TSTP Solution File: ALG406-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG406-1 : 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 : n028.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 10:32:41 EDT 2023
% Result : Unsatisfiable 58.09s 40.30s
% Output : CNFRefutation 58.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 123
% Syntax : Number of formulae : 188 ( 46 unt; 90 typ; 0 def)
% Number of atoms : 184 ( 36 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 181 ( 95 ~; 86 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 109 ( 85 >; 24 *; 0 +; 0 <<)
% Number of predicates : 64 ( 62 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 5 con; 0-3 aty)
% Number of variables : 112 (; 112 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring__1__no__zero__divisors > class_Ring__and__Field_Oring__1 > 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__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > 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_Ofield > class_Ring__and__Field_Odivision__ring > class_Ring__and__Field_Odivision__by__zero > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Oabs__if > 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_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__comm__monoid__add > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add__abs > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Oordered__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add__abs > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Lattices_Oboolean__algebra > class_Int_Onumber__ring > c_Power_Opower__class_Opower > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > 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_HOL_Ouminus__class_Ouminus > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > #nlpp > c_Transcendental_Osin > c_Transcendental_Ocos > c_NthRoot_Osqrt > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > c_Complex_ORe > v_w____ > v_t____ > tc_nat > tc_RealDef_Oreal > 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_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_Transcendental_Osin,type,
c_Transcendental_Osin: $i > $i ).
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_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_HOL_Oinverse__class_Oinverse,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(class_Ring__and__Field_Oring__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(v_t____,type,
v_t____: $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(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
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(class_Ring__and__Field_Odivision__by__zero,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Oordered__field,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(class_Ring__and__Field_Opordered__ring,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $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(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__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_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_nat,type,
tc_nat: $i ).
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_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__mult,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(class_Power_Opower,type,
class_Power_Opower: $i > $o ).
tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(c_NthRoot_Osqrt,type,
c_NthRoot_Osqrt: $i > $i ).
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_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $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(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
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_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
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_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(class_Ring__and__Field_Oring__1,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(class_Ring__and__Field_Olordered__ring,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
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(v_w____,type,
v_w____: $i ).
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(class_Ring__and__Field_Odivision__ring,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
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_Transcendental_Ocos,type,
c_Transcendental_Ocos: $i > $i ).
tff(c_Complex_ORe,type,
c_Complex_ORe: $i > $i ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(f_4398,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_4120,axiom,
! [V_w,V_z] :
( c_lessequals(V_w,V_z,tc_RealDef_Oreal)
| c_lessequals(V_z,V_w,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_4414,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_4415,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_4032,axiom,
c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_923,axiom,
! [T_a,V_z,V_x,V_y] :
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ),
file(unknown,unknown) ).
tff(f_3240,axiom,
! [T_a,V_x] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ),
file(unknown,unknown) ).
tff(f_4127,axiom,
! [T_a,V_y,V_x] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file(unknown,unknown) ).
tff(f_4413,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_203,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_956,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_lessequals(V_y,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ),
file(unknown,unknown) ).
tff(f_4409,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_1924,axiom,
c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3427,axiom,
! [T_a,V_a] :
( ~ class_Ring__and__Field_Oabs__if(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a )
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ),
file(unknown,unknown) ).
tff(f_1488,axiom,
! [V_x] :
( ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_4407,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_4406,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_4396,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3108,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ),
file(unknown,unknown) ).
tff(f_800,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Omonoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ),
file(unknown,unknown) ).
tff(f_3178,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ),
file(unknown,unknown) ).
tff(f_858,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_4367,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_1997,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_4151,axiom,
! [V_w] : c_lessequals(V_w,V_w,tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_1161,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ),
file(unknown,unknown) ).
tff(f_1225,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_4376,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_4029,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(unknown,unknown) ).
tff(f_3069,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ),
file(unknown,unknown) ).
tff(f_4060,axiom,
! [T_a,V_y,V_x] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),V_x,T_a)
| ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ),
file(unknown,unknown) ).
tff(f_4304,axiom,
! [V_z] : ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) = V_z ),
file(unknown,unknown) ).
tff(f_4329,axiom,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(c_1256,plain,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4398]) ).
tff(c_1042,plain,
! [V_z_1386,V_w_1385] :
( c_lessequals(V_z_1386,V_w_1385,tc_RealDef_Oreal)
| c_lessequals(V_w_1385,V_z_1386,tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_4120]) ).
tff(c_1288,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4414]) ).
tff(c_1290,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4415]) ).
tff(c_1016,plain,
c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4032]) ).
tff(c_36741,plain,
! [V_y_2137,V_x_2138,T_a_2139,V_z_2140] :
( ~ c_HOL_Oord__class_Oless(V_y_2137,V_x_2138,T_a_2139)
| ~ c_lessequals(V_z_2140,V_y_2137,T_a_2139)
| c_HOL_Oord__class_Oless(V_z_2140,V_x_2138,T_a_2139)
| ~ class_Orderings_Oorder(T_a_2139) ),
inference(cnfTransformation,[status(thm)],[f_923]) ).
tff(c_36811,plain,
! [V_z_2140] :
( ~ c_lessequals(V_z_2140,v_t____,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(V_z_2140,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1016,c_36741]) ).
tff(c_48213,plain,
! [V_z_2298] :
( ~ c_lessequals(V_z_2298,v_t____,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(V_z_2298,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1290,c_36811]) ).
tff(c_810,plain,
! [V_x_1090,T_a_1089] :
( ~ c_HOL_Oord__class_Oless(V_x_1090,V_x_1090,T_a_1089)
| ~ class_Orderings_Olinorder(T_a_1089) ),
inference(cnfTransformation,[status(thm)],[f_3240]) ).
tff(c_48291,plain,
( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_48213,c_810]) ).
tff(c_48363,plain,
~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1288,c_48291]) ).
tff(c_48431,plain,
c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[c_1042,c_48363]) ).
tff(c_1044,plain,
! [V_x_1389,V_y_1388,T_a_1387] :
( c_lessequals(V_x_1389,V_y_1388,T_a_1387)
| c_lessequals(V_y_1388,V_x_1389,T_a_1387)
| ~ class_Orderings_Olinorder(T_a_1387) ),
inference(cnfTransformation,[status(thm)],[f_4127]) ).
tff(c_1286,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4413]) ).
tff(c_54,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_36328,plain,
! [V_x_2132,V_y_2133,T_a_2134,V_z_2135] :
( ~ c_HOL_Oord__class_Oless(V_x_2132,V_y_2133,T_a_2134)
| ~ c_lessequals(V_y_2133,V_z_2135,T_a_2134)
| c_HOL_Oord__class_Oless(V_x_2132,V_z_2135,T_a_2134)
| ~ class_Orderings_Opreorder(T_a_2134) ),
inference(cnfTransformation,[status(thm)],[f_956]) ).
tff(c_36400,plain,
! [V_z_2135] :
( ~ c_lessequals(v_t____,V_z_2135,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2135,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_54,c_36328]) ).
tff(c_43303,plain,
! [V_z_2231] :
( ~ c_lessequals(v_t____,V_z_2231,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2231,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1286,c_36400]) ).
tff(c_1278,plain,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4409]) ).
tff(c_454,plain,
c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_1924]) ).
tff(c_9241,plain,
! [V_a_1744,T_a_1745] :
( c_HOL_Oord__class_Oless(V_a_1744,c_HOL_Ozero__class_Ozero(T_a_1745),T_a_1745)
| ( c_HOL_Oabs__class_Oabs(V_a_1744,T_a_1745) = V_a_1744 )
| ~ class_Ring__and__Field_Oabs__if(T_a_1745) ),
inference(cnfTransformation,[status(thm)],[f_3427]) ).
tff(c_348,plain,
! [V_x_496] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_496,tc_RealDef_Oreal)
| ( c_NthRoot_Osqrt(V_x_496) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(cnfTransformation,[status(thm)],[f_1488]) ).
tff(c_9261,plain,
( ( c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) != c_HOL_Ozero__class_Ozero(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) )
| ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_9241,c_348]) ).
tff(c_9302,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_1278,c_454,c_9261]) ).
tff(c_1274,plain,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4407]) ).
tff(c_1272,plain,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4406]) ).
tff(c_1252,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4396]) ).
tff(c_4604,plain,
! [V_b_1646,V_a_1647,T_a_1648] :
( ( c_HOL_Oplus__class_Oplus(V_b_1646,V_a_1647,T_a_1648) = c_HOL_Oplus__class_Oplus(V_a_1647,V_b_1646,T_a_1648) )
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a_1648) ),
inference(cnfTransformation,[status(thm)],[f_3108]) ).
tff(c_6515,plain,
! [V_b_1692,V_a_1693] : ( c_HOL_Oplus__class_Oplus(V_b_1692,V_a_1693,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(V_a_1693,V_b_1692,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1252,c_4604]) ).
tff(c_188,plain,
! [T_a_255,V_a_256] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a_255),V_a_256,T_a_255) = V_a_256 )
| ~ class_OrderedGroup_Omonoid__add(T_a_255) ),
inference(cnfTransformation,[status(thm)],[f_800]) ).
tff(c_6563,plain,
! [V_b_1692] :
( ( c_HOL_Oplus__class_Oplus(V_b_1692,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = V_b_1692 )
| ~ class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_6515,c_188]) ).
tff(c_6713,plain,
! [V_b_1692] : ( c_HOL_Oplus__class_Oplus(V_b_1692,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = V_b_1692 ),
inference(demodulation,[status(thm),theory(equality)],[c_1272,c_6563]) ).
tff(c_17805,plain,
! [V_a_1888,T_a_1889,V_b_1890] :
( ( c_HOL_Ouminus__class_Ouminus(V_a_1888,T_a_1889) = V_b_1890 )
| ( c_HOL_Oplus__class_Oplus(V_a_1888,V_b_1890,T_a_1889) != c_HOL_Ozero__class_Ozero(T_a_1889) )
| ~ class_OrderedGroup_Ogroup__add(T_a_1889) ),
inference(cnfTransformation,[status(thm)],[f_3178]) ).
tff(c_17831,plain,
! [V_b_1692] :
( ( c_HOL_Ouminus__class_Ouminus(V_b_1692,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_b_1692 )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_6713,c_17805]) ).
tff(c_18038,plain,
! [V_b_1892] :
( ( c_HOL_Ouminus__class_Ouminus(V_b_1892,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_b_1892 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1274,c_17831]) ).
tff(c_210,plain,
! [V_a_278,T_a_277] :
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a_278,T_a_277),T_a_277) = V_a_278 )
| ~ class_OrderedGroup_Ogroup__add(T_a_277) ),
inference(cnfTransformation,[status(thm)],[f_858]) ).
tff(c_1194,plain,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4367]) ).
tff(c_474,plain,
! [V_a_649,T_a_648] :
( ( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a_649,T_a_648),T_a_648) = c_HOL_Oabs__class_Oabs(V_a_649,T_a_648) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_648) ),
inference(cnfTransformation,[status(thm)],[f_1997]) ).
tff(c_1050,plain,
! [V_w_1398] : c_lessequals(V_w_1398,V_w_1398,tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4151]) ).
tff(c_14071,plain,
! [V_a_1826,T_a_1827,V_b_1828] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a_1826,T_a_1827),V_b_1828,T_a_1827)
| c_lessequals(V_a_1826,V_b_1828,T_a_1827)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_1827) ),
inference(cnfTransformation,[status(thm)],[f_1161]) ).
tff(c_14147,plain,
! [V_a_1826] :
( c_lessequals(V_a_1826,c_HOL_Oabs__class_Oabs(V_a_1826,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1050,c_14071]) ).
tff(c_14176,plain,
! [V_a_1829] : c_lessequals(V_a_1829,c_HOL_Oabs__class_Oabs(V_a_1829,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1194,c_14147]) ).
tff(c_14211,plain,
! [V_a_649] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a_649,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(V_a_649,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_474,c_14176]) ).
tff(c_14450,plain,
! [V_a_1834] : c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a_1834,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(V_a_1834,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1194,c_14211]) ).
tff(c_14517,plain,
! [V_a_278] :
( c_lessequals(V_a_278,c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a_278,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_210,c_14450]) ).
tff(c_14545,plain,
! [V_a_278] : c_lessequals(V_a_278,c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a_278,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1274,c_14517]) ).
tff(c_18047,plain,
! [V_b_1892] :
( c_lessequals(V_b_1892,c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_b_1892 ) ),
inference(superposition,[status(thm),theory(equality)],[c_18038,c_14545]) ).
tff(c_32173,plain,
! [V_b_2071] :
( c_lessequals(V_b_2071,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_b_2071 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_9302,c_18047]) ).
tff(c_292,plain,
! [V_y_416,V_x_415,T_a_414] :
( ~ c_HOL_Oord__class_Oless(V_y_416,V_x_415,T_a_414)
| ~ c_lessequals(V_x_415,V_y_416,T_a_414)
| ~ class_Orderings_Olinorder(T_a_414) ),
inference(cnfTransformation,[status(thm)],[f_1225]) ).
tff(c_32232,plain,
! [V_b_2071] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b_2071,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_b_2071 ) ),
inference(resolution,[status(thm)],[c_32173,c_292]) ).
tff(c_32291,plain,
! [V_b_2071] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b_2071,tc_RealDef_Oreal)
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_b_2071 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1288,c_32232]) ).
tff(c_43650,plain,
! [V_z_2235] :
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_z_2235 )
| ~ c_lessequals(v_t____,V_z_2235,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_43303,c_32291]) ).
tff(c_43690,plain,
! [V_y_1388] :
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_y_1388 )
| c_lessequals(V_y_1388,v_t____,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1044,c_43650]) ).
tff(c_43775,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1288,c_43690]) ).
tff(c_1212,plain,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4376]) ).
tff(c_1012,plain,
! [V_x_1342] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(V_x_1342,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x_1342,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4029]) ).
tff(c_23744,plain,
! [V_a_1973,T_a_1974] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a_1973,T_a_1974),V_a_1973,T_a_1974)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a_1974),V_a_1973,T_a_1974)
| ~ class_OrderedGroup_Oordered__ab__group__add(T_a_1974) ),
inference(cnfTransformation,[status(thm)],[f_3069]) ).
tff(c_23784,plain,
! [V_x_1342] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x_1342,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1012,c_23744]) ).
tff(c_23856,plain,
! [V_x_1342] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x_1342,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1212,c_23784]) ).
tff(c_162384,plain,
! [T_a_3101,V_x_3102,V_y_3103] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a_3101),V_x_3102,T_a_3101)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a_3101),V_y_3103,T_a_3101)
| ~ c_lessequals(V_y_3103,c_HOL_Oone__class_Oone(T_a_3101),T_a_3101)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_y_3103,V_x_3102,T_a_3101),V_x_3102,T_a_3101)
| ~ class_Ring__and__Field_Oordered__idom(T_a_3101) ),
inference(cnfTransformation,[status(thm)],[f_4060]) ).
tff(c_1104,plain,
! [V_z_1479] : ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_z_1479,tc_RealDef_Oreal) = V_z_1479 ),
inference(cnfTransformation,[status(thm)],[f_4304]) ).
tff(c_1118,plain,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4329]) ).
tff(c_1357,plain,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1104,c_1118]) ).
tff(c_162466,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
| ~ c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_162384,c_1357]) ).
tff(c_162720,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1256,c_48431,c_43775,c_23856,c_162466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : ALG406-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15 % 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
% 0.15/0.36 % Computer : n028.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 20:27:54 EDT 2023
% 0.15/0.36 % CPUTime :
% 58.09/40.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.09/40.31
% 58.09/40.31 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 58.09/40.35
% 58.09/40.35 Inference rules
% 58.09/40.35 ----------------------
% 58.09/40.35 #Ref : 24
% 58.09/40.35 #Sup : 36866
% 58.09/40.35 #Fact : 8
% 58.09/40.35 #Define : 0
% 58.09/40.35 #Split : 12
% 58.09/40.35 #Chain : 0
% 58.09/40.35 #Close : 0
% 58.09/40.36
% 58.09/40.36 Ordering : KBO
% 58.09/40.36
% 58.09/40.36 Simplification rules
% 58.09/40.36 ----------------------
% 58.09/40.36 #Subsume : 6184
% 58.09/40.36 #Demod : 23094
% 58.09/40.36 #Tautology : 6168
% 58.09/40.36 #SimpNegUnit : 717
% 58.09/40.36 #BackRed : 5
% 58.09/40.36
% 58.09/40.36 #Partial instantiations: 0
% 58.09/40.36 #Strategies tried : 1
% 58.09/40.36
% 58.09/40.36 Timing (in seconds)
% 58.09/40.36 ----------------------
% 58.09/40.36 Preprocessing : 1.50
% 58.09/40.36 Parsing : 0.87
% 58.09/40.36 CNF conversion : 0.13
% 58.09/40.36 Main loop : 37.77
% 58.09/40.36 Inferencing : 4.38
% 58.09/40.36 Reduction : 20.34
% 58.09/40.36 Demodulation : 16.53
% 58.09/40.36 BG Simplification : 0.44
% 58.09/40.36 Subsumption : 10.45
% 58.09/40.36 Abstraction : 0.43
% 58.09/40.36 MUC search : 0.00
% 58.09/40.36 Cooper : 0.00
% 58.09/40.36 Total : 39.35
% 58.09/40.36 Index Insertion : 0.00
% 58.09/40.36 Index Deletion : 0.00
% 58.09/40.36 Index Matching : 0.00
% 58.09/40.36 BG Taut test : 0.00
%------------------------------------------------------------------------------