TSTP Solution File: SWW256+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW256+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : 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 11:06:56 EDT 2023
% Result : Theorem 35.91s 13.76s
% Output : CNFRefutation 35.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 159
% Syntax : Number of formulae : 178 ( 18 unt; 149 typ; 0 def)
% Number of atoms : 40 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 199 ( 127 >; 72 *; 0 +; 0 <<)
% Number of predicates : 80 ( 78 usr; 1 prp; 0-3 aty)
% Number of functors : 71 ( 71 usr; 22 con; 0-4 aty)
% Number of variables : 22 (; 20 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Rings_Odvd__class_Odvd > c_Orderings_Oord__class_Oless__eq > c_Orderings_Oord__class_Oless > c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant > hBOOL > class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct > class_Rings_Ozero__neq__one > class_Rings_Osemiring__0 > class_Rings_Osemiring > class_Rings_Oring__no__zero__divisors > class_Rings_Oring__1__no__zero__divisors > class_Rings_Oring__1 > class_Rings_Oring > class_Rings_Oordered__semiring > class_Rings_Oordered__ring > class_Rings_Oordered__comm__semiring > class_Rings_Oordered__cancel__semiring > class_Rings_Ono__zero__divisors > class_Rings_Omult__zero > class_Rings_Olinordered__semiring__strict > class_Rings_Olinordered__semiring__1__strict > class_Rings_Olinordered__semiring__1 > class_Rings_Olinordered__semiring > class_Rings_Olinordered__semidom > class_Rings_Olinordered__ring__strict > class_Rings_Olinordered__ring > class_Rings_Olinordered__idom > class_Rings_Olinordered__comm__semiring__strict > class_Rings_Oidom > class_Rings_Odvd > class_Rings_Odivision__ring__inverse__zero > class_Rings_Odivision__ring > class_Rings_Ocomm__semiring__1 > class_Rings_Ocomm__semiring__0 > class_Rings_Ocomm__semiring > class_Rings_Ocomm__ring__1 > class_Rings_Ocomm__ring > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__div__algebra > class_RealVector_Oreal__normed__algebra__1 > class_RealVector_Oreal__normed__algebra > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Oord > class_Orderings_Olinorder > class_Lattices_Oboolean__algebra > class_Lattices_Oab__semigroup__idem__mult > class_Int_Oring__char__0 > class_Int_Onumber__ring > class_Int_Onumber > class_Groups_Ozero > class_Groups_Ouminus > class_Groups_Oordered__comm__monoid__add > class_Groups_Oordered__cancel__ab__semigroup__add > class_Groups_Oordered__ab__semigroup__add__imp__le > class_Groups_Oordered__ab__semigroup__add > class_Groups_Oordered__ab__group__add > class_Groups_Oone > class_Groups_Omonoid__mult > class_Groups_Omonoid__add > class_Groups_Ominus > class_Groups_Olinordered__ab__group__add > class_Groups_Ogroup__add > class_Groups_Ocomm__monoid__mult > class_Groups_Ocomm__monoid__add > class_Groups_Ocancel__semigroup__add > class_Groups_Ocancel__comm__monoid__add > class_Groups_Ocancel__ab__semigroup__add > class_Groups_Oab__semigroup__mult > class_Groups_Oab__semigroup__add > class_Groups_Oab__group__add > class_Fields_Olinordered__field__inverse__zero > class_Fields_Olinordered__field > class_Fields_Ofield__inverse__zero > class_Fields_Ofield > class_Divides_Osemiring__div > class_Divides_Oring__div > c_Power_Opower_Opower > c_Polynomial_Osynthetic__div > c_Polynomial_Osmult > c_Polynomial_Opcompose > c_Polynomial_OpCons > c_Polynomial_Oorder > c_Groups_Oplus__class_Oplus > c_Groups_Ominus__class_Ominus > c_Divides_Odiv__class_Odiv > tc_fun > hAPP > c_Rings_Oinverse__class_Oinverse > c_RealVector_Onorm__class_Onorm > c_Polynomial_Opoly > c_Nat__Transfer_Otsub > c_Int_Onumber__class_Onumber__of > c_Groups_Ouminus__class_Ouminus > c_Fundamental__Theorem__Algebra__Mirabelle_Opsize > #nlpp > tc_Polynomial_Opoly > c_Power_Opower__class_Opower > c_Nat_OSuc > c_Groups_Ozero__class_Ozero > c_Groups_Otimes__class_Otimes > c_Groups_Oone__class_Oone > v_s____ > v_q____ > v_pa____ > v_p > v_k____ > v_c____ > v_a____ > tc_RealDef_Oreal > tc_Nat_Onat > tc_Int_Oint > tc_HOL_Obool > tc_Complex_Ocomplex > c_Complex_Oii > #skF_13 > #skF_25 > #skF_33 > #skF_7 > #skF_6 > #skF_17 > #skF_34 > #skF_26 > #skF_31 > #skF_18 > #skF_12 > #skF_4 > #skF_3 > #skF_8 > #skF_5 > #skF_19 > #skF_10 > #skF_21 > #skF_11 > #skF_32 > #skF_15 > #skF_23 > #skF_30 > #skF_14 > #skF_22 > #skF_29 > #skF_28 > #skF_2 > #skF_24 > #skF_27 > #skF_1 > #skF_9 > #skF_20 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff(class_Groups_Olinordered__ab__group__add,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(class_Rings_Ocomm__semiring__1,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(c_Orderings_Oord__class_Oless__eq,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(class_Int_Oring__char__0,type,
class_Int_Oring__char__0: $i > $o ).
tff('#skF_25',type,
'#skF_25': $i > $i ).
tff('#skF_33',type,
'#skF_33': $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(class_Groups_Omonoid__add,type,
class_Groups_Omonoid__add: $i > $o ).
tff(class_Rings_Oordered__ring,type,
class_Rings_Oordered__ring: $i > $o ).
tff(class_Rings_Olinordered__semiring__strict,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(class_Rings_Osemiring,type,
class_Rings_Osemiring: $i > $o ).
tff(c_Nat__Transfer_Otsub,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(tc_HOL_Obool,type,
tc_HOL_Obool: $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i * $i * $i ) > $i ).
tff(class_Rings_Ocomm__ring__1,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(class_Groups_Oordered__ab__semigroup__add__imp__le,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(class_Groups_Ogroup__add,type,
class_Groups_Ogroup__add: $i > $o ).
tff(tc_Nat_Onat,type,
tc_Nat_Onat: $i ).
tff(class_Groups_Oone,type,
class_Groups_Oone: $i > $o ).
tff(class_Rings_Olinordered__semiring,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(c_Int_Onumber__class_Onumber__of,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(class_Groups_Ocancel__comm__monoid__add,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff('#skF_26',type,
'#skF_26': ( $i * $i ) > $i ).
tff(class_Groups_Ocomm__monoid__add,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff('#skF_31',type,
'#skF_31': $i ).
tff(c_Groups_Otimes__class_Otimes,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(class_Groups_Omonoid__mult,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(tc_Polynomial_Opoly,type,
tc_Polynomial_Opoly: $i > $i ).
tff(class_Rings_Ocomm__ring,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(class_Rings_Olinordered__comm__semiring__strict,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff(class_Groups_Oordered__ab__group__add,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(class_Rings_Odvd,type,
class_Rings_Odvd: $i > $o ).
tff(c_Groups_Oone__class_Oone,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(c_Polynomial_Osynthetic__div,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(tc_Int_Oint,type,
tc_Int_Oint: $i ).
tff(class_Fields_Ofield__inverse__zero,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff(class_Rings_Olinordered__ring,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(c_Power_Opower_Opower,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(tc_RealDef_Oreal,type,
tc_RealDef_Oreal: $i ).
tff(class_Rings_Ocomm__semiring__0,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(class_Int_Onumber,type,
class_Int_Onumber: $i > $o ).
tff(class_Groups_Ocomm__monoid__mult,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff(class_Rings_Oordered__comm__semiring,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(class_Rings_Olinordered__semidom,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(c_Complex_Oii,type,
c_Complex_Oii: $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i * $i ) > $i ).
tff(class_Rings_Odivision__ring,type,
class_Rings_Odivision__ring: $i > $o ).
tff(class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(class_Rings_Ocomm__semiring,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(class_Groups_Ocancel__semigroup__add,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(class_Rings_Oordered__cancel__semiring,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(class_Groups_Ominus,type,
class_Groups_Ominus: $i > $o ).
tff(class_Fields_Ofield,type,
class_Fields_Ofield: $i > $o ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: ( $i * $i * $i ) > $o ).
tff(class_Rings_Olinordered__semiring__1,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(class_Divides_Oring__div,type,
class_Divides_Oring__div: $i > $o ).
tff(class_Groups_Oordered__comm__monoid__add,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(c_Polynomial_Osmult,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(c_Groups_Ominus__class_Ominus,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i ) > $i ).
tff(c_Orderings_Oord__class_Oless,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Groups_Ozero__class_Ozero,type,
c_Groups_Ozero__class_Ozero: $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_Rings_Odivision__ring__inverse__zero,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(class_Rings_Oring__1,type,
class_Rings_Oring__1: $i > $o ).
tff(class_Power_Opower,type,
class_Power_Opower: $i > $o ).
tff(c_Rings_Odvd__class_Odvd,type,
c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
tff(class_Rings_Osemiring__0,type,
class_Rings_Osemiring__0: $i > $o ).
tff(class_Rings_Omult__zero,type,
class_Rings_Omult__zero: $i > $o ).
tff(c_Groups_Oplus__class_Oplus,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(class_Orderings_Oord,type,
class_Orderings_Oord: $i > $o ).
tff(class_RealVector_Oreal__normed__vector,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(class_Groups_Oab__semigroup__add,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(v_k____,type,
v_k____: $i ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(class_Fields_Olinordered__field,type,
class_Fields_Olinordered__field: $i > $o ).
tff('#skF_32',type,
'#skF_32': $i ).
tff(c_Polynomial_Opoly,type,
c_Polynomial_Opoly: ( $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(class_Groups_Ocancel__ab__semigroup__add,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Rings_Oidom,type,
class_Rings_Oidom: $i > $o ).
tff(class_Groups_Ozero,type,
class_Groups_Ozero: $i > $o ).
tff(class_Lattices_Oab__semigroup__idem__mult,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff(class_Rings_Oring__no__zero__divisors,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(class_Rings_Oring,type,
class_Rings_Oring: $i > $o ).
tff(c_Groups_Ouminus__class_Ouminus,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff(class_Rings_Olinordered__semiring__1__strict,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff('#skF_23',type,
'#skF_23': ( $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff(c_Polynomial_OpCons,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(c_Nat_OSuc,type,
c_Nat_OSuc: $i > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff(c_RealVector_Onorm__class_Onorm,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(v_c____,type,
v_c____: $i ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(class_Groups_Oab__semigroup__mult,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(class_Groups_Oordered__cancel__ab__semigroup__add,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(class_Rings_Ozero__neq__one,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(class_Rings_Ono__zero__divisors,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff('#skF_29',type,
'#skF_29': $i ).
tff(class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
tff('#skF_28',type,
'#skF_28': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(c_Polynomial_Opcompose,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(v_p,type,
v_p: $i ).
tff(class_Rings_Oordered__semiring,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(v_a____,type,
v_a____: $i ).
tff(c_Rings_Oinverse__class_Oinverse,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(class_Rings_Olinordered__idom,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(class_Fields_Olinordered__field__inverse__zero,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(v_q____,type,
v_q____: $i ).
tff(class_Groups_Oab__group__add,type,
class_Groups_Oab__group__add: $i > $o ).
tff('#skF_27',type,
'#skF_27': ( $i * $i ) > $i ).
tff(c_Polynomial_Oorder,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(class_Rings_Olinordered__ring__strict,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(class_Rings_Oring__1__no__zero__divisors,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(class_Groups_Oordered__ab__semigroup__add,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(v_s____,type,
v_s____: $i ).
tff(v_pa____,type,
v_pa____: $i ).
tff(class_Groups_Ouminus,type,
class_Groups_Ouminus: $i > $o ).
tff(f_5804,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
tff(f_1641,axiom,
! [T_a] :
( class_Rings_Ozero__neq__one(T_a)
=> ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
tff(f_5805,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
tff(f_1705,axiom,
! [V_n,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
tff(f_5799,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
tff(f_193,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
tff(f_5795,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
tff(f_1669,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
tff(f_2487,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
tff(f_6070,negated_conjecture,
~ ? [B_x,B_y] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_x),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_y),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(c_3310,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5804]) ).
tff(c_3819,plain,
! [T_a_2979] :
( ( c_Groups_Ozero__class_Ozero(T_a_2979) != c_Groups_Oone__class_Oone(T_a_2979) )
| ~ class_Rings_Ozero__neq__one(T_a_2979) ),
inference(cnfTransformation,[status(thm)],[f_1641]) ).
tff(c_3837,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[c_3310,c_3819]) ).
tff(c_3312,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5805]) ).
tff(c_39040,plain,
! [T_a_3757,V_n_3758] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a_3757),c_Groups_Oone__class_Oone(T_a_3757)),V_n_3758) = c_Groups_Oone__class_Oone(T_a_3757) )
| ~ class_Groups_Omonoid__mult(T_a_3757) ),
inference(cnfTransformation,[status(thm)],[f_1705]) ).
tff(c_3300,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5799]) ).
tff(c_31506,plain,
! [T_a_3606,V_a_3607] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a_3606),c_Groups_Ozero__class_Ozero(T_a_3606)),V_a_3607) = c_Groups_Ozero__class_Ozero(T_a_3606) )
| ~ class_Rings_Ocomm__semiring__1(T_a_3606) ),
inference(cnfTransformation,[status(thm)],[f_193]) ).
tff(c_3292,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5795]) ).
tff(c_17221,plain,
! [T_a_3391,V_a_3392] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a_3391),c_Groups_Oone__class_Oone(T_a_3391)),V_a_3392) = V_a_3392 )
| ~ class_Groups_Ocomm__monoid__mult(T_a_3391) ),
inference(cnfTransformation,[status(thm)],[f_1669]) ).
tff(c_1282,plain,
c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(cnfTransformation,[status(thm)],[f_2487]) ).
tff(c_3474,plain,
! [B_y_2876,B_x_2875] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_y_2876),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_y_2876),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_x_2875),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_x_2875),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
inference(cnfTransformation,[status(thm)],[f_6070]) ).
tff(c_3561,plain,
! [B_y_2876,B_x_2875] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_y_2876),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_y_2876),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_x_2875),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_x_2875),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(demodulation,[status(thm),theory(equality)],[c_1282,c_1282,c_3474]) ).
tff(c_17272,plain,
! [B_x_2875] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_x_2875),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_x_2875),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))) )
| ~ class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_17221,c_3561]) ).
tff(c_17348,plain,
! [B_x_2875] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_x_2875),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_x_2875),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(demodulation,[status(thm),theory(equality)],[c_3292,c_17272]) ).
tff(c_31517,plain,
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_31506,c_17348]) ).
tff(c_31595,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(demodulation,[status(thm),theory(equality)],[c_3300,c_31517]) ).
tff(c_39058,plain,
( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
| ~ class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_39040,c_31595]) ).
tff(c_39110,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(demodulation,[status(thm),theory(equality)],[c_3312,c_39058]) ).
tff(c_39112,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3837,c_39110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWW256+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.15 % 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
% 0.15/0.36 % Computer : n001.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 19:42:10 EDT 2023
% 0.15/0.36 % CPUTime :
% 35.91/13.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.91/13.77
% 35.91/13.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 35.97/13.80
% 35.97/13.80 Inference rules
% 35.97/13.80 ----------------------
% 35.97/13.80 #Ref : 14
% 35.97/13.80 #Sup : 7363
% 35.97/13.80 #Fact : 12
% 35.97/13.80 #Define : 0
% 35.97/13.80 #Split : 1
% 35.97/13.80 #Chain : 0
% 35.97/13.80 #Close : 0
% 35.97/13.80
% 35.97/13.80 Ordering : KBO
% 35.97/13.80
% 35.97/13.80 Simplification rules
% 35.97/13.80 ----------------------
% 35.97/13.80 #Subsume : 2512
% 35.97/13.80 #Demod : 4985
% 35.97/13.80 #Tautology : 3686
% 35.97/13.80 #SimpNegUnit : 208
% 35.97/13.80 #BackRed : 19
% 35.97/13.80
% 35.97/13.80 #Partial instantiations: 0
% 35.97/13.80 #Strategies tried : 1
% 35.97/13.80
% 35.97/13.80 Timing (in seconds)
% 35.97/13.80 ----------------------
% 35.97/13.80 Preprocessing : 2.28
% 35.97/13.80 Parsing : 1.31
% 35.97/13.80 CNF conversion : 0.17
% 35.97/13.80 Main loop : 10.45
% 35.97/13.80 Inferencing : 1.63
% 35.97/13.80 Reduction : 5.57
% 35.97/13.81 Demodulation : 4.10
% 36.27/13.81 BG Simplification : 0.22
% 36.27/13.81 Subsumption : 2.32
% 36.27/13.81 Abstraction : 0.13
% 36.27/13.81 MUC search : 0.00
% 36.27/13.81 Cooper : 0.00
% 36.27/13.81 Total : 12.79
% 36.27/13.81 Index Insertion : 0.00
% 36.27/13.81 Index Deletion : 0.00
% 36.27/13.81 Index Matching : 0.00
% 36.27/13.81 BG Taut test : 0.00
%------------------------------------------------------------------------------