%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG438-1 : 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/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 : Wed Apr 9 05:25:13 PM UTC 2025
% Result : Unsatisfiable 59.99s 36.25s
% Output : CNFRefutation 60.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 50 ( 48 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 8 ( 8 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > c_Polynomial_Opos__poly > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odivision__ring > class_Ring__and__Field_Odivision__by__zero > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring__0 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Ocomm__ring__1 > class_RealVector_Oreal__normed__algebra > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__comm__monoid__add > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__comm__monoid__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Int_Onumber__ring > class_HOL_Ozero > c_Polynomial_Osynthetic__div > c_Polynomial_Osmult > c_Polynomial_Opoly > c_Polynomial_Opcompose > c_Polynomial_OpCons > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly > c_HOL_Oinverse__class_Oinverse > #nlpp > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__5__1 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__3__1 > tc_Polynomial_Opoly > c_HOL_Ozero__class_Ozero > v_q > v_p > v_b > v_a > tc_Complex_Ocomplex > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_HOL_Ozero,type,
class_HOL_Ozero: $i > $o ).
tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(class_OrderedGroup_Ocancel__comm__monoid__add,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__0,type,
class_Ring__and__Field_Ocomm__semiring__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(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__5__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__5__1: $i > $i ).
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(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(tc_Polynomial_Opoly,type,
tc_Polynomial_Opoly: $i > $i ).
tff(v_q,type,
v_q: $i ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(c_Polynomial_Osynthetic__div,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(t_a,type,
t_a: $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(v_b,type,
v_b: $i ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
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(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__3__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__3__1: $i > $i ).
tff(class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(class_Ring__and__Field_Oordered__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(class_Ring__and__Field_Ocomm__ring__1,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Polynomial_Osmult,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__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__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_Polynomial_Opos__poly,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(v_a,type,
v_a: $i ).
tff(class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Polynomial_Opoly,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_OpCons,type,
c_Polynomial_OpCons: ( $i * $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(c_Polynomial_Opcompose,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Omult__mono,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(class_Ring__and__Field_Odivision__ring,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(v_p,type,
v_p: $i ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(f_2845,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_2327,axiom,
! [T_a,V_a,V_p,V_q] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_q,T_a),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),tc_Polynomial_Opoly(T_a)) ) ),
file(unknown,unknown) ).
tff(f_2826,axiom,
c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file(unknown,unknown) ).
tff(c_684,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_2845]) ).
tff(c_496,plain,
! [V_a_769,V_q_771,T_a_768,V_p_770] :
( ( c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a_769,V_q_771,T_a_768),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a_768),c_HOL_Otimes__class_Otimes(V_p_770,V_q_771,tc_Polynomial_Opoly(T_a_768)),T_a_768),tc_Polynomial_Opoly(T_a_768)) = c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(V_a_769,V_p_770,T_a_768),V_q_771,tc_Polynomial_Opoly(T_a_768)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a_768) ),
inference(cnfTransformation,[status(thm)],[f_2327]) ).
tff(c_662,plain,
c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnfTransformation,[status(thm)],[f_2826]) ).
tff(c_161388,plain,
~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(superposition,[status(thm),theory(equality)],[c_496,c_662]) ).
tff(c_161401,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_684,c_161388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : ALG438-1 : TPTP v9.0.0. Released v4.1.0.
% 0.09/0.10 % 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
% 0.09/0.30 % Computer : n029.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Mon Apr 7 14:45:49 EDT 2025
% 0.09/0.31 % CPUTime :
% 59.99/36.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 60.02/36.26
% 60.02/36.26 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------