TSTP Solution File: ALG373-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG373-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:32:37 EDT 2023
% Result : Unsatisfiable 26.66s 11.48s
% Output : CNFRefutation 26.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 112
% Syntax : Number of formulae : 206 ( 52 unt; 82 typ; 0 def)
% Number of atoms : 230 ( 67 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 217 ( 111 ~; 106 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 111 ( 77 >; 34 *; 0 +; 0 <<)
% Number of predicates : 49 ( 47 usr; 1 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 5 con; 0-3 aty)
% Number of variables : 145 (; 145 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring__abs > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Olordered__ring > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring__0 > class_Ring__and__Field_Ocomm__ring__1 > class_Ring__and__Field_Ocomm__ring > class_Ring__and__Field_Oabs__if > class_RealVector_Oreal__vector > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__div__algebra > class_RealVector_Oreal__normed__algebra__1 > class_RealVector_Oreal__normed__algebra > class_RealVector_Oreal__algebra__1 > class_RealVector_Oreal__algebra > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__ab__group__add__abs > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Oordered__ab__group__add > class_OrderedGroup_Olordered__ab__group__add__abs > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__group__add > class_Lattices_Oboolean__algebra > class_Int_Oring__char__0 > class_Int_Onumber__ring > class_Int_Onumber > c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__XscaleR__right__Xbounded__1__1 > c_RealVector_OscaleR__class_OscaleR > c_Polynomial_Opoly > c_HOL_Otimes__class_Otimes > v_sko__unknown__thm__rW8__1 > v_sko__local__Xmth1__2 > v_sko__local__Xmth1__1 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 > c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1 > c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1 > c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1 > c_RealVector_Oof__real > c_RealVector_Onorm__class_Onorm > c_Int_Onumber__class_Onumber__of > c_HOL_Ouminus__class_Ouminus > c_HOL_Oabs__class_Oabs > #nlpp > v_xa > v_x > tc_Polynomial_Opoly > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > c_Complex_ORe > v_r > v_p > tc_RealDef_Oreal > tc_Int_Oint > tc_Complex_Ocomplex
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__0,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(class_OrderedGroup_Oordered__ab__group__add,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(class_Ring__and__Field_Opordered__ring__abs,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(class_Int_Oring__char__0,type,
class_Int_Oring__char__0: $i > $o ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(v_xa,type,
v_xa: $i > $i ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Int_Onumber__class_Onumber__of,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__semiring,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(class_RealVector_Oreal__vector,type,
class_RealVector_Oreal__vector: $i > $o ).
tff(c_RealVector_OscaleR__class_OscaleR,type,
c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add__abs,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(tc_Polynomial_Opoly,type,
tc_Polynomial_Opoly: $i > $i ).
tff(tc_Int_Oint,type,
tc_Int_Oint: $i ).
tff(class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(tc_RealDef_Oreal,type,
tc_RealDef_Oreal: $i ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Int_Onumber,type,
class_Int_Onumber: $i > $o ).
tff(class_Ring__and__Field_Opordered__ring,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1: ( $i * $i ) > $i ).
tff(v_sko__unknown__thm__rW8__1,type,
v_sko__unknown__thm__rW8__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(class_Ring__and__Field_Ocomm__ring__1,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(class_RealVector_Oreal__normed__div__algebra,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oabs__if,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(class_RealVector_Oreal__normed__vector,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(class_Ring__and__Field_Ocomm__ring,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(class_RealVector_Oreal__algebra,type,
class_RealVector_Oreal__algebra: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(class_RealVector_Oreal__algebra__1,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(v_r,type,
v_r: $i ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Polynomial_Opoly,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Omult__mono1,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1,type,
c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1: ( $i * $i * $i ) > $i ).
tff(c_RealVector_Onorm__class_Onorm,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Olordered__ab__group__add__abs,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1,type,
c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Olordered__ring,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(v_sko__local__Xmth1__2,type,
v_sko__local__Xmth1__2: ( $i * $i ) > $i ).
tff(c_HOL_Ouminus__class_Ouminus,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(class_Ring__and__Field_Omult__mono,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(c_HOL_Oabs__class_Oabs,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_RealVector_Oof__real,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(v_p,type,
v_p: $i ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(v_x,type,
v_x: $i > $i ).
tff(c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(c_RealVector_Osko__RealVector__XscaleR__right__Xbounded__1__1,type,
c_RealVector_Osko__RealVector__XscaleR__right__Xbounded__1__1: ( $i * $i * $i ) > $i ).
tff(v_sko__local__Xmth1__1,type,
v_sko__local__Xmth1__1: ( $i * $i ) > $i ).
tff(c_Complex_ORe,type,
c_Complex_ORe: $i > $i ).
tff(f_2791,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_2766,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_2792,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_2082,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_2595,axiom,
! [T_a,V_x,V_y] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ),
file(unknown,unknown) ).
tff(f_2586,axiom,
! [T_a,V_y,V_x] :
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file(unknown,unknown) ).
tff(f_2461,axiom,
! [V_z,V_w] :
( ( V_z = V_w )
| ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal)
| ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_1813,axiom,
! [V_r] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_2266,axiom,
! [T_a,V_x] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ),
file(unknown,unknown) ).
tff(f_2787,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_2620,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ),
file(unknown,unknown) ).
tff(f_2779,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_2384,axiom,
! [T_a,V_y,V_x] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ( V_x = V_y ) ),
file(unknown,unknown) ).
tff(f_2699,axiom,
! [V_xb] : ~ c_HOL_Oord__class_Oless(v_x(V_xb),V_xb,tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_2760,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_2804,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_2696,axiom,
! [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(unknown,unknown) ).
tff(f_1809,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ),
file(unknown,unknown) ).
tff(f_889,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_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) ) ),
file(unknown,unknown) ).
tff(f_1062,axiom,
! [T_a,V_a] :
( ~ class_RealVector_Oreal__normed__vector(T_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) ) ),
file(unknown,unknown) ).
tff(f_856,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ),
file(unknown,unknown) ).
tff(f_2540,axiom,
! [T_a,V_y,V_x] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ),
file(unknown,unknown) ).
tff(f_2477,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a) )
| ( V_a = V_b ) ),
file(unknown,unknown) ).
tff(f_816,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_2219,axiom,
! [V_i,V_k,V_j] :
( c_lessequals(V_i,V_k,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_247,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ),
file(unknown,unknown) ).
tff(f_239,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ),
file(unknown,unknown) ).
tff(f_1958,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_2209,axiom,
! [T_a,V_x,V_z,V_y] :
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
file(unknown,unknown) ).
tff(f_1536,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(unknown,unknown) ).
tff(c_862,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_2791]) ).
tff(c_812,plain,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_2766]) ).
tff(c_864,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_2792]) ).
tff(c_540,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_2082]) ).
tff(c_3723,plain,
! [V_y_1212,V_x_1213,T_a_1214] :
( ~ c_HOL_Oord__class_Oless(V_y_1212,V_x_1213,T_a_1214)
| ~ c_lessequals(V_x_1213,V_y_1212,T_a_1214)
| ~ class_Orderings_Olinorder(T_a_1214) ),
inference(cnfTransformation,[status(thm)],[f_2595]) ).
tff(c_3831,plain,
( ~ c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_540,c_3723]) ).
tff(c_3926,plain,
~ c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_864,c_3831]) ).
tff(c_666,plain,
! [V_x_940,V_y_939,T_a_938] :
( c_lessequals(V_x_940,V_y_939,T_a_938)
| c_HOL_Oord__class_Oless(V_y_939,V_x_940,T_a_938)
| ~ class_Orderings_Olinorder(T_a_938) ),
inference(cnfTransformation,[status(thm)],[f_2586]) ).
tff(c_3988,plain,
! [V_z_1215,V_w_1216] :
( ~ c_lessequals(V_z_1215,V_w_1216,tc_RealDef_Oreal)
| ~ c_lessequals(V_w_1216,V_z_1215,tc_RealDef_Oreal)
| ( V_z_1215 = V_w_1216 ) ),
inference(cnfTransformation,[status(thm)],[f_2461]) ).
tff(c_4129,plain,
( ~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r ) ),
inference(resolution,[status(thm)],[c_540,c_3988]) ).
tff(c_5942,plain,
~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(splitLeft,[status(thm)],[c_4129]) ).
tff(c_5947,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_666,c_5942]) ).
tff(c_5961,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_864,c_5947]) ).
tff(c_1324,plain,
! [V_r_1091] :
( c_HOL_Oord__class_Oless(V_r_1091,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(V_r_1091,tc_RealDef_Oreal) = V_r_1091 ) ),
inference(cnfTransformation,[status(thm)],[f_1813]) ).
tff(c_590,plain,
! [V_x_835,T_a_834] :
( ~ c_HOL_Oord__class_Oless(V_x_835,V_x_835,T_a_834)
| ~ class_Orderings_Opreorder(T_a_834) ),
inference(cnfTransformation,[status(thm)],[f_2266]) ).
tff(c_1328,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)],[c_1324,c_590]) ).
tff(c_1347,plain,
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(demodulation,[status(thm),theory(equality)],[c_862,c_1328]) ).
tff(c_854,plain,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_2787]) ).
tff(c_678,plain,
! [V_a_953,T_a_952] :
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a_953,T_a_952),T_a_952) = V_a_953 )
| ~ class_OrderedGroup_Ogroup__add(T_a_952) ),
inference(cnfTransformation,[status(thm)],[f_2620]) ).
tff(c_838,plain,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_2779]) ).
tff(c_6526,plain,
! [V_y_1266,V_x_1267,T_a_1268] :
( ( V_y_1266 = V_x_1267 )
| c_HOL_Oord__class_Oless(V_x_1267,V_y_1266,T_a_1268)
| c_HOL_Oord__class_Oless(V_y_1266,V_x_1267,T_a_1268)
| ~ class_Ring__and__Field_Oordered__idom(T_a_1268) ),
inference(cnfTransformation,[status(thm)],[f_2384]) ).
tff(c_702,plain,
! [V_xb_982] : ~ c_HOL_Oord__class_Oless(v_x(V_xb_982),V_xb_982,tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_2699]) ).
tff(c_6600,plain,
! [V_y_1266] :
( ( v_x(V_y_1266) = V_y_1266 )
| c_HOL_Oord__class_Oless(V_y_1266,v_x(V_y_1266),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_6526,c_702]) ).
tff(c_6720,plain,
! [V_y_1266] :
( ( v_x(V_y_1266) = V_y_1266 )
| c_HOL_Oord__class_Oless(V_y_1266,v_x(V_y_1266),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_838,c_6600]) ).
tff(c_800,plain,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_2760]) ).
tff(c_888,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_2804]) ).
tff(c_700,plain,
! [V_xb_981] : ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(V_xb_981),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(V_xb_981),tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_2696]) ).
tff(c_464,plain,
! [V_r_675] :
( c_HOL_Oord__class_Oless(V_r_675,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(V_r_675,tc_RealDef_Oreal) = V_r_675 ) ),
inference(cnfTransformation,[status(thm)],[f_1813]) ).
tff(c_1466,plain,
! [V_a_1109,T_a_1110] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a_1109,T_a_1110),c_HOL_Ozero__class_Ozero(T_a_1110),T_a_1110)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_1110) ),
inference(cnfTransformation,[status(thm)],[f_1809]) ).
tff(c_1476,plain,
! [V_a_1109] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(V_a_1109,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(V_a_1109,tc_RealDef_Oreal) ) ),
inference(resolution,[status(thm)],[c_464,c_1466]) ).
tff(c_1486,plain,
! [V_a_1109] : ( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(V_a_1109,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(V_a_1109,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_800,c_1476]) ).
tff(c_2711,plain,
! [V_a_1184,T_a_1185] :
( ( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a_1184,T_a_1185),T_a_1185) = c_HOL_Oabs__class_Oabs(V_a_1184,T_a_1185) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_1185) ),
inference(cnfTransformation,[status(thm)],[f_889]) ).
tff(c_2733,plain,
! [V_a_1184] :
( ( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a_1184,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(V_a_1184,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_2711,c_1486]) ).
tff(c_2766,plain,
! [V_a_1184] : ( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a_1184,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(V_a_1184,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_800,c_1486,c_2733]) ).
tff(c_5768,plain,
! [V_xb_1252] : ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(V_xb_1252),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(V_xb_1252),tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_2696]) ).
tff(c_264,plain,
! [V_a_395,T_a_394] :
( ( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_a_395,T_a_394),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_a_395,T_a_394) )
| ~ class_RealVector_Oreal__normed__vector(T_a_394) ),
inference(cnfTransformation,[status(thm)],[f_1062]) ).
tff(c_5774,plain,
! [V_xb_1252] :
( ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(V_xb_1252),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(v_x(V_xb_1252),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_5768,c_264]) ).
tff(c_6392,plain,
! [V_xb_1263] : ( c_HOL_Ouminus__class_Ouminus(v_x(V_xb_1263),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_x(V_xb_1263),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_888,c_700,c_2766,c_5774]) ).
tff(c_6425,plain,
! [V_xb_1263] :
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(v_x(V_xb_1263),tc_RealDef_Oreal),tc_RealDef_Oreal) = v_x(V_xb_1263) )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_6392,c_678]) ).
tff(c_7179,plain,
! [V_xb_1277] : ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(v_x(V_xb_1277),tc_RealDef_Oreal),tc_RealDef_Oreal) = v_x(V_xb_1277) ),
inference(demodulation,[status(thm),theory(equality)],[c_854,c_6425]) ).
tff(c_198,plain,
! [V_a_316,T_a_315] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(V_a_316,T_a_315),T_a_315),c_HOL_Ozero__class_Ozero(T_a_315),T_a_315)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_315) ),
inference(cnfTransformation,[status(thm)],[f_856]) ).
tff(c_7185,plain,
! [V_xb_1277] :
( c_lessequals(v_x(V_xb_1277),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_7179,c_198]) ).
tff(c_7248,plain,
! [V_xb_1278] : c_lessequals(v_x(V_xb_1278),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_800,c_7185]) ).
tff(c_654,plain,
! [V_x_924,V_y_923,T_a_922] :
( ~ c_HOL_Oord__class_Oless(V_x_924,V_y_923,T_a_922)
| ~ c_lessequals(V_y_923,V_x_924,T_a_922)
| ~ class_Orderings_Opreorder(T_a_922) ),
inference(cnfTransformation,[status(thm)],[f_2540]) ).
tff(c_7253,plain,
! [V_xb_1278] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x(V_xb_1278),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_7248,c_654]) ).
tff(c_7271,plain,
! [V_xb_1279] : ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x(V_xb_1279),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_862,c_7253]) ).
tff(c_7278,plain,
v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(resolution,[status(thm)],[c_6720,c_7271]) ).
tff(c_5806,plain,
! [V_xb_1252] : ( c_HOL_Ouminus__class_Ouminus(v_x(V_xb_1252),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_x(V_xb_1252),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_888,c_700,c_2766,c_5774]) ).
tff(c_7296,plain,
c_HOL_Oabs__class_Oabs(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm),theory(equality)],[c_7278,c_5806]) ).
tff(c_7306,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1347,c_7278,c_7296]) ).
tff(c_640,plain,
! [V_b_901,V_a_900,T_a_899] :
( ( V_b_901 = V_a_900 )
| ( c_HOL_Ouminus__class_Ouminus(V_b_901,T_a_899) != c_HOL_Ouminus__class_Ouminus(V_a_900,T_a_899) )
| ~ class_OrderedGroup_Ogroup__add(T_a_899) ),
inference(cnfTransformation,[status(thm)],[f_2477]) ).
tff(c_7379,plain,
! [V_b_901] :
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = V_b_901 )
| ( c_HOL_Ouminus__class_Ouminus(V_b_901,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_7306,c_640]) ).
tff(c_8842,plain,
! [V_b_1302] :
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = V_b_1302 )
| ( c_HOL_Ouminus__class_Ouminus(V_b_1302,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_854,c_7379]) ).
tff(c_8863,plain,
! [V_a_953] :
( ( c_HOL_Ouminus__class_Ouminus(V_a_953,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_a_953 )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_678,c_8842]) ).
tff(c_9839,plain,
! [V_a_1319] :
( ( c_HOL_Ouminus__class_Ouminus(V_a_1319,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_a_1319 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_854,c_8863]) ).
tff(c_9895,plain,
! [V_a_1319] :
( ( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(V_a_1319,tc_RealDef_Oreal) )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_a_1319 ) ),
inference(superposition,[status(thm),theory(equality)],[c_9839,c_2766]) ).
tff(c_10004,plain,
! [V_a_1320] :
( ( c_HOL_Oabs__class_Oabs(V_a_1320,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_a_1320 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1347,c_9895]) ).
tff(c_2770,plain,
! [V_a_1186] : ( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a_1186,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(V_a_1186,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_800,c_1486,c_2733]) ).
tff(c_188,plain,
! [V_a_305,T_a_304] :
( c_lessequals(V_a_305,c_HOL_Oabs__class_Oabs(V_a_305,T_a_304),T_a_304)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_304) ),
inference(cnfTransformation,[status(thm)],[f_816]) ).
tff(c_2798,plain,
! [V_a_1186] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a_1186,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(V_a_1186,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_2770,c_188]) ).
tff(c_2890,plain,
! [V_a_1189] : c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a_1189,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(V_a_1189,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_800,c_2798]) ).
tff(c_2929,plain,
! [V_a_953] :
( c_lessequals(V_a_953,c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a_953,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_678,c_2890]) ).
tff(c_2945,plain,
! [V_a_953] : c_lessequals(V_a_953,c_HOL_Oabs__class_Oabs(V_a_953,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_854,c_2766,c_2929]) ).
tff(c_3750,plain,
! [V_a_953] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a_953,tc_RealDef_Oreal),V_a_953,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_2945,c_3723]) ).
tff(c_3857,plain,
! [V_a_953] : ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a_953,tc_RealDef_Oreal),V_a_953,tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_864,c_3750]) ).
tff(c_10476,plain,
! [V_a_1324] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a_1324,tc_RealDef_Oreal)
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_a_1324 ) ),
inference(superposition,[status(thm),theory(equality)],[c_10004,c_3857]) ).
tff(c_10555,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r,
inference(resolution,[status(thm)],[c_5961,c_10476]) ).
tff(c_7227,plain,
! [V_xb_1277] : c_lessequals(v_x(V_xb_1277),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_800,c_7185]) ).
tff(c_6826,plain,
! [V_i_1270,V_j_1271,V_k_1272] :
( ~ c_lessequals(V_i_1270,V_j_1271,tc_RealDef_Oreal)
| ~ c_lessequals(V_j_1271,V_k_1272,tc_RealDef_Oreal)
| c_lessequals(V_i_1270,V_k_1272,tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_2219]) ).
tff(c_12030,plain,
! [V_k_1370] :
( ~ c_lessequals(v_r,V_k_1370,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_k_1370,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_540,c_6826]) ).
tff(c_58,plain,
! [T_a_77,V_a_78] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a_77),V_a_78,T_a_77)
| ( c_HOL_Oabs__class_Oabs(V_a_78,T_a_77) = V_a_78 )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_77) ),
inference(cnfTransformation,[status(thm)],[f_247]) ).
tff(c_12043,plain,
! [V_k_1370] :
( ( c_HOL_Oabs__class_Oabs(V_k_1370,tc_RealDef_Oreal) = V_k_1370 )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ c_lessequals(v_r,V_k_1370,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_12030,c_58]) ).
tff(c_12076,plain,
! [V_k_1371] :
( ( c_HOL_Oabs__class_Oabs(V_k_1371,tc_RealDef_Oreal) = V_k_1371 )
| ~ c_lessequals(v_r,V_k_1371,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_800,c_12043]) ).
tff(c_12104,plain,
! [V_y_939] :
( ( c_HOL_Oabs__class_Oabs(V_y_939,tc_RealDef_Oreal) = V_y_939 )
| c_HOL_Oord__class_Oless(V_y_939,v_r,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_666,c_12076]) ).
tff(c_12610,plain,
! [V_y_1379] :
( ( c_HOL_Oabs__class_Oabs(V_y_1379,tc_RealDef_Oreal) = V_y_1379 )
| c_HOL_Oord__class_Oless(V_y_1379,v_r,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_864,c_12104]) ).
tff(c_12696,plain,
c_HOL_Oabs__class_Oabs(v_x(v_r),tc_RealDef_Oreal) = v_x(v_r),
inference(resolution,[status(thm)],[c_12610,c_702]) ).
tff(c_56,plain,
! [V_a_76,T_a_75] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a_76,T_a_75),c_HOL_Ozero__class_Ozero(T_a_75),T_a_75)
| ( c_HOL_Ozero__class_Ozero(T_a_75) = V_a_76 )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_75) ),
inference(cnfTransformation,[status(thm)],[f_239]) ).
tff(c_12716,plain,
( ~ c_lessequals(v_x(v_r),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( v_x(v_r) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_12696,c_56]) ).
tff(c_12789,plain,
v_x(v_r) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_800,c_7227,c_12716]) ).
tff(c_12829,plain,
( ( 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(superposition,[status(thm),theory(equality)],[c_12789,c_6720]) ).
tff(c_12840,plain,
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r )
| c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_12789,c_12829]) ).
tff(c_12842,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3926,c_10555,c_12840]) ).
tff(c_12843,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r,
inference(splitRight,[status(thm)],[c_4129]) ).
tff(c_21883,plain,
! [V_xb_1591] : ( c_HOL_Ouminus__class_Ouminus(v_x(V_xb_1591),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_x(V_xb_1591),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_888,c_700,c_2766,c_5774]) ).
tff(c_500,plain,
! [V_a_725,T_a_724] :
( ~ c_lessequals(V_a_725,c_HOL_Ouminus__class_Ouminus(V_a_725,T_a_724),T_a_724)
| c_lessequals(V_a_725,c_HOL_Ozero__class_Ozero(T_a_724),T_a_724)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a_724) ),
inference(cnfTransformation,[status(thm)],[f_1958]) ).
tff(c_21898,plain,
! [V_xb_1591] :
( ~ c_lessequals(v_x(V_xb_1591),c_HOL_Oabs__class_Oabs(v_x(V_xb_1591),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(v_x(V_xb_1591),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_21883,c_500]) ).
tff(c_21976,plain,
! [V_xb_1591] : c_lessequals(v_x(V_xb_1591),v_r,tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_812,c_12843,c_2945,c_21898]) ).
tff(c_22058,plain,
! [V_x_1593,V_y_1594,T_a_1595,V_z_1596] :
( ~ c_lessequals(V_x_1593,V_y_1594,T_a_1595)
| ~ c_HOL_Oord__class_Oless(V_y_1594,V_z_1596,T_a_1595)
| c_HOL_Oord__class_Oless(V_x_1593,V_z_1596,T_a_1595)
| ~ class_Orderings_Opreorder(T_a_1595) ),
inference(cnfTransformation,[status(thm)],[f_2209]) ).
tff(c_22060,plain,
! [V_z_1596,V_xb_1591] :
( ~ c_HOL_Oord__class_Oless(v_r,V_z_1596,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(v_x(V_xb_1591),V_z_1596,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_21976,c_22058]) ).
tff(c_58076,plain,
! [V_z_2054,V_xb_2055] :
( ~ c_HOL_Oord__class_Oless(v_r,V_z_2054,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(v_x(V_xb_2055),V_z_2054,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_862,c_22060]) ).
tff(c_58212,plain,
! [V_z_2054] : ~ c_HOL_Oord__class_Oless(v_r,V_z_2054,tc_RealDef_Oreal),
inference(resolution,[status(thm)],[c_58076,c_702]) ).
tff(c_376,plain,
! [V_p_559,V_r_560] : 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_559,V_r_560),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_1536]) ).
tff(c_13035,plain,
! [V_p_559,V_r_560] : c_HOL_Oord__class_Oless(v_r,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(V_p_559,V_r_560),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_12843,c_376]) ).
tff(c_58223,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_58212,c_13035]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG373-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 20:18:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 26.66/11.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.66/11.50
% 26.66/11.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.83/11.56
% 26.83/11.56 Inference rules
% 26.83/11.56 ----------------------
% 26.83/11.56 #Ref : 15
% 26.83/11.56 #Sup : 12131
% 26.83/11.56 #Fact : 12
% 26.83/11.56 #Define : 0
% 26.83/11.56 #Split : 7
% 26.83/11.56 #Chain : 0
% 26.83/11.56 #Close : 0
% 26.83/11.56
% 26.83/11.56 Ordering : KBO
% 26.83/11.56
% 26.83/11.56 Simplification rules
% 26.83/11.56 ----------------------
% 26.83/11.56 #Subsume : 1936
% 26.83/11.56 #Demod : 11770
% 26.83/11.56 #Tautology : 3298
% 26.83/11.56 #SimpNegUnit : 174
% 26.83/11.56 #BackRed : 87
% 26.83/11.56
% 26.83/11.56 #Partial instantiations: 0
% 26.83/11.56 #Strategies tried : 1
% 26.83/11.56
% 26.83/11.56 Timing (in seconds)
% 26.83/11.56 ----------------------
% 26.83/11.56 Preprocessing : 1.39
% 26.83/11.56 Parsing : 0.80
% 26.83/11.56 CNF conversion : 0.11
% 26.83/11.57 Main loop : 9.06
% 26.83/11.57 Inferencing : 1.72
% 26.83/11.57 Reduction : 4.45
% 26.83/11.57 Demodulation : 3.64
% 26.83/11.57 BG Simplification : 0.21
% 26.83/11.57 Subsumption : 2.18
% 26.83/11.57 Abstraction : 0.16
% 26.83/11.57 MUC search : 0.00
% 26.83/11.57 Cooper : 0.00
% 26.83/11.57 Total : 10.55
% 26.83/11.57 Index Insertion : 0.00
% 26.83/11.57 Index Deletion : 0.00
% 26.83/11.57 Index Matching : 0.00
% 26.83/11.57 BG Taut test : 0.00
%------------------------------------------------------------------------------