%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV617-1 : TPTP v9.0.0. 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 : n005.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 : Wed Apr 9 09:31:24 PM UTC 2025
% Result : Unsatisfiable 48.10s 28.95s
% Output : CNFRefutation 48.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 51 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 47 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 72 ( 38 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 57 ( 55 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 62 ( 62 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_Ring__and__Field_Odvd__class_Odvd > c_HOL_Oord__class_Oless > class_SEQ_Obanach > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring__0 > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring__1__no__zero__divisors > class_Ring__and__Field_Oring__1 > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring__abs > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Olordered__ring > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odvd > 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__ring__1 > class_Ring__and__Field_Oabs__if > class_RealVector_Oreal__normed__field > class_RealVector_Oreal__normed__algebra > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > 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_Olordered__ab__group__add__abs > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > 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_Ominus__class_Ominus > c_HOL_Oinverse__class_Odivide > c_Transcendental_Oexp > c_Int_Onumber__class_Onumber__of > c_HOL_Ouminus__class_Ouminus > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > #nlpp > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > c_FFT__Mirabelle_Oroot > c_Complex_Oexpi > v_n > v_k > tc_nat > tc_Int_Oint > tc_Complex_Ocomplex
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(class_OrderedGroup_Oordered__ab__group__add,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(class_Ring__and__Field_Opordered__ring__abs,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(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_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_HOL_Oinverse__class_Oinverse,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(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_Oring__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $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(class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $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(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(class_SEQ_Obanach,type,
class_SEQ_Obanach: $i > $o ).
tff(c_Complex_Oexpi,type,
c_Complex_Oexpi: $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_Ring__and__Field_Oordered__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(class_Ring__and__Field_Ocomm__ring__1,type,
class_Ring__and__Field_Ocomm__ring__1: $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(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_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_Ring__and__Field_Oabs__if,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
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_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_Ring__and__Field_Odvd__class_Odvd,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
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(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__add__abs,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(class_Ring__and__Field_Oring__1,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(class_Ring__and__Field_Olordered__ring,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(class_Ring__and__Field_Odvd,type,
class_Ring__and__Field_Odvd: $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(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(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(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(f_7175,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_7178,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_5623,axiom,
! [T_a,V_a,V_b] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
file(unknown,unknown) ).
tff(f_7179,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_7165,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_2225,axiom,
! [T_a,V_a] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file(unknown,unknown) ).
tff(f_7164,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_335,axiom,
! [T_a,V_a,V_b] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
file(unknown,unknown) ).
tff(f_7176,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_2084,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ),
file(unknown,unknown) ).
tff(f_4746,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) ) ),
file(unknown,unknown) ).
tff(f_6983,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file(unknown,unknown) ).
tff(f_1267,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a) )
| ( V_a = V_b ) ),
file(unknown,unknown) ).
tff(f_3342,axiom,
! [T_a,V_a,V_b] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) ) ),
file(unknown,unknown) ).
tff(f_6883,axiom,
! [T_a,V_n] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
file(unknown,unknown) ).
tff(f_6947,axiom,
! [V_n] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
file(unknown,unknown) ).
tff(f_7094,axiom,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(c_1510,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_7175]) ).
tff(c_1516,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_7178]) ).
tff(c_1058,plain,
! [V_a_1644,V_b_1645,T_a_1643] :
( ( c_HOL_Otimes__class_Otimes(V_a_1644,c_HOL_Oinverse__class_Oinverse(V_b_1645,T_a_1643),T_a_1643) = c_HOL_Oinverse__class_Odivide(V_a_1644,V_b_1645,T_a_1643) )
| ~ class_Ring__and__Field_Ofield(T_a_1643) ),
inference(cnfTransformation,[status(thm)],[f_5623]) ).
tff(c_1518,plain,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_7179]) ).
tff(c_1490,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_7165]) ).
tff(c_414,plain,
! [V_a_666,T_a_665] :
( ( c_HOL_Otimes__class_Otimes(V_a_666,c_HOL_Ozero__class_Ozero(T_a_665),T_a_665) = c_HOL_Ozero__class_Ozero(T_a_665) )
| ~ class_RealVector_Oreal__normed__algebra(T_a_665) ),
inference(cnfTransformation,[status(thm)],[f_2225]) ).
tff(c_1488,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_7164]) ).
tff(c_3900,plain,
! [V_b_2249,V_a_2250,T_a_2251] :
( ( c_HOL_Otimes__class_Otimes(V_b_2249,V_a_2250,T_a_2251) = c_HOL_Otimes__class_Otimes(V_a_2250,V_b_2249,T_a_2251) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a_2251) ),
inference(cnfTransformation,[status(thm)],[f_335]) ).
tff(c_9149,plain,
! [V_b_2382,V_a_2383] : ( c_HOL_Otimes__class_Otimes(V_b_2382,V_a_2383,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_a_2383,V_b_2382,tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_1488,c_3900]) ).
tff(c_9347,plain,
! [V_a_666] :
( ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),V_a_666,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_414,c_9149]) ).
tff(c_9519,plain,
! [V_a_666] : ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),V_a_666,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_1490,c_9347]) ).
tff(c_1512,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_7176]) ).
tff(c_372,plain,
! [V_a_619,T_a_618] :
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a_619,T_a_618),T_a_618) = V_a_619 )
| ~ class_OrderedGroup_Ogroup__add(T_a_618) ),
inference(cnfTransformation,[status(thm)],[f_2084]) ).
tff(c_2971,plain,
! [T_a_2194,V_a_2195] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a_2194),V_a_2195,T_a_2194) = c_HOL_Ouminus__class_Ouminus(V_a_2195,T_a_2194) )
| ~ class_OrderedGroup_Ogroup__add(T_a_2194) ),
inference(cnfTransformation,[status(thm)],[f_4746]) ).
tff(c_1851,plain,
! [V_a_2112,T_a_2113] :
( ( c_HOL_Ominus__class_Ominus(V_a_2112,V_a_2112,T_a_2113) = c_HOL_Ozero__class_Ozero(T_a_2113) )
| ~ class_OrderedGroup_Ogroup__add(T_a_2113) ),
inference(cnfTransformation,[status(thm)],[f_6983]) ).
tff(c_1856,plain,
! [V_a_2112] : ( c_HOL_Ominus__class_Ominus(V_a_2112,V_a_2112,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_1512,c_1851]) ).
tff(c_2986,plain,
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_2971,c_1856]) ).
tff(c_3006,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(demodulation,[status(thm),theory(equality)],[c_1512,c_2986]) ).
tff(c_216,plain,
! [V_b_366,V_a_365,T_a_364] :
( ( V_b_366 = V_a_365 )
| ( c_HOL_Ouminus__class_Ouminus(V_b_366,T_a_364) != c_HOL_Ouminus__class_Ouminus(V_a_365,T_a_364) )
| ~ class_OrderedGroup_Ogroup__add(T_a_364) ),
inference(cnfTransformation,[status(thm)],[f_1267]) ).
tff(c_3080,plain,
! [V_b_366] :
( ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = V_b_366 )
| ( c_HOL_Ouminus__class_Ouminus(V_b_366,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_3006,c_216]) ).
tff(c_3132,plain,
! [V_b_2199] :
( ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = V_b_2199 )
| ( c_HOL_Ouminus__class_Ouminus(V_b_2199,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1512,c_3080]) ).
tff(c_3147,plain,
! [V_a_619] :
( ( c_HOL_Ouminus__class_Ouminus(V_a_619,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != V_a_619 )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_372,c_3132]) ).
tff(c_3159,plain,
! [V_a_619] :
( ( c_HOL_Ouminus__class_Ouminus(V_a_619,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != V_a_619 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1512,c_3147]) ).
tff(c_26038,plain,
! [V_a_2667,T_a_2668,V_b_2669] :
( ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a_2667,T_a_2668),c_HOL_Ouminus__class_Ouminus(V_b_2669,T_a_2668),T_a_2668) = c_HOL_Otimes__class_Otimes(V_a_2667,V_b_2669,T_a_2668) )
| ~ class_Ring__and__Field_Oring(T_a_2668) ),
inference(cnfTransformation,[status(thm)],[f_3342]) ).
tff(c_26256,plain,
! [V_b_2669,V_a_619] :
( ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(V_b_2669,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_a_619,V_b_2669,tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != V_a_619 ) ),
inference(superposition,[status(thm),theory(equality)],[c_3159,c_26038]) ).
tff(c_30822,plain,
! [V_a_2741,V_b_2742] :
( ( c_HOL_Otimes__class_Otimes(V_a_2741,V_b_2742,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != V_a_2741 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1518,c_9519,c_26256]) ).
tff(c_31091,plain,
! [V_a_1644,V_b_1645] :
( ( c_HOL_Oinverse__class_Odivide(V_a_1644,V_b_1645,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != V_a_1644 )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_1058,c_30822]) ).
tff(c_38359,plain,
! [V_b_1645] : ( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),V_b_1645,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_1516,c_31091]) ).
tff(c_1288,plain,
! [T_a_1988,V_n_1989] :
( ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a_1988),V_n_1989,T_a_1988) = c_HOL_Oone__class_Oone(T_a_1988) )
| ~ class_OrderedGroup_Omonoid__mult(T_a_1988) ),
inference(cnfTransformation,[status(thm)],[f_6883]) ).
tff(c_1304,plain,
! [V_n_2007] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n_2007),V_n_2007,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(cnfTransformation,[status(thm)],[f_6947]) ).
tff(c_1348,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_7094]) ).
tff(c_1533,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(demodulation,[status(thm),theory(equality)],[c_1304,c_1348]) ).
tff(c_146825,plain,
( ( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_1288,c_1533]) ).
tff(c_146832,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1510,c_38359,c_1856,c_146825]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV617-1 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.13 % 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 : n005.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 : Wed Apr 9 04:15:27 EDT 2025
% 0.13/0.35 % CPUTime :
% 48.10/28.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.10/28.96
% 48.10/28.96 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------