( ~ sQ2_spl
| c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal) = v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(forward_demodulation,[status(thm)],[f1211,f6841]) ).
fof(f7180,plain,
( ~ sQ2_spl
| c_HOL_Ouminus__class_Ouminus(v_x(v_r),tc_RealDef_Oreal) = v_x(v_r) ),
inference(forward_demodulation,[status(thm)],[f1211,f7179]) ).
fof(f7265,plain,
( ~ sQ371_spl
| ~ sQ2_spl
| c_HOL_Oord__class_Oless(v_r,v_r,tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f1211,f6975]) ).
fof(f7332,plain,
( ~ sQ371_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7265,f976]) ).
fof(f7333,plain,
( ~ sQ371_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f7332]) ).
fof(f7532,definition,
( sQ383_spl
<=> class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f7534,plain,
( sQ383_spl
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f7532]) ).
fof(f7543,definition,
( sQ386_spl
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f7545,plain,
( sQ386_spl
| ~ class_Int_Onumber__ring(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f7543]) ).
fof(f7550,plain,
( sQ383_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7534,f1067]) ).
fof(f7551,plain,
sQ383_spl,
inference(contradiction_clause,[status(thm)],[f7550]) ).
fof(f7552,plain,
( sQ386_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7545,f1092]) ).
fof(f7553,plain,
sQ386_spl,
inference(contradiction_clause,[status(thm)],[f7552]) ).
fof(f7714,plain,
! [X0,X1] :
( ~ sQ2_spl
| c_lessequals(v_r,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f1211,f3103]) ).
fof(f7792,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),v_r,tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f1211,f3099]) ).
fof(f7938,definition,
( sQ402_spl
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f7940,plain,
( sQ402_spl
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f7938]) ).
fof(f7945,definition,
( sQ404_spl
<=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f7947,plain,
( sQ404_spl
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f7945]) ).
fof(f7952,plain,
( sQ404_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7947,f1068]) ).
fof(f7953,plain,
sQ404_spl,
inference(contradiction_clause,[status(thm)],[f7952]) ).
fof(f7954,plain,
( sQ402_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7940,f1102]) ).
fof(f7955,plain,
sQ402_spl,
inference(contradiction_clause,[status(thm)],[f7954]) ).
fof(f8118,plain,
! [X0] :
( ~ sQ2_spl
| X0 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex) != v_r ),
inference(resolution,[status(thm)],[f1524,f1141]) ).
fof(f8125,plain,
! [X0] :
( ~ sQ350_spl
| ~ sQ2_spl
| v_xa(X0) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f8118,f6390]) ).
fof(f8136,plain,
! [X0,X1] :
( ~ sQ350_spl
| ~ sQ2_spl
| v_xa(X0) = v_xa(X1) ),
inference(paramodulation,[status(thm)],[f8125,f8125]) ).
fof(f8174,definition,
( sQ416_spl
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f8176,plain,
( sQ416_spl
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f8174]) ).
fof(f8181,plain,
( sQ416_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8176,f1151]) ).
fof(f8182,plain,
sQ416_spl,
inference(contradiction_clause,[status(thm)],[f8181]) ).
fof(f8209,plain,
! [X0,X1] :
( ~ sQ350_spl
| ~ sQ2_spl
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(X1),tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f8136,f1047]) ).
fof(f8214,plain,
! [X0,X1] :
( ~ sQ350_spl
| ~ sQ2_spl
| c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(v_x(X1),tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f1047,f8209]) ).
fof(f8411,plain,
! [X0,X1] :
( ~ sQ4_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f1278,f1278]) ).
fof(f8423,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ sQ2_spl
| c_lessequals(X0,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X1,X2),tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1278,f7714]) ).
fof(f8443,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ2_spl
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f8411,f8423]) ).
fof(f8447,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ sQ2_spl
| c_lessequals(X0,X1,X2) ),
inference(paramodulation,[status(thm)],[f8411,f8443]) ).
fof(f8449,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7792,f8447]) ).
fof(f8450,plain,
( ~ sQ2_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f8449]) ).
fof(f8478,definition,
( sQ422_spl
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f8480,plain,
( sQ422_spl
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f8478]) ).
fof(f8489,plain,
( sQ422_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8480,f1063]) ).
fof(f8490,plain,
sQ422_spl,
inference(contradiction_clause,[status(thm)],[f8489]) ).
fof(f8529,definition,
( sQ427_spl
<=> class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f8531,plain,
( sQ427_spl
| ~ class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f8529]) ).
fof(f8540,definition,
( sQ430_spl
<=> class_Ring__and__Field_Omult__mono(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f8542,plain,
( sQ430_spl
| ~ class_Ring__and__Field_Omult__mono(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f8540]) ).
fof(f8562,definition,
( sQ436_spl
<=> class_Ring__and__Field_Omult__mono1(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ436_spl])],[split_symbol_definition]) ).
fof(f8564,plain,
( sQ436_spl
| ~ class_Ring__and__Field_Omult__mono1(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f8562]) ).
fof(f8581,plain,
( sQ430_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8542,f1082]) ).
fof(f8582,plain,
sQ430_spl,
inference(contradiction_clause,[status(thm)],[f8581]) ).
fof(f8583,plain,
( sQ427_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8531,f1077]) ).
fof(f8584,plain,
sQ427_spl,
inference(contradiction_clause,[status(thm)],[f8583]) ).
fof(f8585,plain,
( sQ436_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8564,f1080]) ).
fof(f8586,plain,
sQ436_spl,
inference(contradiction_clause,[status(thm)],[f8585]) ).
fof(f8668,definition,
( sQ448_spl
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f8670,plain,
( sQ448_spl
| ~ class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f8668]) ).
fof(f8679,definition,
( sQ451_spl
<=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f8681,plain,
( sQ451_spl
| ~ class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f8679]) ).
fof(f8698,definition,
( sQ456_spl
<=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f8700,plain,
( sQ456_spl
| ~ class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f8698]) ).
fof(f8708,plain,
( sQ451_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8681,f1120]) ).
fof(f8709,plain,
sQ451_spl,
inference(contradiction_clause,[status(thm)],[f8708]) ).
fof(f8710,plain,
( sQ448_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8670,f1114]) ).
fof(f8711,plain,
sQ448_spl,
inference(contradiction_clause,[status(thm)],[f8710]) ).
fof(f8712,plain,
( sQ456_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8700,f1117]) ).
fof(f8713,plain,
sQ456_spl,
inference(contradiction_clause,[status(thm)],[f8712]) ).
fof(f9204,definition,
( sQ480_spl
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ480_spl])],[split_symbol_definition]) ).
fof(f9206,plain,
( sQ480_spl
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f9204]) ).
fof(f9211,definition,
( sQ482_spl
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ482_spl])],[split_symbol_definition]) ).
fof(f9213,plain,
( sQ482_spl
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f9211]) ).
fof(f9215,plain,
( sQ480_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9206,f1064]) ).
fof(f9216,plain,
sQ480_spl,
inference(contradiction_clause,[status(thm)],[f9215]) ).
fof(f9217,plain,
( sQ482_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9213,f1097]) ).
fof(f9218,plain,
sQ482_spl,
inference(contradiction_clause,[status(thm)],[f9217]) ).
fof(f9512,plain,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f575,f759]) ).
fof(f9513,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X2,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f575,f751]) ).
fof(f9514,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f575,f751]) ).
fof(f9517,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X0,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f575,f747]) ).
fof(f9518,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f575,f747]) ).
fof(f9523,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f575,f741]) ).
fof(f9524,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f575,f739]) ).
fof(f9541,definition,
! [X0,X1] :
( sQ509_spl
<=> ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f9544,plain,
( sQ509_spl
| ~ sQ448_spl ),
inference(split_clause,[status(thm)],[f9512,f8668,f9541]) ).
fof(f9545,definition,
! [X0,X1,X2] :
( sQ510_spl
<=> ( ~ c_lessequals(X2,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f9548,plain,
( sQ510_spl
| ~ sQ448_spl ),
inference(split_clause,[status(thm)],[f9513,f8668,f9545]) ).
fof(f9549,definition,
! [X0,X1,X2] :
( sQ511_spl
<=> ( ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition]) ).
fof(f9552,plain,
( sQ511_spl
| ~ sQ448_spl ),
inference(split_clause,[status(thm)],[f9514,f8668,f9549]) ).
fof(f9555,definition,
! [X0,X1,X2] :
( sQ512_spl
<=> ( ~ c_lessequals(X0,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ512_spl])],[split_symbol_definition]) ).
fof(f9558,plain,
( sQ512_spl
| ~ sQ451_spl ),
inference(split_clause,[status(thm)],[f9517,f8679,f9555]) ).
fof(f9559,definition,
! [X0,X1,X2] :
( sQ513_spl
<=> ( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ513_spl])],[split_symbol_definition]) ).
fof(f9562,plain,
( sQ513_spl
| ~ sQ451_spl ),
inference(split_clause,[status(thm)],[f9518,f8679,f9559]) ).
fof(f9567,definition,
! [X0,X1] :
( sQ514_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ514_spl])],[split_symbol_definition]) ).
fof(f9570,plain,
( sQ514_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f9523,f3018,f9567]) ).
fof(f9571,definition,
! [X0,X1] :
( sQ515_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ515_spl])],[split_symbol_definition]) ).
fof(f9574,plain,
( sQ515_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f9524,f3018,f9571]) ).
fof(f9633,plain,
! [X0] :
( ~ sQ2_spl
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| X0 = v_r ),
inference(forward_demodulation,[status(thm)],[f1211,f905]) ).
fof(f9634,plain,
! [X0] :
( ~ sQ2_spl
| c_HOL_Oord__class_Oless(v_r,c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| X0 = v_r ),
inference(forward_demodulation,[status(thm)],[f1211,f9633]) ).
fof(f9693,plain,
! [X0,X1] :
( c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f6753,f652]) ).
fof(f9694,definition,
! [X0,X1] :
( sQ516_spl
<=> c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ516_spl])],[split_symbol_definition]) ).
fof(f9697,plain,
( sQ516_spl
| ~ sQ482_spl ),
inference(split_clause,[status(thm)],[f9693,f9211,f9694]) ).
fof(f9708,plain,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f2624,f759]) ).
fof(f9709,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X2,X0,tc_Int_Oint)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(X1,X2,tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f2624,f751]) ).
fof(f9710,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X2,X1,tc_Int_Oint)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(X2,X0,tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f2624,f751]) ).
fof(f9713,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X0,X2,tc_Int_Oint)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(X1,X2,tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Omult__mono(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f2624,f747]) ).
fof(f9714,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X1,X2,tc_Int_Oint)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(X2,X0,tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Omult__mono(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f2624,f747]) ).
fof(f9719,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f2624,f741]) ).
fof(f9720,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f2624,f739]) ).
fof(f9736,definition,
! [X0,X1] :
( sQ517_spl
<=> ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ517_spl])],[split_symbol_definition]) ).
fof(f9739,plain,
( sQ517_spl
| ~ sQ427_spl ),
inference(split_clause,[status(thm)],[f9708,f8529,f9736]) ).
fof(f9740,definition,
! [X0,X1,X2] :
( sQ518_spl
<=> ( ~ c_lessequals(X2,X0,tc_Int_Oint)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(X1,X2,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ518_spl])],[split_symbol_definition]) ).
fof(f9743,plain,
( sQ518_spl
| ~ sQ427_spl ),
inference(split_clause,[status(thm)],[f9709,f8529,f9740]) ).
fof(f9744,definition,
! [X0,X1,X2] :
( sQ519_spl
<=> ( ~ c_lessequals(X2,X1,tc_Int_Oint)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(X2,X0,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ519_spl])],[split_symbol_definition]) ).
fof(f9747,plain,
( sQ519_spl
| ~ sQ427_spl ),
inference(split_clause,[status(thm)],[f9710,f8529,f9744]) ).
fof(f9750,definition,
! [X0,X1,X2] :
( sQ520_spl
<=> ( ~ c_lessequals(X0,X2,tc_Int_Oint)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(X1,X2,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f9753,plain,
( sQ520_spl
| ~ sQ430_spl ),
inference(split_clause,[status(thm)],[f9713,f8540,f9750]) ).
fof(f9754,definition,
! [X0,X1,X2] :
( sQ521_spl
<=> ( ~ c_lessequals(X1,X2,tc_Int_Oint)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(X2,X0,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ521_spl])],[split_symbol_definition]) ).
fof(f9757,plain,
( sQ521_spl
| ~ sQ430_spl ),
inference(split_clause,[status(thm)],[f9714,f8540,f9754]) ).
fof(f9762,definition,
! [X0,X1] :
( sQ522_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ522_spl])],[split_symbol_definition]) ).
fof(f9765,plain,
( sQ522_spl
| ~ sQ422_spl ),
inference(split_clause,[status(thm)],[f9719,f8478,f9762]) ).
fof(f9766,definition,
! [X0,X1] :
( sQ523_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ523_spl])],[split_symbol_definition]) ).
fof(f9769,plain,
( sQ523_spl
| ~ sQ422_spl ),
inference(split_clause,[status(thm)],[f9720,f8478,f9766]) ).
fof(f9892,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f2842,f741]) ).
fof(f9893,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f2842,f739]) ).
fof(f9895,definition,
! [X0,X1] :
( sQ531_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ531_spl])],[split_symbol_definition]) ).
fof(f9898,plain,
( ~ sQ75_spl
| sQ531_spl ),
inference(split_clause,[status(thm)],[f9892,f9895,f3018]) ).
fof(f9899,definition,
! [X0,X1] :
( sQ532_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ532_spl])],[split_symbol_definition]) ).
fof(f9902,plain,
( ~ sQ75_spl
| sQ532_spl ),
inference(split_clause,[status(thm)],[f9893,f9899,f3018]) ).
fof(f9920,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3000,f741]) ).
fof(f9921,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3000,f739]) ).
fof(f9923,definition,
! [X0,X1] :
( sQ533_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ533_spl])],[split_symbol_definition]) ).
fof(f9926,plain,
( ~ sQ75_spl
| sQ533_spl ),
inference(split_clause,[status(thm)],[f9920,f9923,f3018]) ).
fof(f9927,definition,
! [X0,X1] :
( sQ534_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ534_spl])],[split_symbol_definition]) ).
fof(f9930,plain,
( ~ sQ75_spl
| sQ534_spl ),
inference(split_clause,[status(thm)],[f9921,f9927,f3018]) ).
fof(f10044,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),tc_Int_Oint) ),
inference(resolution,[status(thm)],[f2843,f741]) ).
fof(f10045,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),tc_Int_Oint) ),
inference(resolution,[status(thm)],[f2843,f739]) ).
fof(f10046,definition,
! [X0,X1] :
( sQ538_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ538_spl])],[split_symbol_definition]) ).
fof(f10049,plain,
( ~ sQ422_spl
| sQ538_spl ),
inference(split_clause,[status(thm)],[f10044,f10046,f8478]) ).
fof(f10050,definition,
! [X0,X1] :
( sQ539_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ539_spl])],[split_symbol_definition]) ).
fof(f10053,plain,
( ~ sQ422_spl
| sQ539_spl ),
inference(split_clause,[status(thm)],[f10045,f10050,f8478]) ).
fof(f10060,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),tc_Int_Oint) ),
inference(resolution,[status(thm)],[f3001,f741]) ).
fof(f10061,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),tc_Int_Oint) ),
inference(resolution,[status(thm)],[f3001,f739]) ).
fof(f10062,definition,
! [X0,X1] :
( sQ540_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ540_spl])],[split_symbol_definition]) ).
fof(f10065,plain,
( ~ sQ422_spl
| sQ540_spl ),
inference(split_clause,[status(thm)],[f10060,f10062,f8478]) ).
fof(f10066,definition,
! [X0,X1] :
( sQ541_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ541_spl])],[split_symbol_definition]) ).
fof(f10069,plain,
( ~ sQ422_spl
| sQ541_spl ),
inference(split_clause,[status(thm)],[f10061,f10066,f8478]) ).
fof(f10631,plain,
( ~ sQ2_spl
| sQ175_spl ),
inference(split_clause,[status(thm)],[f7180,f3745,f1210]) ).
fof(f10714,plain,
( ~ sQ23_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1142,f1492]) ).
fof(f10716,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f10714]) ).
fof(f10758,plain,
( ~ sQ11_spl
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1389,f1131]) ).
fof(f10761,plain,
( ~ sQ11_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f10758,f2634,f1388]) ).
fof(f10877,definition,
( sQ555_spl
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ555_spl])],[split_symbol_definition]) ).
fof(f10879,plain,
( sQ555_spl
| ~ class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f10877]) ).
fof(f10890,plain,
( sQ555_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10879,f1113]) ).
fof(f10891,plain,
sQ555_spl,
inference(contradiction_clause,[status(thm)],[f10890]) ).
fof(f10977,plain,
! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f887,f1098]) ).
fof(f10978,plain,
! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint) = X0
| ~ class_Orderings_Olinorder(tc_Int_Oint) ),
inference(resolution,[status(thm)],[f887,f1065]) ).
fof(f10979,definition,
! [X0] :
( sQ558_spl
<=> ( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ558_spl])],[split_symbol_definition]) ).
fof(f10982,plain,
( sQ558_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f10977,f1903,f10979]) ).
fof(f10983,definition,
! [X0] :
( sQ559_spl
<=> ( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ559_spl])],[split_symbol_definition]) ).
fof(f10986,plain,
( sQ559_spl
| ~ sQ337_spl ),
inference(split_clause,[status(thm)],[f10978,f6107,f10983]) ).
fof(f11259,plain,
! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint),tc_Int_Oint),
inference(resolution,[status(thm)],[f652,f1064]) ).
fof(f11427,plain,
! [X0] :
( c_HOL_Oord__class_Oless(X0,v_x(X0),tc_RealDef_Oreal)
| v_x(X0) = X0 ),
inference(resolution,[status(thm)],[f1196,f3108]) ).
fof(f11480,definition,
! [X2] :
( sQ563_spl
<=> ~ c_lessequals(X2,v_r,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition]) ).
fof(f11481,plain,
! [X0] :
( ~ sQ563_spl
| ~ c_lessequals(X0,v_r,tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f11480]) ).
fof(f11504,plain,
( ~ sQ563_spl
| $false ),
inference(resolution,[status(thm)],[f963,f11481]) ).
fof(f11508,plain,
~ sQ563_spl,
inference(contradiction_clause,[status(thm)],[f11504]) ).
fof(f11519,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f782,f741]) ).
fof(f11520,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f782,f739]) ).
fof(f11523,definition,
! [X0,X1,X2] :
( sQ564_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ564_spl])],[split_symbol_definition]) ).
fof(f11526,plain,
( sQ564_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f11519,f3018,f11523]) ).
fof(f11527,definition,
! [X0,X1,X2] :
( sQ565_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ565_spl])],[split_symbol_definition]) ).
fof(f11530,plain,
( sQ565_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f11520,f3018,f11527]) ).
fof(f11572,definition,
( sQ569_spl
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ569_spl])],[split_symbol_definition]) ).
fof(f11574,plain,
( sQ569_spl
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f11572]) ).
fof(f11581,plain,
( sQ569_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11574,f1141]) ).
fof(f11582,plain,
sQ569_spl,
inference(contradiction_clause,[status(thm)],[f11581]) ).
fof(f11610,definition,
( sQ571_spl
<=> class_RealVector_Oreal__vector(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ571_spl])],[split_symbol_definition]) ).
fof(f11612,plain,
( sQ571_spl
| ~ class_RealVector_Oreal__vector(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f11610]) ).
fof(f11617,plain,
( sQ571_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11612,f1123]) ).
fof(f11618,plain,
sQ571_spl,
inference(contradiction_clause,[status(thm)],[f11617]) ).
fof(f11974,definition,
( sQ579_spl
<=> class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ579_spl])],[split_symbol_definition]) ).
fof(f11976,plain,
( sQ579_spl
| ~ class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f11974]) ).
fof(f11981,plain,
( sQ579_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11976,f1146]) ).
fof(f11982,plain,
sQ579_spl,
inference(contradiction_clause,[status(thm)],[f11981]) ).
fof(f12277,plain,
! [X0] : c_lessequals(X0,v_x(X0),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f3108,f1048]) ).
fof(f12283,plain,
! [X0] :
( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_lessequals(X0,X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3108,f975]) ).
fof(f12286,plain,
( ~ sQ44_spl
| sQ318_spl ),
inference(split_clause,[status(thm)],[f12283,f5579,f1826]) ).
fof(f12408,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f2700,f927]) ).
fof(f12409,definition,
! [X0] :
( sQ583_spl
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ583_spl])],[split_symbol_definition]) ).
fof(f12412,plain,
( sQ583_spl
| ~ sQ579_spl ),
inference(split_clause,[status(thm)],[f12408,f11974,f12409]) ).
fof(f12807,plain,
! [X0,X1] :
( ~ sQ350_spl
| ~ sQ2_spl
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal) = v_x(X1) ),
inference(paramodulation,[status(thm)],[f8214,f2345]) ).
fof(f12824,definition,
! [X1] :
( sQ587_spl
<=> v_r = v_x(X1) ),
introduced(definition,[new_symbols(definition,[sQ587_spl])],[split_symbol_definition]) ).
fof(f12825,plain,
! [X0] :
( ~ sQ587_spl
| v_r = v_x(X0) ),
inference(component_clause,[status(thm)],[f12824]) ).
fof(f12829,plain,
! [X0,X1] :
( ~ sQ350_spl
| ~ sQ2_spl
| v_x(X0) = v_x(X1) ),
inference(forward_demodulation,[status(thm)],[f2345,f12807]) ).
fof(f12843,plain,
! [X0] :
( ~ sQ587_spl
| ~ c_HOL_Oord__class_Oless(v_r,X0,tc_RealDef_Oreal) ),
inference(backward_demodulation,[status(thm)],[f12825,f1048]) ).
fof(f12926,plain,
! [X0] :
( ~ sQ162_spl
| ~ sQ350_spl
| ~ sQ2_spl
| v_r = v_x(X0) ),
inference(paramodulation,[status(thm)],[f3643,f12829]) ).
fof(f12934,plain,
( ~ sQ162_spl
| ~ sQ350_spl
| ~ sQ2_spl
| sQ587_spl ),
inference(split_clause,[status(thm)],[f12926,f12824,f1210,f6389,f3642]) ).
fof(f12942,definition,
! [X0,X1] :
( sQ588_spl
<=> c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ588_spl])],[split_symbol_definition]) ).
fof(f12943,plain,
! [X0,X1] :
( ~ sQ588_spl
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f12942]) ).
fof(f12956,plain,
! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f963,f1013]) ).
fof(f12958,definition,
! [X0] :
( sQ589_spl
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ589_spl])],[split_symbol_definition]) ).
fof(f12961,plain,
( sQ589_spl
| ~ sQ402_spl ),
inference(split_clause,[status(thm)],[f12956,f7938,f12958]) ).
fof(f12974,plain,
! [X0,X1] :
( ~ sQ588_spl
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(backward_subsumption_resolution,[status(thm)],[f2842,f12943]) ).
fof(f12981,plain,
( ~ sQ588_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12974,f12943]) ).
fof(f12982,plain,
~ sQ588_spl,
inference(contradiction_clause,[status(thm)],[f12981]) ).
fof(f12985,plain,
! [X0] :
( c_lessequals(X0,X0,tc_Int_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
inference(resolution,[status(thm)],[f1822,f1012]) ).
fof(f12986,plain,
! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
inference(resolution,[status(thm)],[f1822,f1013]) ).
fof(f12987,definition,
! [X0] :
( sQ590_spl
<=> c_lessequals(X0,X0,tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ590_spl])],[split_symbol_definition]) ).
fof(f12990,plain,
( sQ590_spl
| ~ sQ404_spl ),
inference(split_clause,[status(thm)],[f12985,f7945,f12987]) ).
fof(f12991,definition,
! [X0] :
( sQ591_spl
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ591_spl])],[split_symbol_definition]) ).
fof(f12994,plain,
( sQ591_spl
| ~ sQ404_spl ),
inference(split_clause,[status(thm)],[f12986,f7945,f12991]) ).
fof(f13014,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ587_spl
| X0 = v_r ),
inference(backward_subsumption_resolution,[status(thm)],[f9634,f12843]) ).
fof(f13015,plain,
( ~ sQ2_spl
| ~ sQ587_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f13014,f1277,f12824,f1210]) ).
fof(f13030,plain,
! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f12277,f1013]) ).
fof(f13032,definition,
! [X0] :
( sQ593_spl
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ593_spl])],[split_symbol_definition]) ).
fof(f13035,plain,
( sQ593_spl
| ~ sQ402_spl ),
inference(split_clause,[status(thm)],[f13030,f7938,f13032]) ).
fof(f13074,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f2345,f1036]) ).
fof(f13075,plain,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f2345,f1012]) ).
fof(f13076,plain,
! [X0,X1] :
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f2345,f1012]) ).
fof(f13077,definition,
! [X0,X1] :
( sQ597_spl
<=> ( ~ c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ597_spl])],[split_symbol_definition]) ).
fof(f13080,plain,
( sQ597_spl
| ~ sQ402_spl ),
inference(split_clause,[status(thm)],[f13074,f7938,f13077]) ).
fof(f13081,definition,
! [X0,X1] :
( sQ598_spl
<=> ( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ598_spl])],[split_symbol_definition]) ).
fof(f13084,plain,
( sQ598_spl
| ~ sQ402_spl ),
inference(split_clause,[status(thm)],[f13075,f7938,f13081]) ).
fof(f13085,definition,
! [X0,X1] :
( sQ599_spl
<=> ( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ599_spl])],[split_symbol_definition]) ).
fof(f13088,plain,
( sQ599_spl
| ~ sQ402_spl ),
inference(split_clause,[status(thm)],[f13076,f7938,f13085]) ).
fof(f13090,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f2346,f1036]) ).
fof(f13091,plain,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),X0,tc_Int_Oint)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),X1,tc_Int_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f2346,f1012]) ).
fof(f13092,plain,
! [X0,X1] :
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint)
| c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f2346,f1012]) ).
fof(f13093,definition,
! [X0,X1] :
( sQ600_spl
<=> ( ~ c_HOL_Oord__class_Oless(X1,X0,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ600_spl])],[split_symbol_definition]) ).
fof(f13096,plain,
( sQ600_spl
| ~ sQ404_spl ),
inference(split_clause,[status(thm)],[f13090,f7945,f13093]) ).
fof(f13097,definition,
! [X0,X1] :
( sQ601_spl
<=> ( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),X0,tc_Int_Oint)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),X1,tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ601_spl])],[split_symbol_definition]) ).
fof(f13100,plain,
( sQ601_spl
| ~ sQ404_spl ),
inference(split_clause,[status(thm)],[f13091,f7945,f13097]) ).
fof(f13101,definition,
! [X0,X1] :
( sQ602_spl
<=> ( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint)
| c_lessequals(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ602_spl])],[split_symbol_definition]) ).
fof(f13104,plain,
( sQ602_spl
| ~ sQ404_spl ),
inference(split_clause,[status(thm)],[f13092,f7945,f13101]) ).
fof(f13105,plain,
! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint),tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
inference(resolution,[status(thm)],[f11259,f1013]) ).
fof(f13106,definition,
! [X0] :
( sQ603_spl
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint),tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ603_spl])],[split_symbol_definition]) ).
fof(f13109,plain,
( sQ603_spl
| ~ sQ404_spl ),
inference(split_clause,[status(thm)],[f13105,f7945,f13106]) ).
fof(f13111,plain,
! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f2247,f1013]) ).
fof(f13113,definition,
! [X0] :
( sQ604_spl
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ604_spl])],[split_symbol_definition]) ).
fof(f13116,plain,
( sQ604_spl
| ~ sQ402_spl ),
inference(split_clause,[status(thm)],[f13111,f7938,f13113]) ).
fof(f13129,plain,
! [X0] :
( ~ sQ24_spl
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,v_r,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f5904,f1017]) ).
fof(f13130,definition,
! [X0] :
( sQ605_spl
<=> ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,v_r,tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ605_spl])],[split_symbol_definition]) ).
fof(f13133,plain,
( ~ sQ24_spl
| sQ605_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f13129,f1826,f13130,f1520]) ).
fof(f13134,plain,
! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1046,f1013]) ).
fof(f13137,definition,
! [X0] :
( sQ606_spl
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ606_spl])],[split_symbol_definition]) ).
fof(f13140,plain,
( sQ606_spl
| ~ sQ402_spl ),
inference(split_clause,[status(thm)],[f13134,f7938,f13137]) ).
fof(f13141,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f938,f1013]) ).
fof(f13142,definition,
( sQ607_spl
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ607_spl])],[split_symbol_definition]) ).
fof(f13145,plain,
( sQ607_spl
| ~ sQ402_spl ),
inference(split_clause,[status(thm)],[f13141,f7938,f13142]) ).
fof(f13146,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f992,f938]) ).
fof(f13151,plain,
( sQ2_spl
| sQ290_spl ),
inference(split_clause,[status(thm)],[f13146,f5146,f1210]) ).
fof(f13205,plain,
! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_x(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal)),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| v_x(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f11427,f1036]) ).
fof(f13206,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,v_x(X0),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| v_x(X0) = X0 ),
inference(resolution,[status(thm)],[f11427,f1017]) ).
fof(f13211,definition,
! [X0] :
( sQ608_spl
<=> ( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_x(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal)),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| v_x(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ608_spl])],[split_symbol_definition]) ).
fof(f13214,plain,
( ~ sQ402_spl
| sQ608_spl ),
inference(split_clause,[status(thm)],[f13205,f13211,f7938]) ).
fof(f13215,definition,
! [X0,X1] :
( sQ609_spl
<=> ( ~ c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,v_x(X0),tc_RealDef_Oreal)
| v_x(X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ609_spl])],[split_symbol_definition]) ).
fof(f13218,plain,
( ~ sQ44_spl
| sQ609_spl ),
inference(split_clause,[status(thm)],[f13206,f13215,f1826]) ).
fof(f13225,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f947,f1012]) ).
fof(f13229,definition,
! [X0,X1] :
( sQ610_spl
<=> ( c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ610_spl])],[split_symbol_definition]) ).
fof(f13232,plain,
( ~ sQ402_spl
| sQ610_spl ),
inference(split_clause,[status(thm)],[f13225,f13229,f7938]) ).
fof(f13235,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f971,f741]) ).
fof(f13236,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f971,f739]) ).
fof(f13238,definition,
! [X0,X1] :
( sQ611_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ611_spl])],[split_symbol_definition]) ).
fof(f13241,plain,
( ~ sQ75_spl
| sQ611_spl ),
inference(split_clause,[status(thm)],[f13235,f13238,f3018]) ).
fof(f13242,definition,
! [X0,X1] :
( sQ612_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ612_spl])],[split_symbol_definition]) ).
fof(f13245,plain,
( ~ sQ75_spl
| sQ612_spl ),
inference(split_clause,[status(thm)],[f13236,f13242,f3018]) ).
fof(f13277,plain,
! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f983,f1013]) ).
fof(f13282,definition,
! [X0] :
( sQ614_spl
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ614_spl])],[split_symbol_definition]) ).
fof(f13285,plain,
( sQ614_spl
| ~ sQ402_spl ),
inference(split_clause,[status(thm)],[f13277,f7938,f13282]) ).
fof(f13295,plain,
! [X0,X1] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f934,f1013]) ).
fof(f13296,definition,
! [X0,X1] :
( sQ615_spl
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ615_spl])],[split_symbol_definition]) ).
fof(f13299,plain,
( sQ615_spl
| ~ sQ402_spl ),
inference(split_clause,[status(thm)],[f13295,f7938,f13296]) ).
fof(f13307,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3108,f1012]) ).
fof(f13310,plain,
! [X0,X1] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f3108,f1013]) ).
fof(f13311,definition,
! [X0,X1] :
( sQ616_spl
<=> ( c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ616_spl])],[split_symbol_definition]) ).
fof(f13314,plain,
( ~ sQ402_spl
| sQ616_spl ),
inference(split_clause,[status(thm)],[f13307,f13311,f7938]) ).
fof(f13315,definition,
! [X0,X1] :
( sQ617_spl
<=> ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ617_spl])],[split_symbol_definition]) ).
fof(f13318,plain,
( ~ sQ402_spl
| sQ617_spl ),
inference(split_clause,[status(thm)],[f13310,f13315,f7938]) ).
fof(f13321,plain,
! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_Complex_ORe(X0),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f935,f1013]) ).
fof(f13325,definition,
! [X0] :
( sQ618_spl
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_Complex_ORe(X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ618_spl])],[split_symbol_definition]) ).
fof(f13328,plain,
( sQ618_spl
| ~ sQ402_spl ),
inference(split_clause,[status(thm)],[f13321,f7938,f13325]) ).
fof(f13335,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_Int_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint) ),
inference(resolution,[status(thm)],[f2853,f1012]) ).
fof(f13337,definition,
! [X0,X1] :
( sQ619_spl
<=> ( c_lessequals(X0,X1,tc_Int_Oint)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(X1,tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ619_spl])],[split_symbol_definition]) ).
fof(f13340,plain,
( ~ sQ404_spl
| sQ619_spl ),
inference(split_clause,[status(thm)],[f13335,f13337,f7945]) ).
fof(f13342,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ),
inference(resolution,[status(thm)],[f2964,f741]) ).
fof(f13343,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ),
inference(resolution,[status(thm)],[f2964,f739]) ).
fof(f13344,definition,
! [X0,X1] :
( sQ620_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ620_spl])],[split_symbol_definition]) ).
fof(f13347,plain,
( ~ sQ422_spl
| sQ620_spl ),
inference(split_clause,[status(thm)],[f13342,f13344,f8478]) ).
fof(f13348,definition,
! [X0,X1] :
( sQ621_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ621_spl])],[split_symbol_definition]) ).
fof(f13351,plain,
( ~ sQ422_spl
| sQ621_spl ),
inference(split_clause,[status(thm)],[f13343,f13348,f8478]) ).
fof(f13365,plain,
( sQ169_spl
| ~ sQ162_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f3643,f3671]) ).
fof(f13366,plain,
( sQ169_spl
| ~ sQ162_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13365,f5904]) ).
fof(f13367,plain,
( sQ169_spl
| ~ sQ162_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f13366]) ).
fof(f13368,plain,
$false,
inference(sat_refutation,[status(thm)],[f1216,f1381,f1386,f1391,f1399,f1401,f1582,f1645,f1649,f1657,f1659,f1740,f1747,f1749,f1751,f1794,f1799,f1818,f1820,f1832,f1834,f1933,f2028,f2197,f2205,f2287,f2317,f2500,f2507,f2640,f2642,f3009,f3011,f3024,f3028,f3032,f3034,f3171,f3238,f3480,f3547,f3615,f3645,f3672,f3915,f4520,f4522,f4524,f4526,f4647,f4651,f4660,f4883,f5171,f5187,f5231,f5285,f5593,f5720,f5856,f5956,f5985,f6106,f6113,f6115,f6394,f6478,f6814,f6824,f6827,f6847,f6851,f6858,f6861,f6943,f6949,f6956,f6977,f7080,f7097,f7333,f7551,f7553,f7953,f7955,f8182,f8450,f8490,f8582,f8584,f8586,f8709,f8711,f8713,f9216,f9218,f9544,f9548,f9552,f9558,f9562,f9570,f9574,f9697,f9739,f9743,f9747,f9753,f9757,f9765,f9769,f9898,f9902,f9926,f9930,f10049,f10053,f10065,f10069,f10631,f10716,f10761,f10891,f10982,f10986,f11508,f11526,f11530,f11582,f11618,f11982,f12286,f12412,f12934,f12961,f12982,f12990,f12994,f13015,f13035,f13080,f13084,f13088,f13096,f13100,f13104,f13109,f13116,f13133,f13140,f13145,f13151,f13214,f13218,f13232,f13241,f13245,f13285,f13299,f13314,f13318,f13328,f13340,f13347,f13351,f13367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG373-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 13:18:21 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.39 % Drodi V4.1.1
% 18.07/2.80 % Refutation found
% 18.07/2.80 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 18.07/2.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.86/2.85 % Elapsed time: 2.483202 seconds
% 7.86/2.85 % CPU time: 18.912149 seconds
% 7.86/2.85 % Total memory used: 243.520 MB
% 7.86/2.85 % Net memory used: 231.479 MB
%------------------------------------------------------------------------------