TSTP Solution File: ALG371-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG371-1 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:32:37 EDT 2023
% Result : Unsatisfiable 13.94s 4.33s
% Output : CNFRefutation 14.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 82
% Syntax : Number of formulae : 117 ( 21 unt; 68 typ; 0 def)
% Number of atoms : 91 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 93 ( 51 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 81 ( 63 >; 18 *; 0 +; 0 <<)
% Number of predicates : 53 ( 51 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 47 (; 47 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osgn__if > 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_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__vector > class_RealVector_Oreal__normed__field > class_RealVector_Oreal__normed__div__algebra > class_RealVector_Oreal__normed__algebra > 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_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__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_Int_Onumber__ring > c_Power_Opower__class_Opower > c_Polynomial_Opoly > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Oinverse__class_Odivide > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 > c_RealVector_Onorm__class_Onorm > c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1 > c_HOL_Osgn__class_Osgn > #nlpp > c_Transcendental_Oln > c_RealDef_Oreal__of__preal > c_HOL_Ozero__class_Ozero > v_x > v_r > v_p > tc_RealDef_Oreal > tc_Complex_Ocomplex
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(c_Transcendental_Oln,type,
c_Transcendental_Oln: $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(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_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_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(c_RealDef_Oreal__of__preal,type,
c_RealDef_Oreal__of__preal: $i > $i ).
tff(c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1,type,
c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1: ( $i * $i ) > $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(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_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(class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
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(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(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $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(v_r,type,
v_r: $i ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(c_HOL_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_Polynomial_Opoly,type,
c_Polynomial_Opoly: ( $i * $i * $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(c_HOL_Osgn__class_Osgn,type,
c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).
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_Ring__and__Field_Osgn__if,type,
class_Ring__and__Field_Osgn__if: $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(v_p,type,
v_p: $i ).
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(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(f_4168,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_4106,axiom,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_4154,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3757,axiom,
! [V_x,V_y] :
( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_4105,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_4155,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3765,axiom,
! [T_a,V_x,V_y] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ),
file(unknown,unknown) ).
tff(f_4107,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3734,axiom,
! [V_i,V_k,V_j] :
( c_lessequals(V_i,V_k,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_4013,axiom,
! [T_a,V_x] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_3801,axiom,
! [T_a] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file(unknown,unknown) ).
tff(f_4096,axiom,
! [T_a,V_y,V_x] :
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file(unknown,unknown) ).
tff(f_3986,axiom,
! [V_z,V_w] :
( ( V_z = V_w )
| ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal)
| ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_4019,axiom,
! [T_a,V_x] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(c_978,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_4168]) ).
tff(c_856,plain,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4106]) ).
tff(c_950,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4154]) ).
tff(c_770,plain,
! [V_x_1268,V_y_1269] :
( ~ c_HOL_Oord__class_Oless(V_x_1268,V_y_1269,tc_RealDef_Oreal)
| c_lessequals(V_x_1268,V_y_1269,tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_3757]) ).
tff(c_2261,plain,
! [V_y_1451,V_x_1452,T_a_1453] :
( ~ c_HOL_Oord__class_Oless(V_y_1451,V_x_1452,T_a_1453)
| ~ c_lessequals(V_x_1452,V_y_1451,T_a_1453)
| ~ class_Orderings_Olinorder(T_a_1453) ),
inference(cnfTransformation,[status(thm)],[f_4105]) ).
tff(c_2273,plain,
! [V_y_1269,V_x_1268] :
( ~ c_HOL_Oord__class_Oless(V_y_1269,V_x_1268,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_x_1268,V_y_1269,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_770,c_2261]) ).
tff(c_2327,plain,
! [V_y_1456,V_x_1457] :
( ~ c_HOL_Oord__class_Oless(V_y_1456,V_x_1457,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_x_1457,V_y_1456,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_950,c_2273]) ).
tff(c_2342,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(resolution,[status(thm)],[c_856,c_2327]) ).
tff(c_952,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4155]) ).
tff(c_772,plain,
! [V_x_1271,V_y_1272,T_a_1270] :
( ~ c_HOL_Oord__class_Oless(V_x_1271,V_y_1272,T_a_1270)
| c_lessequals(V_x_1271,V_y_1272,T_a_1270)
| ~ class_Orderings_Oorder(T_a_1270) ),
inference(cnfTransformation,[status(thm)],[f_3765]) ).
tff(c_858,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4107]) ).
tff(c_4839,plain,
! [V_i_1535,V_j_1536,V_k_1537] :
( ~ c_lessequals(V_i_1535,V_j_1536,tc_RealDef_Oreal)
| ~ c_lessequals(V_j_1536,V_k_1537,tc_RealDef_Oreal)
| c_lessequals(V_i_1535,V_k_1537,tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_3734]) ).
tff(c_6357,plain,
! [V_k_1582] :
( ~ c_lessequals(v_r,V_k_1582,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),V_k_1582,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_858,c_4839]) ).
tff(c_832,plain,
! [V_x_1345,T_a_1344] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_x_1345,T_a_1344),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Ozero__class_Ozero(T_a_1344) = V_x_1345 )
| ~ class_RealVector_Oreal__normed__vector(T_a_1344) ),
inference(cnfTransformation,[status(thm)],[f_4013]) ).
tff(c_6372,plain,
( ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_x )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_6357,c_832]) ).
tff(c_6401,plain,
( ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_x )
| ~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_978,c_6372]) ).
tff(c_6412,plain,
~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(splitLeft,[status(thm)],[c_6401]) ).
tff(c_6418,plain,
( ~ c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_772,c_6412]) ).
tff(c_6438,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_952,c_856,c_6418]) ).
tff(c_6439,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_x,
inference(splitRight,[status(thm)],[c_6401]) ).
tff(c_784,plain,
! [T_a_1283] :
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a_1283),T_a_1283) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__normed__vector(T_a_1283) ),
inference(cnfTransformation,[status(thm)],[f_3801]) ).
tff(c_6525,plain,
( ( c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_6439,c_784]) ).
tff(c_6600,plain,
c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_978,c_6525]) ).
tff(c_852,plain,
! [V_x_1374,V_y_1373,T_a_1372] :
( c_lessequals(V_x_1374,V_y_1373,T_a_1372)
| c_HOL_Oord__class_Oless(V_y_1373,V_x_1374,T_a_1372)
| ~ class_Orderings_Olinorder(T_a_1372) ),
inference(cnfTransformation,[status(thm)],[f_4096]) ).
tff(c_4403,plain,
! [V_z_1524,V_w_1525] :
( ~ c_lessequals(V_z_1524,V_w_1525,tc_RealDef_Oreal)
| ~ c_lessequals(V_w_1525,V_z_1524,tc_RealDef_Oreal)
| ( V_z_1524 = V_w_1525 ) ),
inference(cnfTransformation,[status(thm)],[f_3986]) ).
tff(c_4472,plain,
( ~ c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex) = v_r ) ),
inference(resolution,[status(thm)],[c_858,c_4403]) ).
tff(c_5706,plain,
~ c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(splitLeft,[status(thm)],[c_4472]) ).
tff(c_5717,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_852,c_5706]) ).
tff(c_5731,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_950,c_5717]) ).
tff(c_7899,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_6600,c_5731]) ).
tff(c_7904,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2342,c_7899]) ).
tff(c_7905,plain,
c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex) = v_r,
inference(splitRight,[status(thm)],[c_4472]) ).
tff(c_834,plain,
! [V_x_1347,T_a_1346] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x_1347,T_a_1346),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a_1346) ),
inference(cnfTransformation,[status(thm)],[f_4019]) ).
tff(c_7921,plain,
( ~ c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_7905,c_834]) ).
tff(c_7932,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_978,c_856,c_7921]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG371-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 20:35:31 EDT 2023
% 0.13/0.35 % CPUTime :
% 13.94/4.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.94/4.34
% 13.94/4.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.35/4.38
% 14.35/4.38 Inference rules
% 14.35/4.38 ----------------------
% 14.35/4.38 #Ref : 5
% 14.35/4.38 #Sup : 1315
% 14.35/4.38 #Fact : 10
% 14.35/4.38 #Define : 0
% 14.35/4.38 #Split : 3
% 14.35/4.38 #Chain : 0
% 14.35/4.38 #Close : 0
% 14.35/4.38
% 14.35/4.38 Ordering : KBO
% 14.35/4.38
% 14.35/4.38 Simplification rules
% 14.35/4.38 ----------------------
% 14.35/4.38 #Subsume : 217
% 14.35/4.38 #Demod : 1052
% 14.35/4.38 #Tautology : 882
% 14.35/4.38 #SimpNegUnit : 23
% 14.35/4.38 #BackRed : 13
% 14.35/4.38
% 14.35/4.38 #Partial instantiations: 0
% 14.35/4.38 #Strategies tried : 1
% 14.35/4.38
% 14.35/4.38 Timing (in seconds)
% 14.35/4.38 ----------------------
% 14.35/4.38 Preprocessing : 1.44
% 14.35/4.38 Parsing : 0.83
% 14.35/4.38 CNF conversion : 0.12
% 14.35/4.38 Main loop : 1.82
% 14.35/4.38 Inferencing : 0.46
% 14.35/4.38 Reduction : 0.73
% 14.35/4.38 Demodulation : 0.52
% 14.35/4.38 BG Simplification : 0.15
% 14.35/4.38 Subsumption : 0.42
% 14.35/4.38 Abstraction : 0.05
% 14.35/4.38 MUC search : 0.00
% 14.35/4.38 Cooper : 0.00
% 14.35/4.38 Total : 3.32
% 14.35/4.38 Index Insertion : 0.00
% 14.35/4.38 Index Deletion : 0.00
% 14.35/4.38 Index Matching : 0.00
% 14.35/4.38 BG Taut test : 0.00
%------------------------------------------------------------------------------