TSTP Solution File: SWW213+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW213+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/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 : n025.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 11:06:51 EDT 2023
% Result : Theorem 112.01s 83.15s
% Output : CNFRefutation 112.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 147
% Syntax : Number of formulae : 158 ( 7 unt; 142 typ; 0 def)
% Number of atoms : 28 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 8 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 219 ( 133 >; 86 *; 0 +; 0 <<)
% Number of predicates : 78 ( 76 usr; 2 prp; 0-5 aty)
% Number of functors : 66 ( 66 usr; 8 con; 0-5 aty)
% Number of variables : 22 (; 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Polynomial_Opdivmod__rel > c_Rings_Odvd__class_Odvd > c_Orderings_Oord__class_Oless__eq > c_Orderings_Oord__class_Oless > c_SEQ_Odecseq > c_Polynomial_Opos__poly > c_Groups_Osemigroup > 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__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_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_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_Polynomial_Opoly__rec > c_If > c_Power_Opower_Opower > c_Polynomial_Osynthetic__div > c_Polynomial_Osmult > c_Polynomial_Opoly__gcd > c_Polynomial_Opcompose > c_Polynomial_OpCons > c_Polynomial_Oorder > c_Polynomial_Omonom > c_Nat_Onat_Onat__case > c_Groups_Oplus__class_Oplus > c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly > c_Divides_Odiv__class_Omod > tc_fun > hAPP > c_fequal > c_Rings_Oinverse__class_Oinverse > c_RealDef_Oreal > c_Polynomial_Opoly > c_Polynomial_Odegree > c_Polynomial_Ocoeff > c_Polynomial_OAbs__poly > c_NthRoot_Oroot > c_Groups_Ouminus__class_Ouminus > c_Fundamental__Theorem__Algebra__Mirabelle_Opsize > #nlpp > tc_Polynomial_Opoly > c_RComplete_Onatfloor > c_RComplete_Onatceiling > c_Power_Opower__class_Opower > c_Nat_OSuc > c_Groups_Ozero__class_Ozero > c_Groups_Otimes__class_Otimes > c_Groups_Oone__class_Oone > v_z > v_thesis____ > v_p > v_e > tc_RealDef_Oreal > tc_Nat_Onat > tc_Int_Oint > tc_HOL_Obool > tc_Complex_Ocomplex > #skF_13 > #skF_7 > #skF_6 > #skF_24 > #skF_17 > #skF_20 > #skF_22 > #skF_12 > #skF_18 > #skF_19 > #skF_8 > #skF_11 > #skF_23 > #skF_4 > #skF_15 > #skF_3 > #skF_2 > #skF_14 > #skF_1 > #skF_16 > #skF_21 > #skF_9 > #skF_5 > #skF_10
%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(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(c_RealDef_Oreal,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(c_If,type,
c_If: ( $i * $i * $i * $i ) > $i ).
tff(class_Rings_Osemiring,type,
class_Rings_Osemiring: $i > $o ).
tff(tc_HOL_Obool,type,
tc_HOL_Obool: $i ).
tff('#skF_6',type,
'#skF_6': ( $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('#skF_24',type,
'#skF_24': $i > $i ).
tff(class_Groups_Ocancel__comm__monoid__add,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(class_Groups_Ocomm__monoid__add,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(c_SEQ_Odecseq,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
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('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff(class_Rings_Olinordered__comm__semiring__strict,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(class_Groups_Oordered__ab__group__add,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(c_Nat_Onat_Onat__case,type,
c_Nat_Onat_Onat__case: ( $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i ) > $i ).
tff(class_Rings_Odvd,type,
class_Rings_Odvd: $i > $o ).
tff(v_e,type,
v_e: $i ).
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('#skF_22',type,
'#skF_22': $i > $i ).
tff(tc_Int_Oint,type,
tc_Int_Oint: $i ).
tff(v_thesis____,type,
v_thesis____: $o ).
tff(c_Polynomial_Omonom,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $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(v_z,type,
v_z: $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_Groups_Ocomm__monoid__mult,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(c_NthRoot_Oroot,type,
c_NthRoot_Oroot: ( $i * $i ) > $i ).
tff(c_RComplete_Onatfloor,type,
c_RComplete_Onatfloor: $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(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(c_fequal,type,
c_fequal: ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i ) > $i ).
tff(c_Polynomial_OAbs__poly,type,
c_Polynomial_OAbs__poly: ( $i * $i ) > $i ).
tff(class_Fields_Ofield,type,
class_Fields_Ofield: $i > $o ).
tff('#skF_19',type,
'#skF_19': ( $i * $i ) > $i ).
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(c_Polynomial_Osmult,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(c_Orderings_Oord__class_Oless,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
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_Rings_Odivision__ring__inverse__zero,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
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(c_Polynomial_Opos__poly,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(class_Rings_Osemiring__0,type,
class_Rings_Osemiring__0: $i > $o ).
tff(c_Polynomial_Opdivmod__rel,type,
c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $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('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(class_Groups_Oab__semigroup__add,type,
class_Groups_Oab__semigroup__add: $i > $o ).
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(c_RComplete_Onatceiling,type,
c_RComplete_Onatceiling: $i > $i ).
tff(c_Polynomial_Opoly,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
tff('#skF_23',type,
'#skF_23': $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('#skF_4',type,
'#skF_4': ( $i * $i * $i * $i ) > $i ).
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(c_Polynomial_OpCons,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(c_Nat_OSuc,type,
c_Nat_OSuc: $i > $i ).
tff(c_Groups_Osemigroup,type,
c_Groups_Osemigroup: ( $i * $i ) > $o ).
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(c_Polynomial_Ocoeff,type,
c_Polynomial_Ocoeff: ( $i * $i ) > $i ).
tff(class_Rings_Ono__zero__divisors,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(c_Polynomial_Odegree,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(c_Polynomial_Opcompose,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i ).
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_Rings_Oordered__semiring,type,
class_Rings_Oordered__semiring: $i > $o ).
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(class_Groups_Oab__group__add,type,
class_Groups_Oab__group__add: $i > $o ).
tff(c_Polynomial_Oorder,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_Opoly__gcd,type,
c_Polynomial_Opoly__gcd: ( $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_14',type,
'#skF_14': ( $i * $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i ) > $i ).
tff(class_Groups_Oordered__ab__semigroup__add,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(c_Polynomial_Opoly__rec,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(class_Groups_Ouminus,type,
class_Groups_Ouminus: $i > $o ).
tff(f_5989,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
tff(f_92,axiom,
! [V_h,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( c_Polynomial_Odegree(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)) = c_Polynomial_Odegree(T_a,V_p) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__offset__poly) ).
tff(f_40,axiom,
! [V_x,V_h,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),c_Groups_Oplus__class_Oplus(T_a,V_h,V_x)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__offset__poly) ).
tff(f_6260,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f_6258,hypothesis,
! [B_q] :
( ( c_Polynomial_Odegree(tc_Complex_Ocomplex,B_q) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) )
=> ( ! [B_x] : ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,B_x)) )
=> v_thesis____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(c_3216,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5989]) ).
tff(c_37,plain,
! [T_a_53,V_p_52,V_h_51] :
( ( c_Polynomial_Odegree(T_a_53,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a_53,V_p_52,V_h_51)) = c_Polynomial_Odegree(T_a_53,V_p_52) )
| ~ class_Rings_Ocomm__semiring__0(T_a_53) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_257296,plain,
! [T_a_726607,V_p_726608,V_h_726609,V_x_726610] :
( ( hAPP(c_Polynomial_Opoly(T_a_726607,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a_726607,V_p_726608,V_h_726609)),V_x_726610) = hAPP(c_Polynomial_Opoly(T_a_726607,V_p_726608),c_Groups_Oplus__class_Oplus(T_a_726607,V_h_726609,V_x_726610)) )
| ~ class_Rings_Ocomm__semiring__0(T_a_726607) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_3382,plain,
~ v_thesis____,
inference(cnfTransformation,[status(thm)],[f_6260]) ).
tff(c_3380,plain,
! [B_q_2848] :
( v_thesis____
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,'#skF_24'(B_q_2848))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q_2848),'#skF_24'(B_q_2848)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Polynomial_Odegree(tc_Complex_Ocomplex,B_q_2848) ) ),
inference(cnfTransformation,[status(thm)],[f_6258]) ).
tff(c_3383,plain,
! [B_q_2848] :
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,'#skF_24'(B_q_2848))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q_2848),'#skF_24'(B_q_2848)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Polynomial_Odegree(tc_Complex_Ocomplex,B_q_2848) ) ),
inference(negUnitSimplification,[status(thm)],[c_3382,c_3380]) ).
tff(c_257483,plain,
! [V_p_726608,V_h_726609] :
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,'#skF_24'(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,V_p_726608,V_h_726609)))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p_726608),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_h_726609,'#skF_24'(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,V_p_726608,V_h_726609)))) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,V_p_726608,V_h_726609)) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_257296,c_3383]) ).
tff(c_257600,plain,
! [V_p_726608,V_h_726609] :
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,'#skF_24'(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,V_p_726608,V_h_726609)))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p_726608),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_h_726609,'#skF_24'(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,V_p_726608,V_h_726609)))) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,V_p_726608,V_h_726609)) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3216,c_257483]) ).
tff(c_257604,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,v_z)) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
inference(reflexivity,[status(thm),theory(equality)],[c_257600]) ).
tff(c_258005,plain,
~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(superposition,[status(thm),theory(equality)],[c_37,c_257604]) ).
tff(c_258009,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3216,c_258005]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW213+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % 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
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 19:53:19 EDT 2023
% 0.15/0.36 % CPUTime :
% 112.01/83.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 112.01/83.15
% 112.01/83.15 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 112.01/83.18
% 112.01/83.18 Inference rules
% 112.01/83.18 ----------------------
% 112.01/83.18 #Ref : 94
% 112.01/83.18 #Sup : 52932
% 112.01/83.18 #Fact : 18
% 112.01/83.18 #Define : 0
% 112.01/83.18 #Split : 64
% 112.01/83.18 #Chain : 0
% 112.01/83.18 #Close : 0
% 112.01/83.18
% 112.01/83.18 Ordering : KBO
% 112.01/83.18
% 112.01/83.18 Simplification rules
% 112.01/83.18 ----------------------
% 112.01/83.18 #Subsume : 15998
% 112.01/83.18 #Demod : 32438
% 112.01/83.18 #Tautology : 11451
% 112.01/83.18 #SimpNegUnit : 1866
% 112.01/83.18 #BackRed : 33
% 112.01/83.18
% 112.01/83.18 #Partial instantiations: 306357
% 112.01/83.18 #Strategies tried : 1
% 112.01/83.18
% 112.01/83.18 Timing (in seconds)
% 112.01/83.18 ----------------------
% 112.01/83.19 Preprocessing : 2.30
% 112.01/83.19 Parsing : 1.32
% 112.01/83.19 CNF conversion : 0.17
% 112.01/83.19 Main loop : 79.73
% 112.01/83.19 Inferencing : 9.12
% 112.01/83.19 Reduction : 43.76
% 112.01/83.19 Demodulation : 35.19
% 112.01/83.19 BG Simplification : 0.56
% 112.01/83.19 Subsumption : 21.11
% 112.01/83.19 Abstraction : 0.71
% 112.01/83.19 MUC search : 0.00
% 112.01/83.19 Cooper : 0.00
% 112.01/83.19 Total : 82.08
% 112.01/83.19 Index Insertion : 0.00
% 112.01/83.19 Index Deletion : 0.00
% 112.01/83.19 Index Matching : 0.00
% 112.01/83.19 BG Taut test : 0.00
%------------------------------------------------------------------------------