%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV629-1 : 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 09:31:25 PM UTC 2025
% Result : Unsatisfiable 9.48s 3.01s
% Output : CNFRefutation 9.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 14 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 35 ( 33 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 3 con; 0-3 aty)
% Number of variables : 6 ( 6 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Ring__and__Field_Odvd__class_Odvd > c_Parity_Oeven__odd__class_Oeven > c_Int_Oiszero > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osgn__if > class_Ring__and__Field_Osemiring__1 > 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_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_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_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_Power_Opower > class_OrderedGroup_Opordered__ab__group__add__abs > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_Nat_Osemiring__char__0 > class_Int_Onumber__ring > class_Divides_Osemiring__div > c_Power_Opower__class_Opower > c_HOL_Otimes__class_Otimes > c_HOL_Oinverse__class_Odivide > c_GCD_Ogcd__class_Olcm > c_GCD_Ogcd__class_Ogcd > c_Divides_Odiv__class_Odiv > c_Nat_Osemiring__1__class_Oof__nat > c_HOL_Osgn__class_Osgn > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > c_Fact_Ofact__class_Ofact > #nlpp > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > c_FFT__Mirabelle_Oroot > c_Complex_Ocnj > tc_nat > tc_Complex_Ocomplex > 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(c_GCD_Ogcd__class_Olcm,type,
c_GCD_Ogcd__class_Olcm: ( $i * $i * $i ) > $i ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_Parity_Oeven__odd__class_Oeven,type,
c_Parity_Oeven__odd__class_Oeven: ( $i * $i ) > $o ).
tff(c_HOL_Oinverse__class_Oinverse,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $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_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(c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(c_GCD_Ogcd__class_Ogcd,type,
c_GCD_Ogcd__class_Ogcd: ( $i * $i * $i ) > $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_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(c_Complex_Oii,type,
c_Complex_Oii: $i ).
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(tc_nat,type,
tc_nat: $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_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_RealVector_Oreal__normed__vector,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $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_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_HOL_Osgn__class_Osgn,type,
c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).
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(class_Ring__and__Field_Odvd,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
tff(c_HOL_Oabs__class_Oabs,type,
c_HOL_Oabs__class_Oabs: ( $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(c_Int_Oiszero,type,
c_Int_Oiszero: ( $i * $i ) > $o ).
tff(class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(f_2075,axiom,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_2095,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_1923,axiom,
! [T_a,V_x] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_x ) ),
file(unknown,unknown) ).
tff(f_1999,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(c_704,plain,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_2075]) ).
tff(c_744,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_2095]) ).
tff(c_1492,plain,
! [V_x_893,T_a_894] :
( ( c_Power_Opower__class_Opower(V_x_893,c_HOL_Oone__class_Oone(tc_nat),T_a_894) = V_x_893 )
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a_894) ),
inference(cnfTransformation,[status(thm)],[f_1923]) ).
tff(c_668,plain,
! [V_n_812] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n_812),V_n_812,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(cnfTransformation,[status(thm)],[f_1999]) ).
tff(c_1499,plain,
( ( c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_1492,c_668]) ).
tff(c_1509,plain,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(demodulation,[status(thm),theory(equality)],[c_744,c_1499]) ).
tff(c_1511,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_704,c_1509]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV629-1 : TPTP v9.0.0. Released v4.1.0.
% 0.10/0.13 % 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 : n010.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 04:17:18 EDT 2025
% 0.13/0.35 % CPUTime :
% 9.48/3.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.48/3.02
% 9.48/3.02 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------