TSTP Solution File: SWV573-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWV573-1 : 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 : n001.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 11:05:14 EDT 2023

% Result   : Unsatisfiable 22.28s 7.44s
% Output   : CNFRefutation 22.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  121
% Syntax   : Number of formulae    :  133 (  18 unt; 115 typ;   0 def)
%            Number of atoms       :   18 (  17 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  142 ( 108   >;  34   *;   0   +;   0  <<)
%            Number of predicates  :   77 (  75 usr;   1 prp; 0-3 aty)
%            Number of functors    :   40 (  40 usr;   7 con; 0-3 aty)
%            Number of variables   :   12 (;  12   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > class_SEQ_Obanach > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osgn__if > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring__abs > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Olordered__ring > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odivision__ring > class_Ring__and__Field_Odivision__by__zero > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Oabs__if > class_RealVector_Osgn__div__norm > class_RealVector_Oreal__vector > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__field > class_RealVector_Oreal__normed__div__algebra > class_RealVector_Oreal__normed__algebra__1 > class_RealVector_Oreal__normed__algebra > class_RealVector_Oreal__field > class_RealVector_Oreal__div__algebra > class_RealVector_Oreal__algebra__1 > class_RealVector_Oreal__algebra > class_RealVector_Ometric__space > class_RealVector_Odist__norm > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__comm__monoid__add > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add__abs > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Oordered__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add__abs > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Nat_Osemiring__char__0 > class_Lattices_Oboolean__algebra > class_Int_Oring__char__0 > class_Int_Onumber__ring > class_Int_Onumber > class_Divides_Osemiring__div > class_Divides_Oring__div > c_RealVector_OscaleR__class_OscaleR > c_RealVector_Odist__class_Odist > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_HOL_Oinverse__class_Odivide > c_Divides_Odiv__class_Omod > c_Divides_Odiv__class_Odiv > c_Transcendental_Oexp > c_RealVector_Oof__real > c_RealVector_Onorm__class_Onorm > c_OrderedGroup_Olordered__ab__group__add__class_Opprt > c_NthRoot_Oroot > c_Nat_Osemiring__1__class_Oof__nat > c_Log_Opowr > c_Int_Onumber__class_Onumber__of > c_HOL_Ouminus__class_Ouminus > c_HOL_Osgn__class_Osgn > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > c_Fact_Ofact__class_Ofact > c_Complex_Ocomplex_OComplex > #nlpp > c_Transcendental_Otan > c_Transcendental_Osin > c_Transcendental_Ocos > c_Transcendental_Oarctan > c_NthRoot_Osqrt > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > c_Complex_Ocnj > c_Complex_Oarg > c_Complex_ORe > c_Complex_OIm > v_n > tc_nat > tc_RealDef_Oreal > tc_Int_Oint > tc_Complex_Ocomplex > c_Transcendental_Opi > c_Complex_Oii

%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_Transcendental_Osin,type,
    c_Transcendental_Osin: $i > $i ).

tff(class_Int_Oring__char__0,type,
    class_Int_Oring__char__0: $i > $o ).

tff(class_Orderings_Olinorder,type,
    class_Orderings_Olinorder: $i > $o ).

tff(class_OrderedGroup_Opordered__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).

tff(class_Int_Onumber__ring,type,
    class_Int_Onumber__ring: $i > $o ).

tff(c_HOL_Oord__class_Oless,type,
    c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(c_Complex_OIm,type,
    c_Complex_OIm: $i > $i ).

tff(c_OrderedGroup_Olordered__ab__group__add__class_Opprt,type,
    c_OrderedGroup_Olordered__ab__group__add__class_Opprt: ( $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(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_RealVector_Oreal__normed__algebra__1,type,
    class_RealVector_Oreal__normed__algebra__1: $i > $o ).

tff(class_RealVector_Oreal__vector,type,
    class_RealVector_Oreal__vector: $i > $o ).

tff(c_RealVector_OscaleR__class_OscaleR,type,
    c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).

tff(class_Ring__and__Field_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_Opordered__ab__group__add__abs,type,
    class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).

tff(c_Complex_Ocomplex_OComplex,type,
    c_Complex_Ocomplex_OComplex: ( $i * $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(v_n,type,
    v_n: $i ).

tff(class_RealVector_Ometric__space,type,
    class_RealVector_Ometric__space: $i > $o ).

tff(c_Log_Opowr,type,
    c_Log_Opowr: ( $i * $i ) > $i ).

tff(tc_Int_Oint,type,
    tc_Int_Oint: $i ).

tff(class_Ring__and__Field_Omult__zero,type,
    class_Ring__and__Field_Omult__zero: $i > $o ).

tff(class_OrderedGroup_Olordered__ab__group__add,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

tff(class_Orderings_Oorder,type,
    class_Orderings_Oorder: $i > $o ).

tff(class_Orderings_Opreorder,type,
    class_Orderings_Opreorder: $i > $o ).

tff(tc_RealDef_Oreal,type,
    tc_RealDef_Oreal: $i ).

tff(class_OrderedGroup_Oab__semigroup__mult,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

tff(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(c_NthRoot_Oroot,type,
    c_NthRoot_Oroot: ( $i * $i ) > $i ).

tff(class_Ring__and__Field_Ozero__neq__one,type,
    class_Ring__and__Field_Ozero__neq__one: $i > $o ).

tff(c_Complex_Oii,type,
    c_Complex_Oii: $i ).

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_Complex_Oarg,type,
    c_Complex_Oarg: $i > $i ).

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_Divides_Oring__div,type,
    class_Divides_Oring__div: $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(c_Divides_Odiv__class_Omod,type,
    c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).

tff(class_RealVector_Oreal__normed__algebra,type,
    class_RealVector_Oreal__normed__algebra: $i > $o ).

tff(class_RealVector_Oreal__normed__div__algebra,type,
    class_RealVector_Oreal__normed__div__algebra: $i > $o ).

tff(class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

tff(class_OrderedGroup_Ocomm__monoid__mult,type,
    class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).

tff(class_OrderedGroup_Ocomm__monoid__add,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

tff(class_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_Ring__and__Field_Oabs__if,type,
    class_Ring__and__Field_Oabs__if: $i > $o ).

tff(class_RealVector_Oreal__normed__vector,type,
    class_RealVector_Oreal__normed__vector: $i > $o ).

tff(class_OrderedGroup_Omonoid__add,type,
    class_OrderedGroup_Omonoid__add: $i > $o ).

tff(c_Transcendental_Otan,type,
    c_Transcendental_Otan: $i > $i ).

tff(class_RealVector_Oreal__algebra,type,
    class_RealVector_Oreal__algebra: $i > $o ).

tff(class_Ring__and__Field_Oordered__semiring__strict,type,
    class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).

tff(class_RealVector_Oreal__algebra__1,type,
    class_RealVector_Oreal__algebra__1: $i > $o ).

tff(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_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_Divides_Odiv__class_Odiv,type,
    c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).

tff(c_HOL_Ozero__class_Ozero,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

tff(c_HOL_Oone__class_Oone,type,
    c_HOL_Oone__class_Oone: $i > $i ).

tff(class_OrderedGroup_Omonoid__mult,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

tff(c_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_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_OrderedGroup_Olordered__ab__group__add__abs,type,
    class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).

tff(class_Ring__and__Field_Olordered__ring,type,
    class_Ring__and__Field_Olordered__ring: $i > $o ).

tff(c_Fact_Ofact__class_Ofact,type,
    c_Fact_Ofact__class_Ofact: ( $i * $i ) > $i ).

tff(class_Ring__and__Field_Osgn__if,type,
    class_Ring__and__Field_Osgn__if: $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_Divides_Osemiring__div,type,
    class_Divides_Osemiring__div: $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(c_Complex_Ocnj,type,
    c_Complex_Ocnj: $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_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(c_Transcendental_Ocos,type,
    c_Transcendental_Ocos: $i > $i ).

tff(c_Complex_ORe,type,
    c_Complex_ORe: $i > $i ).

tff(class_Ring__and__Field_Osemiring__1,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

tff(class_RealVector_Osgn__div__norm,type,
    class_RealVector_Osgn__div__norm: $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_Oreal__div__algebra,type,
    class_RealVector_Oreal__div__algebra: $i > $o ).

tff(class_RealVector_Odist__norm,type,
    class_RealVector_Odist__norm: $i > $o ).

tff(f_1526,axiom,
    c_Complex_ORe(c_Complex_Oii) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_9246,axiom,
    ! [V_r] : ( c_RealVector_Oof__real(V_r,tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file(unknown,unknown) ).

tff(f_9263,axiom,
    ! [V_n] : ( c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file(unknown,unknown) ).

tff(f_9265,axiom,
    ! [V_n] : ( c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) = c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal) ),
    file(unknown,unknown) ).

tff(f_6996,axiom,
    ! [V_z] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
    file(unknown,unknown) ).

tff(f_9285,axiom,
    c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file(unknown,unknown) ).

tff(c_324,plain,
    c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_ORe(c_Complex_Oii),
    inference(cnfTransformation,[status(thm)],[f_1526]) ).

tff(c_2118,plain,
    ! [V_r_3023] : ( c_Complex_Ocomplex_OComplex(V_r_3023,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_r_3023,tc_Complex_Ocomplex) ),
    inference(cnfTransformation,[status(thm)],[f_9246]) ).

tff(c_2618,plain,
    ! [V_r_3023] : ( c_Complex_Ocomplex_OComplex(V_r_3023,c_Complex_ORe(c_Complex_Oii)) = c_RealVector_Oof__real(V_r_3023,tc_Complex_Ocomplex) ),
    inference(demodulation,[status(thm),theory(equality)],[c_324,c_2118]) ).

tff(c_2126,plain,
    ! [V_n_3031] : ( c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n_3031,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(cnfTransformation,[status(thm)],[f_9263]) ).

tff(c_2570,plain,
    ! [V_n_3031] : ( c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n_3031,tc_Complex_Ocomplex)) = c_Complex_ORe(c_Complex_Oii) ),
    inference(demodulation,[status(thm),theory(equality)],[c_324,c_2126]) ).

tff(c_3540,plain,
    ! [V_n_3112] : ( c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n_3112,tc_Complex_Ocomplex)) = c_Nat_Osemiring__1__class_Oof__nat(V_n_3112,tc_RealDef_Oreal) ),
    inference(cnfTransformation,[status(thm)],[f_9265]) ).

tff(c_1520,plain,
    ! [V_z_2283] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z_2283),c_Complex_OIm(V_z_2283)) = V_z_2283 ),
    inference(cnfTransformation,[status(thm)],[f_6996]) ).

tff(c_3555,plain,
    ! [V_n_3112] : ( c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(V_n_3112,tc_RealDef_Oreal),c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n_3112,tc_Complex_Ocomplex))) = c_Nat_Osemiring__1__class_Oof__nat(V_n_3112,tc_Complex_Ocomplex) ),
    inference(superposition,[status(thm),theory(equality)],[c_3540,c_1520]) ).

tff(c_3563,plain,
    ! [V_n_3112] : ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n_3112,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(V_n_3112,tc_Complex_Ocomplex) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2618,c_2570,c_3555]) ).

tff(c_2136,plain,
    c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) != c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex),
    inference(cnfTransformation,[status(thm)],[f_9285]) ).

tff(c_2529,plain,
    c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) != c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex),
    inference(demodulation,[status(thm),theory(equality)],[c_2118,c_2136]) ).

tff(c_6480,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3563,c_2529]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SWV573-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.08  % 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
% 0.08/0.26  % Computer : n001.cluster.edu
% 0.08/0.26  % Model    : x86_64 x86_64
% 0.08/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26  % Memory   : 8042.1875MB
% 0.08/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26  % CPULimit : 300
% 0.08/0.26  % WCLimit  : 300
% 0.08/0.26  % DateTime : Thu Aug  3 23:48:10 EDT 2023
% 0.08/0.27  % CPUTime  : 
% 22.28/7.44  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.28/7.44  
% 22.41/7.44  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.49/7.47  
% 22.49/7.47  Inference rules
% 22.49/7.47  ----------------------
% 22.49/7.47  #Ref     : 15
% 22.49/7.47  #Sup     : 937
% 22.49/7.47  #Fact    : 2
% 22.49/7.47  #Define  : 0
% 22.49/7.47  #Split   : 1
% 22.49/7.47  #Chain   : 0
% 22.49/7.47  #Close   : 0
% 22.49/7.47  
% 22.49/7.47  Ordering : KBO
% 22.49/7.47  
% 22.49/7.47  Simplification rules
% 22.49/7.47  ----------------------
% 22.49/7.47  #Subsume      : 398
% 22.49/7.47  #Demod        : 711
% 22.49/7.47  #Tautology    : 598
% 22.49/7.47  #SimpNegUnit  : 30
% 22.49/7.47  #BackRed      : 1
% 22.49/7.47  
% 22.49/7.47  #Partial instantiations: 0
% 22.49/7.47  #Strategies tried      : 1
% 22.49/7.47  
% 22.49/7.47  Timing (in seconds)
% 22.49/7.47  ----------------------
% 22.49/7.47  Preprocessing        : 2.11
% 22.49/7.48  Parsing              : 1.25
% 22.49/7.48  CNF conversion       : 0.16
% 22.49/7.48  Main loop            : 4.45
% 22.49/7.48  Inferencing          : 0.51
% 22.49/7.48  Reduction            : 2.39
% 22.49/7.48  Demodulation         : 1.59
% 22.49/7.48  BG Simplification    : 0.23
% 22.49/7.48  Subsumption          : 0.99
% 22.49/7.48  Abstraction          : 0.08
% 22.49/7.48  MUC search           : 0.00
% 22.49/7.48  Cooper               : 0.00
% 22.49/7.48  Total                : 6.61
% 22.49/7.48  Index Insertion      : 0.00
% 22.49/7.48  Index Deletion       : 0.00
% 22.49/7.48  Index Matching       : 0.00
% 22.49/7.48  BG Taut test         : 0.00
%------------------------------------------------------------------------------