TSTP Solution File: ALG341-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG341-1 : 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 : n029.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 10:32:34 EDT 2023
% Result : Unsatisfiable 60.62s 41.88s
% Output : CNFRefutation 60.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 119
% Syntax : Number of formulae : 169 ( 32 unt; 98 typ; 0 def)
% Number of atoms : 123 ( 46 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 104 ( 52 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 122 ( 88 >; 34 *; 0 +; 0 <<)
% Number of predicates : 63 ( 61 usr; 1 prp; 0-3 aty)
% Number of functors : 37 ( 37 usr; 10 con; 0-3 aty)
% Number of variables : 102 (; 102 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > class_SEQ_Obanach > 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__abs > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__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_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_RealVector_Oreal__vector > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__field > class_RealVector_Oreal__normed__algebra > class_RealVector_Oreal__field > class_RealVector_Oreal__algebra__1 > class_RealVector_Oreal__algebra > class_RealVector_Ometric__space > class_RealVector_Odist__norm > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__comm__monoid__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_Nat_Osemiring__char__0 > class_Lattices_Oboolean__algebra > class_Int_Onumber__ring > c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1 > c_RealVector_OscaleR__class_OscaleR > c_RealVector_Odist__class_Odist > 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 > c_Transcendental_Oexp > c_RealVector_Osko__RealVector__XscaleR__left__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__XscaleR__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__Xof__real__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__Xdivide__Xnonneg__bounded__1__1 > c_RealVector_Oof__real > c_RealVector_Onorm__class_Onorm > c_RealDef_Oreal > c_OrderedGroup_Olordered__ab__group__add__class_Onprt > c_Nat_Osemiring__1__class_Oof__nat > c_HOL_Ouminus__class_Ouminus > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > #nlpp > c_Transcendental_Osko__Transcendental__Xtan__total__pos__1__1 > c_NthRoot_Osqrt > c_HOL_Ozero__class_Ozero > v_z____ > v_r > tc_nat > tc_RealDef_Oreal > tc_Complex_Ocomplex > c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1 > c_Transcendental_Opi > c_Complex_Osko__Complex__Xcnj__Xnonneg__bounded__1__1 > c_Complex_Osko__Complex__XRe__Xnonneg__bounded__1__1 > c_Complex_Osko__Complex__XIm__Xnonneg__bounded__1__1
%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_Ring__and__Field_Opordered__ring__abs,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(class_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(c_Complex_Osko__Complex__Xcnj__Xnonneg__bounded__1__1,type,
c_Complex_Osko__Complex__Xcnj__Xnonneg__bounded__1__1: $i ).
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_RealVector_Osko__RealVector__XscaleR__Xnonneg__bounded__1__1,type,
c_RealVector_Osko__RealVector__XscaleR__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
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_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(c_Complex_Osko__Complex__XRe__Xnonneg__bounded__1__1,type,
c_Complex_Osko__Complex__XRe__Xnonneg__bounded__1__1: $i ).
tff(class_RealVector_Oreal__vector,type,
class_RealVector_Oreal__vector: $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(c_RealVector_OscaleR__class_OscaleR,type,
c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).
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(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_RealVector_Oreal__normed__field,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add__abs,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(c_Transcendental_Osko__Transcendental__Xtan__total__pos__1__1,type,
c_Transcendental_Osko__Transcendental__Xtan__total__pos__1__1: $i > $i ).
tff(c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(c_Complex_Osko__Complex__XIm__Xnonneg__bounded__1__1,type,
c_Complex_Osko__Complex__XIm__Xnonneg__bounded__1__1: $i ).
tff(class_RealVector_Ometric__space,type,
class_RealVector_Ometric__space: $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(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_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_SEQ_Obanach,type,
class_SEQ_Obanach: $i > $o ).
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__Xof__real__Xnonneg__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xof__real__Xnonneg__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__Xdivide__Xnonneg__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xdivide__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(c_OrderedGroup_Olordered__ab__group__add__class_Onprt,type,
c_OrderedGroup_Olordered__ab__group__add__class_Onprt: ( $i * $i ) > $i ).
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_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(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_RealVector_Oreal__algebra,type,
class_RealVector_Oreal__algebra: $i > $o ).
tff(class_RealVector_Oreal__algebra__1,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(v_r,type,
v_r: $i ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $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(c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1,type,
c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1: $i ).
tff(c_Transcendental_Oexp,type,
c_Transcendental_Oexp: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Omult__mono1,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(c_RealVector_Osko__RealVector__XscaleR__left__Xnonneg__bounded__1__1,type,
c_RealVector_Osko__RealVector__XscaleR__left__Xnonneg__bounded__1__1: ( $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(v_z____,type,
v_z____: $i ).
tff(class_OrderedGroup_Olordered__ab__group__add__abs,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1,type,
c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Olordered__ring,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(c_HOL_Ouminus__class_Ouminus,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(class_Ring__and__Field_Omult__mono,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(c_HOL_Oabs__class_Oabs,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_RealVector_Oof__real,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(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_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_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
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_RealVector_Odist__class_Odist,type,
c_RealVector_Odist__class_Odist: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(class_RealVector_Odist__norm,type,
class_RealVector_Odist__norm: $i > $o ).
tff(f_3429,axiom,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3468,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3524,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_3541,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_3530,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_2385,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_672,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
file(unknown,unknown) ).
tff(f_112,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_3533,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_401,axiom,
! [T_a,V_x] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file(unknown,unknown) ).
tff(f_594,axiom,
! [T_a,V_x,V_x_H,V_y_H] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) )
| ( V_x_H = V_y_H ) ),
file(unknown,unknown) ).
tff(f_2125,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ),
file(unknown,unknown) ).
tff(f_1159,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Ocomm__monoid__add(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_102,axiom,
! [T_a,V_a,V_b] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a) ) ),
file(unknown,unknown) ).
tff(f_3214,axiom,
! [T_a,V_x] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_2892,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| ( c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ),
file(unknown,unknown) ).
tff(f_3427,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3511,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3335,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_3353,axiom,
! [T_a,V_z,V_x,V_y] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ),
file(unknown,unknown) ).
tff(f_1590,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| ( c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) = V_a )
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ),
file(unknown,unknown) ).
tff(c_948,plain,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_3429]) ).
tff(c_1026,plain,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_3468]) ).
tff(c_1138,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_3524]) ).
tff(c_1172,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_3541]) ).
tff(c_1150,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_3530]) ).
tff(c_2365,plain,
! [V_b_1478,V_a_1479,T_a_1480] :
( ( c_HOL_Oplus__class_Oplus(V_b_1478,V_a_1479,T_a_1480) = c_HOL_Oplus__class_Oplus(V_a_1479,V_b_1478,T_a_1480) )
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a_1480) ),
inference(cnfTransformation,[status(thm)],[f_2385]) ).
tff(c_2373,plain,
! [V_b_1478,V_a_1479] : ( c_HOL_Oplus__class_Oplus(V_b_1478,V_a_1479,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(V_a_1479,V_b_1478,tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_1150,c_2365]) ).
tff(c_4288,plain,
! [V_a_1539,V_b_1540,T_a_1541] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a_1539,V_b_1540,T_a_1541),V_b_1540,T_a_1541) = V_a_1539 )
| ~ class_OrderedGroup_Ogroup__add(T_a_1541) ),
inference(cnfTransformation,[status(thm)],[f_672]) ).
tff(c_4357,plain,
! [V_a_1479,V_a_1539] :
( ( c_HOL_Oplus__class_Oplus(V_a_1479,c_HOL_Ominus__class_Ominus(V_a_1539,V_a_1479,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = V_a_1539 )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_2373,c_4288]) ).
tff(c_12521,plain,
! [V_a_1722,V_a_1723] : ( c_HOL_Oplus__class_Oplus(V_a_1722,c_HOL_Ominus__class_Ominus(V_a_1723,V_a_1722,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = V_a_1723 ),
inference(demodulation,[status(thm),theory(equality)],[c_1172,c_4357]) ).
tff(c_26,plain,
! [V_a_43,V_b_44,T_a_42] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a_43,V_b_44,T_a_42),V_b_44,T_a_42) = V_a_43 )
| ~ class_OrderedGroup_Ogroup__add(T_a_42) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_12547,plain,
! [V_a_1723,V_a_1722] :
( ( c_HOL_Ominus__class_Ominus(V_a_1723,c_HOL_Ominus__class_Ominus(V_a_1723,V_a_1722,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = V_a_1722 )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_12521,c_26]) ).
tff(c_15353,plain,
! [V_a_1770,V_a_1771] : ( c_HOL_Ominus__class_Ominus(V_a_1770,c_HOL_Ominus__class_Ominus(V_a_1770,V_a_1771,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = V_a_1771 ),
inference(demodulation,[status(thm),theory(equality)],[c_1172,c_12547]) ).
tff(c_1156,plain,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_3533]) ).
tff(c_1378,plain,
! [V_x_1393,T_a_1394] :
( ( c_HOL_Ominus__class_Ominus(V_x_1393,V_x_1393,T_a_1394) = c_HOL_Ozero__class_Ozero(T_a_1394) )
| ~ class_OrderedGroup_Oab__group__add(T_a_1394) ),
inference(cnfTransformation,[status(thm)],[f_401]) ).
tff(c_1384,plain,
! [V_x_1393] : ( c_HOL_Ominus__class_Ominus(V_x_1393,V_x_1393,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_1156,c_1378]) ).
tff(c_8270,plain,
! [V_y_H_1632,V_x_H_1633,T_a_1634,V_x_1635] :
( ( V_y_H_1632 = V_x_H_1633 )
| ( c_HOL_Ominus__class_Ominus(V_x_H_1633,V_y_H_1632,T_a_1634) != c_HOL_Ominus__class_Ominus(V_x_1635,V_x_1635,T_a_1634) )
| ~ class_OrderedGroup_Oab__group__add(T_a_1634) ),
inference(cnfTransformation,[status(thm)],[f_594]) ).
tff(c_8296,plain,
! [V_y_H_1632,V_x_H_1633] :
( ( V_y_H_1632 = V_x_H_1633 )
| ( c_HOL_Ominus__class_Ominus(V_x_H_1633,V_y_H_1632,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_1384,c_8270]) ).
tff(c_8318,plain,
! [V_y_H_1632,V_x_H_1633] :
( ( V_y_H_1632 = V_x_H_1633 )
| ( c_HOL_Ominus__class_Ominus(V_x_H_1633,V_y_H_1632,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1156,c_8296]) ).
tff(c_25301,plain,
! [V_a_1770] : ( c_HOL_Ominus__class_Ominus(V_a_1770,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = V_a_1770 ),
inference(superposition,[status(thm),theory(equality)],[c_15353,c_8318]) ).
tff(c_11082,plain,
! [V_a_1691,V_b_1692,T_a_1693] :
( ( c_HOL_Oplus__class_Oplus(V_a_1691,c_HOL_Ouminus__class_Ouminus(V_b_1692,T_a_1693),T_a_1693) = c_HOL_Ominus__class_Ominus(V_a_1691,V_b_1692,T_a_1693) )
| ~ class_OrderedGroup_Ogroup__add(T_a_1693) ),
inference(cnfTransformation,[status(thm)],[f_2125]) ).
tff(c_3782,plain,
! [V_b_1528,V_a_1529] : ( c_HOL_Oplus__class_Oplus(V_b_1528,V_a_1529,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(V_a_1529,V_b_1528,tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_1150,c_2365]) ).
tff(c_354,plain,
! [V_a_540,T_a_539] :
( ( c_HOL_Oplus__class_Oplus(V_a_540,c_HOL_Ozero__class_Ozero(T_a_539),T_a_539) = V_a_540 )
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a_539) ),
inference(cnfTransformation,[status(thm)],[f_1159]) ).
tff(c_3812,plain,
! [V_a_1529] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),V_a_1529,tc_Complex_Ocomplex) = V_a_1529 )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_3782,c_354]) ).
tff(c_3938,plain,
! [V_a_1529] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),V_a_1529,tc_Complex_Ocomplex) = V_a_1529 ),
inference(demodulation,[status(thm),theory(equality)],[c_1150,c_3812]) ).
tff(c_11127,plain,
! [V_b_1692] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),V_b_1692,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(V_b_1692,tc_Complex_Ocomplex) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_11082,c_3938]) ).
tff(c_11294,plain,
! [V_b_1692] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),V_b_1692,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(V_b_1692,tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_1172,c_11127]) ).
tff(c_28192,plain,
! [V_b_1940,V_a_1941,T_a_1942] :
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_b_1940,V_a_1941,T_a_1942),T_a_1942) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a_1941,V_b_1940,T_a_1942),T_a_1942) )
| ~ class_RealVector_Oreal__normed__vector(T_a_1942) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_28274,plain,
! [V_b_1692] :
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_b_1692,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_b_1692,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_11294,c_28192]) ).
tff(c_28784,plain,
! [V_b_1948] : ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_b_1948,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(V_b_1948,tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_1138,c_25301,c_28274]) ).
tff(c_870,plain,
! [V_x_1292,T_a_1291] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x_1292,T_a_1291),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a_1291) ),
inference(cnfTransformation,[status(thm)],[f_3214]) ).
tff(c_28798,plain,
! [V_b_1948] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_b_1948,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_28784,c_870]) ).
tff(c_28863,plain,
! [V_b_1949] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_b_1949,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1138,c_28798]) ).
tff(c_794,plain,
! [T_a_1210,V_a_1211] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a_1210),V_a_1211,T_a_1210)
| ( c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a_1211,T_a_1210) = c_HOL_Ozero__class_Ozero(T_a_1210) )
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a_1210) ),
inference(cnfTransformation,[status(thm)],[f_2892]) ).
tff(c_28874,plain,
! [V_b_1949] :
( ( c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_RealVector_Onorm__class_Onorm(V_b_1949,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_28863,c_794]) ).
tff(c_28916,plain,
! [V_b_1949] : ( c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_RealVector_Onorm__class_Onorm(V_b_1949,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1026,c_28874]) ).
tff(c_946,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_3427]) ).
tff(c_1112,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_3511]) ).
tff(c_1273,plain,
! [V_z_1379,V_w_1380] :
( c_lessequals(V_z_1379,V_w_1380,tc_RealDef_Oreal)
| c_lessequals(V_w_1380,V_z_1379,tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_3335]) ).
tff(c_1288,plain,
c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[c_1273,c_948]) ).
tff(c_28409,plain,
! [V_y_1944,V_x_1945,T_a_1946,V_z_1947] :
( ~ c_lessequals(V_y_1944,V_x_1945,T_a_1946)
| ~ c_lessequals(V_z_1947,V_y_1944,T_a_1946)
| c_lessequals(V_z_1947,V_x_1945,T_a_1946)
| ~ class_Orderings_Oorder(T_a_1946) ),
inference(cnfTransformation,[status(thm)],[f_3353]) ).
tff(c_28549,plain,
! [V_z_1947] :
( ~ c_lessequals(V_z_1947,v_r,tc_RealDef_Oreal)
| c_lessequals(V_z_1947,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1288,c_28409]) ).
tff(c_153478,plain,
! [V_z_3160] :
( ~ c_lessequals(V_z_3160,v_r,tc_RealDef_Oreal)
| c_lessequals(V_z_3160,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1112,c_28549]) ).
tff(c_466,plain,
! [V_a_697,T_a_696] :
( ~ c_lessequals(V_a_697,c_HOL_Ozero__class_Ozero(T_a_696),T_a_696)
| ( c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a_697,T_a_696) = V_a_697 )
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a_696) ),
inference(cnfTransformation,[status(thm)],[f_1590]) ).
tff(c_153738,plain,
! [V_z_3160] :
( ( c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_z_3160,tc_RealDef_Oreal) = V_z_3160 )
| ~ class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal)
| ~ c_lessequals(V_z_3160,v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_153478,c_466]) ).
tff(c_154191,plain,
! [V_z_3164] :
( ( c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_z_3164,tc_RealDef_Oreal) = V_z_3164 )
| ~ c_lessequals(V_z_3164,v_r,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1026,c_153738]) ).
tff(c_154290,plain,
c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[c_946,c_154191]) ).
tff(c_154356,plain,
c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_28916,c_154290]) ).
tff(c_154467,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_154356,c_946]) ).
tff(c_154469,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_948,c_154467]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG341-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.13 % 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
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 20:36:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 60.62/41.88 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 60.69/41.89
% 60.69/41.89 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 60.69/41.93
% 60.69/41.93 Inference rules
% 60.69/41.93 ----------------------
% 60.69/41.93 #Ref : 32
% 60.69/41.93 #Sup : 36179
% 60.69/41.93 #Fact : 6
% 60.69/41.93 #Define : 0
% 60.69/41.93 #Split : 14
% 60.69/41.93 #Chain : 0
% 60.69/41.93 #Close : 0
% 60.69/41.93
% 60.69/41.93 Ordering : KBO
% 60.69/41.93
% 60.69/41.93 Simplification rules
% 60.69/41.93 ----------------------
% 60.69/41.93 #Subsume : 5842
% 60.69/41.93 #Demod : 24755
% 60.69/41.93 #Tautology : 7147
% 60.69/41.93 #SimpNegUnit : 515
% 60.69/41.93 #BackRed : 9
% 60.69/41.93
% 60.69/41.93 #Partial instantiations: 0
% 60.69/41.93 #Strategies tried : 1
% 60.69/41.93
% 60.69/41.93 Timing (in seconds)
% 60.69/41.93 ----------------------
% 60.69/41.94 Preprocessing : 1.47
% 60.69/41.94 Parsing : 0.87
% 60.69/41.94 CNF conversion : 0.11
% 60.69/41.94 Main loop : 39.34
% 60.69/41.94 Inferencing : 4.94
% 60.69/41.94 Reduction : 21.41
% 60.69/41.94 Demodulation : 17.51
% 60.69/41.94 BG Simplification : 0.53
% 60.69/41.94 Subsumption : 10.30
% 60.69/41.94 Abstraction : 0.55
% 60.69/41.94 MUC search : 0.00
% 60.69/41.94 Cooper : 0.00
% 60.69/41.94 Total : 40.87
% 60.69/41.94 Index Insertion : 0.00
% 60.69/41.94 Index Deletion : 0.00
% 60.69/41.94 Index Matching : 0.00
% 60.69/41.94 BG Taut test : 0.00
%------------------------------------------------------------------------------