TSTP Solution File: SWV620-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWV620-1 : 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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/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 11:05:20 EDT 2023
% Result : Unsatisfiable 256.99s 208.65s
% Output : CNFRefutation 257.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 122
% Syntax : Number of formulae : 237 ( 71 unt; 80 typ; 0 def)
% Number of atoms : 293 ( 112 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 278 ( 142 ~; 136 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 90 ( 72 >; 18 *; 0 +; 0 <<)
% Number of predicates : 57 ( 55 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 8 con; 0-3 aty)
% Number of variables : 234 (; 234 !; 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 > class_Ring__and__Field_Opordered__semiring > 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_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odivision__by__zero > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring > class_RealVector_Oreal__normed__field > class_RealVector_Oreal__normed__algebra > class_RealVector_Oreal__field > 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 > class_OrderedGroup_Oordered__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > 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_Oring__char__0 > class_Int_Onumber__ring > class_Int_Onumber > c_Power_Opower__class_Opower > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_HOL_Oinverse__class_Odivide > hAPP > c_RealDef_Oreal > c_Int_Onumber__class_Onumber__of > c_HOL_Ouminus__class_Ouminus > #nlpp > c_Transcendental_Osko__Transcendental__Xtan__total__1__1 > c_Transcendental_Osko__Transcendental__Xlemma__tan__total1__1__1 > c_Transcendental_Oarctan > c_Int_OBit1 > c_Int_OBit0 > c_HOL_Ozero__class_Ozero > c_FFT__Mirabelle_Oroot > c_Complex_Ocis > v_n > v_k > tc_nat > tc_RealDef_Oreal > tc_Int_Oint > tc_Complex_Ocomplex > c_Transcendental_Opi > c_Int_OPls
%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(c_Transcendental_Opi,type,
c_Transcendental_Opi: $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_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_RealDef_Oreal,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $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_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $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(class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(class_RealVector_Oreal__normed__field,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(v_n,type,
v_n: $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(c_HOL_Oinverse__class_Odivide,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
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_Int_Onumber,type,
class_Int_Onumber: $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_Int_OPls,type,
c_Int_OPls: $i ).
tff(c_Int_OBit0,type,
c_Int_OBit0: $i > $i ).
tff(c_Transcendental_Osko__Transcendental__Xlemma__tan__total1__1__1,type,
c_Transcendental_Osko__Transcendental__Xlemma__tan__total1__1__1: $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(v_k,type,
v_k: $i ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(c_Int_OBit1,type,
c_Int_OBit1: $i > $i ).
tff(class_Ring__and__Field_Oordered__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(c_FFT__Mirabelle_Oroot,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
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_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(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(c_Transcendental_Osko__Transcendental__Xtan__total__1__1,type,
c_Transcendental_Osko__Transcendental__Xtan__total__1__1: $i > $i ).
tff(class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $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(class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
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(hAPP,type,
hAPP: ( $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(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(class_RealVector_Oreal__field,type,
class_RealVector_Oreal__field: $i > $o ).
tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(c_Transcendental_Oarctan,type,
c_Transcendental_Oarctan: $i > $i ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(c_Complex_Ocis,type,
c_Complex_Ocis: $i > $i ).
tff(f_6977,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6990,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_1409,axiom,
! [T_a,V_a] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ),
file(unknown,unknown) ).
tff(f_1394,axiom,
! [V_x,V_z] : ( V_x = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_x,V_z,tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_1530,axiom,
! [V_x] : ( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_5287,axiom,
! [V_r,V_s] : ( c_HOL_Ominus__class_Ominus(V_r,V_s,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(V_r,c_HOL_Ouminus__class_Ouminus(V_s,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_3367,axiom,
! [V_x,V_a] :
( ( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( V_x = V_a ) ),
file(unknown,unknown) ).
tff(f_3211,axiom,
! [V_y,V_z] : ( V_y = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_y,V_z,tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_7003,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_5783,axiom,
! [T_a,V_z,V_y] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = V_y ) ),
file(unknown,unknown) ).
tff(f_5900,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) ) ),
file(unknown,unknown) ).
tff(f_7009,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_1392,axiom,
! [T_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ),
file(unknown,unknown) ).
tff(f_1465,axiom,
! [T_a,V_x,V_y,V_z] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y )
| ( V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ),
file(unknown,unknown) ).
tff(f_7013,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_7018,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3378,axiom,
! [T_a,V_x,V_a] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file(unknown,unknown) ).
tff(f_6999,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_5660,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_5335,axiom,
! [T_a,V_x,V_y,V_z] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) )
| ( V_y = V_z ) ),
file(unknown,unknown) ).
tff(f_6981,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_1414,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Ocomm__monoid__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_5928,axiom,
! [V_w] : c_lessequals(V_w,V_w,tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3870,axiom,
! [T_a,V_y,V_x_H,V_x,V_y_H] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) )
| c_lessequals(V_y_H,V_x_H,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ),
file(unknown,unknown) ).
tff(f_7016,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_4488,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_1308,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_1399,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
file(unknown,unknown) ).
tff(f_5324,axiom,
! [V_W,V_S] :
( c_HOL_Oord__class_Oless(V_W,V_S,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_S,c_HOL_Ouminus__class_Ouminus(V_W,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_5864,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ),
file(unknown,unknown) ).
tff(f_5752,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ),
file(unknown,unknown) ).
tff(f_6996,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_4485,axiom,
! [V_n] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(V_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6988,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6833,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(unknown,unknown) ).
tff(f_6564,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_4135,axiom,
! [T_a,V_b,V_a] :
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_3172,axiom,
! [T_a,V_x,V_y] :
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ),
file(unknown,unknown) ).
tff(f_6502,axiom,
! [T_a,V_z] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),V_z,T_a) = c_HOL_Oplus__class_Oplus(V_z,V_z,T_a) ) ),
file(unknown,unknown) ).
tff(f_6893,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6890,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
file(unknown,unknown) ).
tff(f_6889,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_k,v_n,tc_nat) ),
file(unknown,unknown) ).
tff(c_1610,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6977]) ).
tff(c_1636,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6990]) ).
tff(c_338,plain,
! [V_a_567,T_a_566] :
( ( c_HOL_Oplus__class_Oplus(V_a_567,c_HOL_Ozero__class_Ozero(T_a_566),T_a_566) = V_a_567 )
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a_566) ),
inference(cnfTransformation,[status(thm)],[f_1409]) ).
tff(c_2038,plain,
! [V_x_2270,V_z_2271] : ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_x_2270,V_z_2271,tc_RealDef_Oreal),V_z_2271,tc_RealDef_Oreal) = V_x_2270 ),
inference(cnfTransformation,[status(thm)],[f_1394]) ).
tff(c_2055,plain,
! [V_a_567] :
( ( c_HOL_Ominus__class_Ominus(V_a_567,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = V_a_567 )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_338,c_2038]) ).
tff(c_2087,plain,
! [V_a_2273] : ( c_HOL_Ominus__class_Ominus(V_a_2273,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = V_a_2273 ),
inference(demodulation,[status(thm),theory(equality)],[c_1636,c_2055]) ).
tff(c_332,plain,
! [V_x_559,V_z_560] : ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_x_559,V_z_560,tc_RealDef_Oreal),V_z_560,tc_RealDef_Oreal) = V_x_559 ),
inference(cnfTransformation,[status(thm)],[f_1394]) ).
tff(c_2098,plain,
! [V_x_559] : ( c_HOL_Oplus__class_Oplus(V_x_559,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x_559 ),
inference(superposition,[status(thm),theory(equality)],[c_2087,c_332]) ).
tff(c_378,plain,
! [V_x_617] : ( c_HOL_Oplus__class_Oplus(V_x_617,c_HOL_Ouminus__class_Ouminus(V_x_617,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_1530]) ).
tff(c_1044,plain,
! [V_r_1707,V_s_1708] : ( c_HOL_Oplus__class_Oplus(V_r_1707,c_HOL_Ouminus__class_Ouminus(V_s_1708,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(V_r_1707,V_s_1708,tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_5287]) ).
tff(c_678,plain,
! [V_x_1159,V_a_1160] :
( ( V_x_1159 = V_a_1160 )
| ( c_HOL_Oplus__class_Oplus(V_x_1159,c_HOL_Ouminus__class_Ouminus(V_a_1160,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(cnfTransformation,[status(thm)],[f_3367]) ).
tff(c_2722,plain,
! [V_x_2298,V_a_2299] :
( ( V_x_2298 = V_a_2299 )
| ( c_HOL_Ominus__class_Ominus(V_x_2298,V_a_2299,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1044,c_678]) ).
tff(c_2874,plain,
! [V_x_2307,V_z_2308] :
( ( c_HOL_Oplus__class_Oplus(V_x_2307,V_z_2308,tc_RealDef_Oreal) = V_z_2308 )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_x_2307 ) ),
inference(superposition,[status(thm),theory(equality)],[c_332,c_2722]) ).
tff(c_2936,plain,
! [V_x_617] :
( ( c_HOL_Ouminus__class_Ouminus(V_x_617,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_x_617 ) ),
inference(superposition,[status(thm),theory(equality)],[c_378,c_2874]) ).
tff(c_5569,plain,
! [V_r_2360,V_s_2361] : ( c_HOL_Oplus__class_Oplus(V_r_2360,c_HOL_Ouminus__class_Ouminus(V_s_2361,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(V_r_2360,V_s_2361,tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_5287]) ).
tff(c_5633,plain,
! [V_r_2360,V_x_617] :
( ( c_HOL_Oplus__class_Oplus(V_r_2360,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(V_r_2360,V_x_617,tc_RealDef_Oreal) )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_x_617 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2936,c_5569]) ).
tff(c_5715,plain,
! [V_r_2362,V_x_2363] :
( ( c_HOL_Ominus__class_Ominus(V_r_2362,V_x_2363,tc_RealDef_Oreal) = V_r_2362 )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_x_2363 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2098,c_5633]) ).
tff(c_638,plain,
! [V_y_1090,V_z_1091] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_y_1090,V_z_1091,tc_RealDef_Oreal),V_z_1091,tc_RealDef_Oreal) = V_y_1090 ),
inference(cnfTransformation,[status(thm)],[f_3211]) ).
tff(c_5735,plain,
! [V_r_2362,V_x_2363] :
( ( c_HOL_Oplus__class_Oplus(V_r_2362,V_x_2363,tc_RealDef_Oreal) = V_r_2362 )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_x_2363 ) ),
inference(superposition,[status(thm),theory(equality)],[c_5715,c_638]) ).
tff(c_1662,plain,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_7003]) ).
tff(c_18977,plain,
! [V_z_2587,T_a_2588,V_y_2589] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_z_2587,T_a_2588),c_HOL_Oplus__class_Oplus(V_y_2589,V_z_2587,T_a_2588),T_a_2588) = V_y_2589 )
| ~ class_OrderedGroup_Oab__group__add(T_a_2588) ),
inference(cnfTransformation,[status(thm)],[f_5783]) ).
tff(c_19228,plain,
! [V_z_1091,V_y_1090] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_z_1091,tc_RealDef_Oreal),V_y_1090,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(V_y_1090,V_z_1091,tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_638,c_18977]) ).
tff(c_19341,plain,
! [V_z_1091,V_y_1090] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_z_1091,tc_RealDef_Oreal),V_y_1090,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(V_y_1090,V_z_1091,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1662,c_19228]) ).
tff(c_1194,plain,
! [V_a_1918,T_a_1917,V_b_1919] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(V_a_1918,T_a_1917),c_HOL_Ouminus__class_Ouminus(V_b_1919,T_a_1917),T_a_1917) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a_1918,V_b_1919,T_a_1917),T_a_1917) )
| ~ class_OrderedGroup_Oab__group__add(T_a_1917) ),
inference(cnfTransformation,[status(thm)],[f_5900]) ).
tff(c_1674,plain,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_7009]) ).
tff(c_330,plain,
! [V_b_558,T_a_557] :
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b_558,T_a_557),T_a_557) = V_b_558 )
| ~ class_OrderedGroup_Ogroup__add(T_a_557) ),
inference(cnfTransformation,[status(thm)],[f_1392]) ).
tff(c_5652,plain,
! [V_r_2360,V_b_558] :
( ( c_HOL_Ominus__class_Ominus(V_r_2360,c_HOL_Ouminus__class_Ouminus(V_b_558,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(V_r_2360,V_b_558,tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_330,c_5569]) ).
tff(c_111753,plain,
! [V_r_3350,V_b_3351] : ( c_HOL_Ominus__class_Ominus(V_r_3350,c_HOL_Ouminus__class_Ouminus(V_b_3351,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(V_r_3350,V_b_3351,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1674,c_5652]) ).
tff(c_111884,plain,
! [V_a_1918,V_b_1919] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a_1918,tc_RealDef_Oreal),V_b_1919,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a_1918,V_b_1919,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_1194,c_111753]) ).
tff(c_111995,plain,
! [V_a_1918,V_b_1919] : ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a_1918,V_b_1919,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(V_b_1919,V_a_1918,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1662,c_19341,c_111884]) ).
tff(c_32498,plain,
! [V_z_2788,T_a_2789,V_x_2790,V_y_2791] :
( ( c_HOL_Ouminus__class_Ouminus(V_z_2788,T_a_2789) = V_x_2790 )
| ( c_HOL_Oplus__class_Oplus(V_x_2790,c_HOL_Oplus__class_Oplus(V_y_2791,V_z_2788,T_a_2789),T_a_2789) != V_y_2791 )
| ~ class_OrderedGroup_Oab__group__add(T_a_2789) ),
inference(cnfTransformation,[status(thm)],[f_1465]) ).
tff(c_32740,plain,
! [V_y_2791,V_z_2788] :
( ( c_HOL_Ominus__class_Ominus(V_y_2791,c_HOL_Oplus__class_Oplus(V_y_2791,V_z_2788,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(V_z_2788,tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_638,c_32498]) ).
tff(c_103413,plain,
! [V_y_3307,V_z_3308] : ( c_HOL_Ominus__class_Ominus(V_y_3307,c_HOL_Oplus__class_Oplus(V_y_3307,V_z_3308,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(V_z_3308,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1662,c_32740]) ).
tff(c_1682,plain,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_7013]) ).
tff(c_1692,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_7018]) ).
tff(c_17154,plain,
! [T_a_2560,V_a_2561,V_x_2562] :
( ( c_HOL_Ozero__class_Ozero(T_a_2560) = V_a_2561 )
| ( c_HOL_Oplus__class_Oplus(V_x_2562,V_a_2561,T_a_2560) != V_x_2562 )
| ~ class_Int_Onumber__ring(T_a_2560)
| ~ class_Ring__and__Field_Oidom(T_a_2560) ),
inference(cnfTransformation,[status(thm)],[f_3378]) ).
tff(c_17226,plain,
! [V_z_1091,V_y_1090] :
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = V_z_1091 )
| ( c_HOL_Ominus__class_Ominus(V_y_1090,V_z_1091,tc_RealDef_Oreal) != V_y_1090 )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_638,c_17154]) ).
tff(c_17296,plain,
! [V_z_1091,V_y_1090] :
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = V_z_1091 )
| ( c_HOL_Ominus__class_Ominus(V_y_1090,V_z_1091,tc_RealDef_Oreal) != V_y_1090 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1682,c_1692,c_17226]) ).
tff(c_186076,plain,
! [V_y_3907,V_z_3908] :
( ( c_HOL_Oplus__class_Oplus(V_y_3907,V_z_3908,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Ouminus__class_Ouminus(V_z_3908,tc_RealDef_Oreal) != V_y_3907 ) ),
inference(superposition,[status(thm),theory(equality)],[c_103413,c_17296]) ).
tff(c_1654,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6999]) ).
tff(c_9497,plain,
! [V_b_2448,V_a_2449,T_a_2450] :
( ( c_HOL_Oplus__class_Oplus(V_b_2448,V_a_2449,T_a_2450) = c_HOL_Oplus__class_Oplus(V_a_2449,V_b_2448,T_a_2450) )
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a_2450) ),
inference(cnfTransformation,[status(thm)],[f_5660]) ).
tff(c_9506,plain,
! [V_b_2448,V_a_2449] : ( c_HOL_Oplus__class_Oplus(V_b_2448,V_a_2449,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(V_a_2449,V_b_2448,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1654,c_9497]) ).
tff(c_42095,plain,
! [V_z_2908,V_y_2909,V_x_2910,T_a_2911] :
( ( V_z_2908 = V_y_2909 )
| ( c_HOL_Oplus__class_Oplus(V_x_2910,V_z_2908,T_a_2911) != c_HOL_Oplus__class_Oplus(V_x_2910,V_y_2909,T_a_2911) )
| ~ class_Int_Onumber__ring(T_a_2911)
| ~ class_Ring__and__Field_Oidom(T_a_2911) ),
inference(cnfTransformation,[status(thm)],[f_5335]) ).
tff(c_42273,plain,
! [V_z_1091,V_y_2909,V_y_1090] :
( ( V_z_1091 = V_y_2909 )
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_y_1090,V_z_1091,tc_RealDef_Oreal),V_y_2909,tc_RealDef_Oreal) != V_y_1090 )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_638,c_42095]) ).
tff(c_92414,plain,
! [V_z_3212,V_y_3213,V_y_3214] :
( ( V_z_3212 = V_y_3213 )
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_y_3214,V_z_3212,tc_RealDef_Oreal),V_y_3213,tc_RealDef_Oreal) != V_y_3214 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1682,c_1692,c_42273]) ).
tff(c_92506,plain,
! [V_z_3212,V_a_2449,V_y_3214] :
( ( V_z_3212 = V_a_2449 )
| ( c_HOL_Oplus__class_Oplus(V_a_2449,c_HOL_Ominus__class_Ominus(V_y_3214,V_z_3212,tc_RealDef_Oreal),tc_RealDef_Oreal) != V_y_3214 ) ),
inference(superposition,[status(thm),theory(equality)],[c_9506,c_92414]) ).
tff(c_186095,plain,
! [V_z_3212,V_y_3907,V_y_3214] :
( ( V_z_3212 = V_y_3907 )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_y_3214 )
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_y_3214,V_z_3212,tc_RealDef_Oreal),tc_RealDef_Oreal) != V_y_3907 ) ),
inference(superposition,[status(thm),theory(equality)],[c_186076,c_92506]) ).
tff(c_210355,plain,
! [V_z_3212] : ( c_HOL_Ominus__class_Ominus(V_z_3212,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = V_z_3212 ),
inference(demodulation,[status(thm),theory(equality)],[c_111995,c_186095]) ).
tff(c_1618,plain,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6981]) ).
tff(c_103461,plain,
! [V_y_3307,V_z_3308] :
( ( c_HOL_Oplus__class_Oplus(V_y_3307,V_z_3308,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Ouminus__class_Ouminus(V_z_3308,tc_RealDef_Oreal) != V_y_3307 ) ),
inference(superposition,[status(thm),theory(equality)],[c_103413,c_17296]) ).
tff(c_17172,plain,
! [V_b_2448,V_a_2449] :
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = V_b_2448 )
| ( c_HOL_Oplus__class_Oplus(V_b_2448,V_a_2449,tc_RealDef_Oreal) != V_a_2449 )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_9506,c_17154]) ).
tff(c_17255,plain,
! [V_b_2448,V_a_2449] :
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = V_b_2448 )
| ( c_HOL_Oplus__class_Oplus(V_b_2448,V_a_2449,tc_RealDef_Oreal) != V_a_2449 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1682,c_1692,c_17172]) ).
tff(c_213730,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(superposition,[status(thm),theory(equality)],[c_186076,c_17255]) ).
tff(c_2827,plain,
! [V_x_2306] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(V_x_2306,tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x_2306 ),
inference(superposition,[status(thm),theory(equality)],[c_378,c_2038]) ).
tff(c_2850,plain,
! [V_b_558] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b_558,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(V_b_558,tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_330,c_2827]) ).
tff(c_2866,plain,
! [V_b_558] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b_558,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(V_b_558,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1674,c_2850]) ).
tff(c_340,plain,
! [T_a_568,V_a_569] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a_568),V_a_569,T_a_568) = V_a_569 )
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a_568) ),
inference(cnfTransformation,[status(thm)],[f_1414]) ).
tff(c_2048,plain,
! [V_a_569] :
( ( c_HOL_Ominus__class_Ominus(V_a_569,V_a_569,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_340,c_2038]) ).
tff(c_2071,plain,
! [V_a_569] : ( c_HOL_Ominus__class_Ominus(V_a_569,V_a_569,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1654,c_2048]) ).
tff(c_1206,plain,
! [V_w_1931] : c_lessequals(V_w_1931,V_w_1931,tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_5928]) ).
tff(c_93155,plain,
! [V_y_H_3225,V_y_3222,V_x_H_3223,V_x_3224,T_a_3221] :
( ~ c_lessequals(V_y_3222,V_x_3224,T_a_3221)
| c_lessequals(V_y_H_3225,V_x_H_3223,T_a_3221)
| ( c_HOL_Ominus__class_Ominus(V_x_H_3223,V_y_H_3225,T_a_3221) != c_HOL_Ominus__class_Ominus(V_x_3224,V_y_3222,T_a_3221) )
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_3221) ),
inference(cnfTransformation,[status(thm)],[f_3870]) ).
tff(c_93303,plain,
! [V_y_H_3225,V_x_H_3223,V_w_1931] :
( c_lessequals(V_y_H_3225,V_x_H_3223,tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(V_x_H_3223,V_y_H_3225,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(V_w_1931,V_w_1931,tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1206,c_93155]) ).
tff(c_113770,plain,
! [V_y_H_3363,V_x_H_3364] :
( c_lessequals(V_y_H_3363,V_x_H_3364,tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(V_x_H_3364,V_y_H_3363,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1618,c_2071,c_93303]) ).
tff(c_1688,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_7016]) ).
tff(c_918,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4488]) ).
tff(c_31408,plain,
! [V_y_2769,V_x_2770,T_a_2771,V_z_2772] :
( ~ c_HOL_Oord__class_Oless(V_y_2769,V_x_2770,T_a_2771)
| ~ c_lessequals(V_z_2772,V_y_2769,T_a_2771)
| c_HOL_Oord__class_Oless(V_z_2772,V_x_2770,T_a_2771)
| ~ class_Orderings_Oorder(T_a_2771) ),
inference(cnfTransformation,[status(thm)],[f_1308]) ).
tff(c_31452,plain,
! [V_z_2772] :
( ~ c_lessequals(V_z_2772,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(V_z_2772,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_918,c_31408]) ).
tff(c_31510,plain,
! [V_z_2772] :
( ~ c_lessequals(V_z_2772,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(V_z_2772,c_Transcendental_Opi,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1688,c_31452]) ).
tff(c_113854,plain,
! [V_y_H_3363] :
( c_HOL_Oord__class_Oless(V_y_H_3363,c_Transcendental_Opi,tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_H_3363,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(resolution,[status(thm)],[c_113770,c_31510]) ).
tff(c_113987,plain,
! [V_y_H_3363] :
( c_HOL_Oord__class_Oless(V_y_H_3363,c_Transcendental_Opi,tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(V_y_H_3363,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2866,c_113854]) ).
tff(c_334,plain,
! [V_a_562,V_b_563,T_a_561] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a_562,V_b_563,T_a_561),V_b_563,T_a_561) = V_a_562 )
| ~ class_OrderedGroup_Ogroup__add(T_a_561) ),
inference(cnfTransformation,[status(thm)],[f_1399]) ).
tff(c_1058,plain,
! [V_S_1727,V_W_1726] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_S_1727,c_HOL_Ouminus__class_Ouminus(V_W_1726,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(V_W_1726,V_S_1727,tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_5324]) ).
tff(c_22253,plain,
! [V_S_2622,V_W_2623] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(V_S_2622,V_W_2623,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(V_W_2623,V_S_2622,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1044,c_1058]) ).
tff(c_22274,plain,
! [V_a_562,V_b_563] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a_562,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(V_b_563,c_HOL_Oplus__class_Oplus(V_a_562,V_b_563,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_334,c_22253]) ).
tff(c_327425,plain,
! [V_a_4738,V_b_4739] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a_4738,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(V_b_4739,c_HOL_Oplus__class_Oplus(V_a_4738,V_b_4739,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1674,c_22274]) ).
tff(c_327485,plain,
! [V_b_4739] :
( c_HOL_Oord__class_Oless(V_b_4739,c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,V_b_4739,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( 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(resolution,[status(thm)],[c_113987,c_327425]) ).
tff(c_327640,plain,
! [V_b_4740] : c_HOL_Oord__class_Oless(V_b_4740,c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,V_b_4740,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_213730,c_327485]) ).
tff(c_347375,plain,
! [V_z_4841] :
( c_HOL_Oord__class_Oless(V_z_4841,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(V_z_4841,tc_RealDef_Oreal) != c_Transcendental_Opi ) ),
inference(superposition,[status(thm),theory(equality)],[c_103461,c_327640]) ).
tff(c_1182,plain,
! [V_a_1908,V_b_1909,T_a_1907] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a_1908,V_b_1909,T_a_1907),c_HOL_Ozero__class_Ozero(T_a_1907),T_a_1907)
| c_HOL_Oord__class_Oless(V_a_1908,V_b_1909,T_a_1907)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_1907) ),
inference(cnfTransformation,[status(thm)],[f_5864]) ).
tff(c_347593,plain,
! [V_a_1908,V_b_1909] :
( c_HOL_Oord__class_Oless(V_a_1908,V_b_1909,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a_1908,V_b_1909,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_Transcendental_Opi ) ),
inference(resolution,[status(thm)],[c_347375,c_1182]) ).
tff(c_349344,plain,
! [V_a_4848,V_b_4849] :
( c_HOL_Oord__class_Oless(V_a_4848,V_b_4849,tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(V_b_4849,V_a_4848,tc_RealDef_Oreal) != c_Transcendental_Opi ) ),
inference(demodulation,[status(thm),theory(equality)],[c_111995,c_1618,c_347593]) ).
tff(c_22302,plain,
! [V_a_562,V_b_563] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a_562,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(V_b_563,c_HOL_Oplus__class_Oplus(V_a_562,V_b_563,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1674,c_22274]) ).
tff(c_349419,plain,
! [V_b_563,V_b_4849] :
( c_HOL_Oord__class_Oless(V_b_563,c_HOL_Oplus__class_Oplus(V_b_4849,V_b_563,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(V_b_4849,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) != c_Transcendental_Opi ) ),
inference(resolution,[status(thm)],[c_349344,c_22302]) ).
tff(c_362848,plain,
! [V_b_4910,V_b_4911] :
( c_HOL_Oord__class_Oless(V_b_4910,c_HOL_Oplus__class_Oplus(V_b_4911,V_b_4910,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Transcendental_Opi != V_b_4911 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_210355,c_349419]) ).
tff(c_372420,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
inference(superposition,[status(thm),theory(equality)],[c_5735,c_362848]) ).
tff(c_1154,plain,
! [T_a_1871,V_a_1872,V_b_1873] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a_1871),V_a_1872,T_a_1871)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a_1871),V_b_1873,T_a_1871)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a_1871),c_HOL_Oplus__class_Oplus(V_a_1872,V_b_1873,T_a_1871),T_a_1871)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a_1871) ),
inference(cnfTransformation,[status(thm)],[f_5752]) ).
tff(c_1648,plain,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6996]) ).
tff(c_2735,plain,
! [V_x_559,V_z_560] :
( ( c_HOL_Oplus__class_Oplus(V_x_559,V_z_560,tc_RealDef_Oreal) = V_z_560 )
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_x_559 ) ),
inference(superposition,[status(thm),theory(equality)],[c_332,c_2722]) ).
tff(c_914,plain,
! [V_n_1503] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(V_n_1503,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4485]) ).
tff(c_1632,plain,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6988]) ).
tff(c_1422,plain,
! [V_z_2211,V_w_2212] : ( c_HOL_Otimes__class_Otimes(V_z_2211,V_w_2212,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w_2212,V_z_2211,tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_6833]) ).
tff(c_1322,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6564]) ).
tff(c_1761,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1422,c_1322]) ).
tff(c_201499,plain,
! [T_a_3986,V_a_3987,V_b_3988] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a_3986),c_HOL_Oinverse__class_Odivide(V_a_3987,V_b_3988,T_a_3986),T_a_3986)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a_3986),V_b_3988,T_a_3986)
| c_HOL_Oord__class_Oless(V_b_3988,c_HOL_Ozero__class_Ozero(T_a_3986),T_a_3986)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a_3986)
| ~ class_Ring__and__Field_Oordered__field(T_a_3986) ),
inference(cnfTransformation,[status(thm)],[f_4135]) ).
tff(c_201502,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealDef_Oreal(v_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1761,c_201499]) ).
tff(c_201642,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealDef_Oreal(v_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1648,c_1632,c_201502]) ).
tff(c_201643,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),
inference(negUnitSimplification,[status(thm)],[c_914,c_201642]) ).
tff(c_337696,plain,
! [V_b_4803] : c_HOL_Oord__class_Oless(V_b_4803,c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(v_n,tc_nat),V_b_4803,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[c_201643,c_327425]) ).
tff(c_343024,plain,
! [V_b_4821] : c_HOL_Oord__class_Oless(V_b_4821,c_HOL_Oplus__class_Oplus(V_b_4821,c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm),theory(equality)],[c_9506,c_337696]) ).
tff(c_343443,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),
inference(superposition,[status(thm),theory(equality)],[c_2735,c_343024]) ).
tff(c_630,plain,
! [T_a_1079,V_x_1080,V_y_1081] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a_1079),V_x_1080,T_a_1079)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a_1079),V_y_1081,T_a_1079)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a_1079),c_HOL_Oinverse__class_Odivide(V_x_1080,V_y_1081,T_a_1079),T_a_1079)
| ~ class_Ring__and__Field_Oordered__field(T_a_1079) ),
inference(cnfTransformation,[status(thm)],[f_3172]) ).
tff(c_30351,plain,
! [T_a_2752,V_z_2753] :
( ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a_2752),V_z_2753,T_a_2752) = c_HOL_Oplus__class_Oplus(V_z_2753,V_z_2753,T_a_2752) )
| ~ class_Int_Onumber__ring(T_a_2752) ),
inference(cnfTransformation,[status(thm)],[f_6502]) ).
tff(c_30784,plain,
! [V_z_2211] :
( ( c_HOL_Otimes__class_Otimes(V_z_2211,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(V_z_2211,V_z_2211,tc_RealDef_Oreal) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_1422,c_30351]) ).
tff(c_30932,plain,
! [V_z_2211] : ( c_HOL_Otimes__class_Otimes(V_z_2211,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(V_z_2211,V_z_2211,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1692,c_30784]) ).
tff(c_1442,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6893]) ).
tff(c_1438,plain,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
inference(cnfTransformation,[status(thm)],[f_6890]) ).
tff(c_1436,plain,
( ~ c_HOL_Oord__class_Oless(v_k,v_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_6889]) ).
tff(c_1756,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1438,c_1436]) ).
tff(c_1757,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(negUnitSimplification,[status(thm)],[c_1442,c_1756]) ).
tff(c_1759,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1422,c_1757]) ).
tff(c_404489,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_30932,c_1759]) ).
tff(c_617517,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_630,c_404489]) ).
tff(c_617572,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1648,c_343443,c_617517]) ).
tff(c_617608,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1154,c_617572]) ).
tff(c_617666,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1610,c_372420,c_617608]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWV620-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.10 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.10/0.30 % Computer : n010.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Thu Aug 3 22:22:43 EDT 2023
% 0.10/0.30 % CPUTime :
% 256.99/208.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 256.99/208.67
% 256.99/208.67 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 257.15/208.72
% 257.15/208.72 Inference rules
% 257.15/208.72 ----------------------
% 257.15/208.72 #Ref : 157
% 257.15/208.72 #Sup : 130254
% 257.15/208.72 #Fact : 26
% 257.15/208.72 #Define : 0
% 257.15/208.72 #Split : 16
% 257.15/208.72 #Chain : 0
% 257.15/208.72 #Close : 0
% 257.15/208.72
% 257.15/208.72 Ordering : KBO
% 257.15/208.72
% 257.15/208.72 Simplification rules
% 257.15/208.72 ----------------------
% 257.15/208.72 #Subsume : 34265
% 257.15/208.72 #Demod : 132038
% 257.15/208.72 #Tautology : 20970
% 257.15/208.72 #SimpNegUnit : 1731
% 257.15/208.72 #BackRed : 33
% 257.15/208.72
% 257.15/208.72 #Partial instantiations: 0
% 257.15/208.72 #Strategies tried : 1
% 257.15/208.72
% 257.15/208.72 Timing (in seconds)
% 257.15/208.72 ----------------------
% 257.15/208.73 Preprocessing : 1.70
% 257.15/208.73 Parsing : 0.98
% 257.15/208.73 CNF conversion : 0.14
% 257.15/208.73 Main loop : 206.03
% 257.15/208.73 Inferencing : 13.63
% 257.15/208.73 Reduction : 107.73
% 257.15/208.73 Demodulation : 90.19
% 257.15/208.73 BG Simplification : 1.23
% 257.15/208.73 Subsumption : 53.58
% 257.15/208.73 Abstraction : 1.57
% 257.15/208.73 MUC search : 0.00
% 257.15/208.73 Cooper : 0.00
% 257.15/208.73 Total : 207.82
% 257.15/208.73 Index Insertion : 0.00
% 257.15/208.73 Index Deletion : 0.00
% 257.15/208.73 Index Matching : 0.00
% 257.15/208.73 BG Taut test : 0.00
%------------------------------------------------------------------------------