%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW286+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:10:13 PM UTC 2026
% Result : Theorem 19.93s 3.75s
% Output : CNFRefutation 19.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 57
% Syntax : Number of formulae : 213 ( 89 unt; 0 def)
% Number of atoms : 464 ( 235 equ)
% Maximal formula atoms : 42 ( 2 avg)
% Number of connectives : 431 ( 180 ~; 169 |; 27 &)
% ( 6 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-5 aty)
% Number of functors : 26 ( 26 usr; 5 con; 0-3 aty)
% Number of variables : 336 ( 27 sgn 204 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_power__one,axiom,
! [X4,X6] :
( class_Groups_Omonoid__mult(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_Groups_Oone__class_Oone(X6)),X4) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(fact_poly__1,axiom,
! [X18,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6))),X18) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__1) ).
fof(fact_poly__power,axiom,
! [X18,X4,X20,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(c_Polynomial_Opoly(X6,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X6)),X20),X4)),X18) = hAPP(hAPP(c_Power_Opower__class_Opower(X6),hAPP(c_Polynomial_Opoly(X6,X20),X18)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__power) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(fact_poly__eq__iff,axiom,
! [X13,X7,X6] :
( ( class_Rings_Oidom(X6)
& class_Int_Oring__char__0(X6) )
=> ( c_Polynomial_Opoly(X6,X7) = c_Polynomial_Opoly(X6,X13)
<=> X7 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(fact_one__poly__def,axiom,
! [X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6)) = c_Polynomial_OpCons(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__poly__def) ).
fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
! [X82] :
( class_Groups_Oab__group__add(X82)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(fact_power__eq__0__iff,axiom,
! [X14,X8,X6] :
( ( class_Rings_Ozero__neq__one(X6)
& class_Rings_Ono__zero__divisors(X6)
& class_Rings_Omult__zero(X6)
& class_Power_Opower(X6) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X6),X8),X14) = c_Groups_Ozero__class_Ozero(X6)
<=> ( X14 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X8 = c_Groups_Ozero__class_Ozero(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_power__Suc,axiom,
! [X4,X5,X6] :
( class_Power_Opower(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),c_Nat_OSuc(X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc) ).
fof(fact_Suc__eq__plus1,axiom,
! [X4] : c_Nat_OSuc(X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(fact_pCons__eq__iff,axiom,
! [X13,X10,X7,X8,X6] :
( class_Groups_Ozero(X6)
=> ( c_Polynomial_OpCons(X6,X8,X7) = c_Polynomial_OpCons(X6,X10,X13)
<=> ( X7 = X13
& X8 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
fof(fact_diff__0,axiom,
! [X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,c_Groups_Ozero__class_Ozero(X6),X5) = c_Groups_Ouminus__class_Ouminus(X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0) ).
fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(fact_pdivmod__rel__def,axiom,
! [X66,X13,X25,X23,X6] :
( class_Fields_Ofield(X6)
=> ( c_Polynomial_Opdivmod__rel(X6,X23,X25,X13,X66)
<=> ( ( X25 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X6,X66),c_Polynomial_Odegree(X6,X25))
| X66 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ) )
& ( X25 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> X13 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) )
& X23 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X13),X25),X66) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__def) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(fact_minus__pCons,axiom,
! [X20,X5,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X5,X20)) = c_Polynomial_OpCons(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__pCons) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(fact_pCons__0__0,axiom,
! [X6] :
( class_Groups_Ozero(X6)
=> c_Polynomial_OpCons(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__0__0) ).
fof(fact_diff__self,axiom,
! [X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,X5,X5) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
fof(arity_Polynomial__Opoly__Power_Opower,axiom,
! [X82] :
( class_Rings_Ocomm__semiring__1(X82)
=> class_Power_Opower(tc_Polynomial_Opoly(X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(fact_add__poly__code_I2_J,axiom,
! [X20,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),X20,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Oone__class_Oone(X6)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_smult__0__right,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(fact_mod__poly__eq,axiom,
! [X49,X21,X17,X18,X6] :
( class_Fields_Ofield(X6)
=> ( c_Polynomial_Opdivmod__rel(X6,X18,X17,X21,X49)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),X18,X17) = X49 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__poly__eq) ).
fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(fact_smult__pCons,axiom,
! [X20,X9,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,X5,c_Polynomial_OpCons(X6,X9,X20)) = c_Polynomial_OpCons(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X9),c_Polynomial_Osmult(X6,X5,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__pCons) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(fact_coeff__pCons__0,axiom,
! [X20,X5,X6] :
( class_Groups_Ozero(X6)
=> hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X5,X20)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__pCons__0) ).
fof(fact_mod__smult__left,axiom,
! [X17,X18,X5,X6] :
( class_Fields_Ofield(X6)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X5,X18),X17) = c_Polynomial_Osmult(X6,X5,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),X18,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__smult__left) ).
fof(fact_k_I1_J,axiom,
v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex,v_k____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_k_I1_J) ).
fof(fact_degree__mod__less,axiom,
! [X18,X17,X6] :
( class_Fields_Ofield(X6)
=> ( X17 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X6,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),X18,X17)),c_Polynomial_Odegree(X6,X17))
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),X18,X17) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__mod__less) ).
fof(fact_pe,axiom,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pe) ).
fof(fact_less__zeroE,axiom,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_add__poly__code_I1_J,axiom,
! [X21,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X21) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(conj_0,conjecture,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_k____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_poly__gcd_Osimps_I2_J,axiom,
! [X18,X17,X6] :
( class_Fields_Ofield(X6)
=> ( X17 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> c_Polynomial_Opoly__gcd(X6,X18,X17) = c_Polynomial_Opoly__gcd(X6,X17,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),X18,X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Osimps_I2_J) ).
fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
! [X9,X5,X6] :
( class_Divides_Osemiring__div(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Divides_Odiv__class_Omod(X6,X5,X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Divides_Odiv__class_Odiv(X6,X5,X9)),X9)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).
fof(fact_dp,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dp) ).
fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
! [X82] :
( class_Fields_Ofield(X82)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(fact_div__by__1,axiom,
! [X5,X6] :
( class_Divides_Osemiring__div(X6)
=> c_Divides_Odiv__class_Odiv(X6,X5,c_Groups_Oone__class_Oone(X6)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__1) ).
fof(fact_poly__gcd__1__left,axiom,
! [X17,X6] :
( class_Fields_Ofield(X6)
=> c_Polynomial_Opoly__gcd(X6,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6)),X17) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X18,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X18),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_poly__gcd_Ocommute,axiom,
! [X9,X5,X6] :
( class_Fields_Ofield(X6)
=> c_Polynomial_Opoly__gcd(X6,X5,X9) = c_Polynomial_Opoly__gcd(X6,X9,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Ocommute) ).
fof(fact_inverse__eq__divide,axiom,
! [X5,X6] :
( class_Rings_Odivision__ring(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,X5) = c_Rings_Oinverse__class_Odivide(X6,c_Groups_Oone__class_Oone(X6),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__divide) ).
fof(fact_mult__smult__right,axiom,
! [X21,X5,X20,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X20),c_Polynomial_Osmult(X6,X5,X21)) = c_Polynomial_Osmult(X6,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X20),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__smult__right) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [X82] :
( class_Rings_Ocomm__semiring__1(X82)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(fact_poly__gcd_Osimps_I1_J,axiom,
! [X18,X6] :
( class_Fields_Ofield(X6)
=> c_Polynomial_Opoly__gcd(X6,X18,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) = c_Polynomial_Osmult(X6,c_Rings_Oinverse__class_Oinverse(X6,hAPP(c_Polynomial_Ocoeff(X6,X18),c_Polynomial_Odegree(X6,X18))),X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Osimps_I1_J) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
fof(c_0_57,plain,
! [X176,X177] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X177),c_Groups_Oone__class_Oone(X177)),X176) = c_Groups_Oone__class_Oone(X177)
| ~ class_Groups_Omonoid__mult(X177) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])])]) ).
fof(c_0_58,plain,
! [X83,X84] :
( X84 = X83
| hAPP(X84,esk1_2(X83,X84)) != hAPP(X83,esk1_2(X83,X84)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
cnf(c_0_59,plain,
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_60,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]) ).
cnf(c_0_61,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_62,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
fof(c_0_63,plain,
! [X310,X311] :
( hAPP(c_Polynomial_Opoly(X311,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X311))),X310) = c_Groups_Oone__class_Oone(X311)
| ~ class_Rings_Ocomm__semiring__1(X311) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__1])])]) ).
cnf(c_0_64,plain,
( hAPP(X1,esk1_2(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1)) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| X1 = hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_66,plain,
! [X306,X307,X308,X309] :
( hAPP(c_Polynomial_Opoly(X309,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X309)),X308),X307)),X306) = hAPP(hAPP(c_Power_Opower__class_Opower(X309),hAPP(c_Polynomial_Opoly(X309,X308),X306)),X307)
| ~ class_Rings_Ocomm__semiring__1(X309) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__power])])]) ).
cnf(c_0_67,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oone__class_Oone(X1) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))) = hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
fof(c_0_69,plain,
! [X244,X245,X246] :
( ( ~ class_Rings_Oidom(X246)
| ~ class_Int_Oring__char__0(X246)
| c_Polynomial_Opoly(X246,X245) = c_Polynomial_Opoly(X246,X244)
| X245 != X244 )
& ( ~ class_Rings_Oidom(X246)
| ~ class_Int_Oring__char__0(X246)
| X245 = X244
| c_Polynomial_Opoly(X246,X245) != c_Polynomial_Opoly(X246,X244) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__iff])])])]) ).
cnf(c_0_70,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_71,plain,
c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_67]),c_0_68])]) ).
fof(c_0_72,plain,
! [X89] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X89)) = c_Polynomial_OpCons(X89,c_Groups_Oone__class_Oone(X89),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X89)))
| ~ class_Rings_Ocomm__semiring__1(X89) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__poly__def])])]) ).
fof(c_0_73,plain,
! [X3017] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X3017))
| ~ class_Groups_Oab__group__add(X3017) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add])])]) ).
fof(c_0_74,plain,
! [X14,X8,X6] :
( ( class_Rings_Ozero__neq__one(X6)
& class_Rings_Ono__zero__divisors(X6)
& class_Rings_Omult__zero(X6)
& class_Power_Opower(X6) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X6),X8),X14) = c_Groups_Ozero__class_Ozero(X6)
<=> ( X14 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X8 = c_Groups_Ozero__class_Ozero(X6) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__eq__0__iff]) ).
fof(c_0_75,plain,
! [X936,X937,X938] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X938),X937),c_Nat_OSuc(X936)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X938),X937),hAPP(hAPP(c_Power_Opower__class_Opower(X938),X937),X936))
| ~ class_Power_Opower(X938) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])])]) ).
fof(c_0_76,plain,
! [X1051] : c_Nat_OSuc(X1051) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1051,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
cnf(c_0_77,plain,
( ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_78,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
cnf(c_0_79,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]) ).
cnf(c_0_80,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X1)),X2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_62]),c_0_62]),c_0_68])]) ).
fof(c_0_81,plain,
! [X130,X131,X132,X133,X134] :
( ( ~ class_Groups_Ozero(X134)
| c_Polynomial_OpCons(X134,X133,X132) = c_Polynomial_OpCons(X134,X131,X130)
| X132 != X130
| X133 != X131 )
& ( ~ class_Groups_Ozero(X134)
| c_Polynomial_OpCons(X134,X133,X132) != c_Polynomial_OpCons(X134,X131,X130)
| X132 = X130 )
& ( ~ class_Groups_Ozero(X134)
| c_Polynomial_OpCons(X134,X133,X132) != c_Polynomial_OpCons(X134,X131,X130)
| X133 = X131 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__iff])])])]) ).
cnf(c_0_82,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
fof(c_0_83,plain,
! [X1321,X1322] :
( c_Groups_Ominus__class_Ominus(X1322,c_Groups_Ozero__class_Ozero(X1322),X1321) = c_Groups_Ouminus__class_Ouminus(X1322,X1321)
| ~ class_Groups_Ogroup__add(X1322) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])])]) ).
cnf(c_0_84,plain,
( ~ class_Groups_Oab__group__add(X1)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_85,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]) ).
fof(c_0_86,plain,
! [X153,X154,X155] :
( ( ~ class_Rings_Ozero__neq__one(X155)
| ~ class_Rings_Ono__zero__divisors(X155)
| ~ class_Rings_Omult__zero(X155)
| ~ class_Power_Opower(X155)
| hAPP(hAPP(c_Power_Opower__class_Opower(X155),X154),X153) = c_Groups_Ozero__class_Ozero(X155)
| X153 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X154 != c_Groups_Ozero__class_Ozero(X155) )
& ( ~ class_Rings_Ozero__neq__one(X155)
| ~ class_Rings_Ono__zero__divisors(X155)
| ~ class_Rings_Omult__zero(X155)
| ~ class_Power_Opower(X155)
| hAPP(hAPP(c_Power_Opower__class_Opower(X155),X154),X153) != c_Groups_Ozero__class_Ozero(X155)
| X153 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ class_Rings_Ozero__neq__one(X155)
| ~ class_Rings_Ono__zero__divisors(X155)
| ~ class_Rings_Omult__zero(X155)
| ~ class_Power_Opower(X155)
| hAPP(hAPP(c_Power_Opower__class_Opower(X155),X154),X153) != c_Groups_Ozero__class_Ozero(X155)
| X154 = c_Groups_Ozero__class_Ozero(X155) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])])]) ).
fof(c_0_87,plain,
! [X66,X13,X25,X23,X6] :
( class_Fields_Ofield(X6)
=> ( c_Polynomial_Opdivmod__rel(X6,X23,X25,X13,X66)
<=> ( ( X25 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X6,X66),c_Polynomial_Odegree(X6,X25))
| X66 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ) )
& ( X25 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> X13 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) )
& X23 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X13),X25),X66) ) ) ),
inference(fof_simplification,[status(thm)],[fact_pdivmod__rel__def]) ).
cnf(c_0_88,plain,
( ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_89,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_90,plain,
( c_Polynomial_Opoly(tc_Complex_Ocomplex,X1) != hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_71]),c_0_78]),c_0_79])]) ).
cnf(c_0_91,plain,
c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X1)) = hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_64,c_0_80]) ).
cnf(c_0_92,plain,
( ~ class_Groups_Ozero(X3)
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X3,X2,X5)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_93,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_82,c_0_68]) ).
cnf(c_0_94,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
fof(c_0_95,plain,
! [X509,X510,X511] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X511),c_Polynomial_OpCons(X511,X510,X509)) = c_Polynomial_OpCons(X511,c_Groups_Ouminus__class_Ouminus(X511,X510),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X511),X509))
| ~ class_Groups_Oab__group__add(X511) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__pCons])])]) ).
cnf(c_0_96,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_97,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
cnf(c_0_98,plain,
class_Groups_Ogroup__add(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
fof(c_0_99,plain,
! [X90] :
( c_Polynomial_OpCons(X90,c_Groups_Ozero__class_Ozero(X90),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X90))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X90))
| ~ class_Groups_Ozero(X90) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__0__0])])]) ).
fof(c_0_100,plain,
! [X1204,X1205] :
( c_Groups_Ominus__class_Ominus(X1205,X1204,X1204) = c_Groups_Ozero__class_Ozero(X1205)
| ~ class_Groups_Ogroup__add(X1205) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])])]) ).
cnf(c_0_101,plain,
( ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
fof(c_0_102,plain,
! [X1539,X1540,X1541,X1542,X1543] :
( ( ~ class_Fields_Ofield(X1543)
| c_Polynomial_Opdivmod__rel(X1543,X1542,X1541,X1540,X1539)
| X1542 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1543)),X1540),X1541),X1539)
| X1540 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1543,X1539),c_Polynomial_Odegree(X1543,X1541)) )
& ( ~ class_Fields_Ofield(X1543)
| c_Polynomial_Opdivmod__rel(X1543,X1542,X1541,X1540,X1539)
| X1542 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1543)),X1540),X1541),X1539)
| X1540 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543))
| X1539 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543)) )
& ( ~ class_Fields_Ofield(X1543)
| c_Polynomial_Opdivmod__rel(X1543,X1542,X1541,X1540,X1539)
| X1542 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1543)),X1540),X1541),X1539)
| X1540 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543))
| X1541 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543)) )
& ( ~ class_Fields_Ofield(X1543)
| c_Polynomial_Opdivmod__rel(X1543,X1542,X1541,X1540,X1539)
| X1542 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1543)),X1540),X1541),X1539)
| X1541 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1543,X1539),c_Polynomial_Odegree(X1543,X1541)) )
& ( ~ class_Fields_Ofield(X1543)
| c_Polynomial_Opdivmod__rel(X1543,X1542,X1541,X1540,X1539)
| X1542 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1543)),X1540),X1541),X1539)
| X1541 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543))
| X1539 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543)) )
& ( ~ class_Fields_Ofield(X1543)
| c_Polynomial_Opdivmod__rel(X1543,X1542,X1541,X1540,X1539)
| X1542 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1543)),X1540),X1541),X1539)
| X1541 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543))
| X1541 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543)) )
& ( ~ class_Fields_Ofield(X1543)
| ~ c_Polynomial_Opdivmod__rel(X1543,X1542,X1541,X1540,X1539)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1543,X1539),c_Polynomial_Odegree(X1543,X1541))
| X1539 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543))
| X1541 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543)) )
& ( ~ class_Fields_Ofield(X1543)
| ~ c_Polynomial_Opdivmod__rel(X1543,X1542,X1541,X1540,X1539)
| X1540 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543))
| X1541 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1543)) )
& ( ~ class_Fields_Ofield(X1543)
| ~ c_Polynomial_Opdivmod__rel(X1543,X1542,X1541,X1540,X1539)
| X1542 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1543)),X1540),X1541),X1539) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])])])]) ).
cnf(c_0_103,plain,
( ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) ),
inference(rw,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_104,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X1) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
fof(c_0_105,plain,
! [X3026] :
( class_Power_Opower(tc_Polynomial_Opoly(X3026))
| ~ class_Rings_Ocomm__semiring__1(X3026) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower])])]) ).
fof(c_0_106,plain,
! [X876,X877] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X877),X876,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X877))) = X876
| ~ class_Groups_Ocomm__monoid__add(X877) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J])])]) ).
cnf(c_0_107,plain,
( c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| X1 = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94])]) ).
cnf(c_0_108,plain,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3)) = c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_109,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_110,plain,
c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),
inference(spm,[status(thm)],[c_0_96,c_0_98]) ).
cnf(c_0_111,plain,
( ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_112,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_113,plain,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(er,[status(thm)],[c_0_101]) ).
cnf(c_0_114,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]) ).
cnf(c_0_115,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]) ).
cnf(c_0_116,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]) ).
cnf(c_0_117,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]) ).
cnf(c_0_118,plain,
( ~ class_Fields_Ofield(X2)
| X4 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X5),X3),X1)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opdivmod__rel(X2,X4,X3,X5,X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_119,plain,
( ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_104]) ).
cnf(c_0_120,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Power_Opower(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_121,plain,
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_122,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]) ).
cnf(c_0_123,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]),c_0_110]),c_0_85])]) ).
cnf(c_0_124,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_111,c_0_94]) ).
cnf(c_0_125,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_112,c_0_97]) ).
cnf(c_0_126,plain,
c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_112,c_0_98]) ).
cnf(c_0_127,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_62]),c_0_114]),c_0_115]),c_0_116]),c_0_117])]) ).
fof(c_0_128,plain,
! [X232,X233] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X233),X232),c_Groups_Oone__class_Oone(X233)) = X232
| ~ class_Rings_Ocomm__semiring__1(X233) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])])]) ).
fof(c_0_129,plain,
! [X1274,X1275] :
( c_Polynomial_Osmult(X1275,X1274,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1275))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1275))
| ~ class_Rings_Ocomm__semiring__0(X1275) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__right])])]) ).
fof(c_0_130,plain,
! [X1564,X1565,X1566,X1567,X1568] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1568),X1567,X1566) = X1564
| ~ c_Polynomial_Opdivmod__rel(X1568,X1567,X1566,X1565,X1564)
| ~ class_Fields_Ofield(X1568) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__poly__eq])])]) ).
cnf(c_0_131,plain,
( ~ class_Fields_Ofield(X2)
| c_Polynomial_Opdivmod__rel(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X3),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X1,X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_118])]) ).
cnf(c_0_132,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_68])]) ).
cnf(c_0_133,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X1,
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_134,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]) ).
cnf(c_0_135,plain,
c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]),c_0_126]),c_0_127]) ).
fof(c_0_136,plain,
! [X1343,X1344,X1345,X1346] :
( c_Polynomial_Osmult(X1346,X1345,c_Polynomial_OpCons(X1346,X1344,X1343)) = c_Polynomial_OpCons(X1346,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1346),X1345),X1344),c_Polynomial_Osmult(X1346,X1345,X1343))
| ~ class_Rings_Ocomm__semiring__0(X1346) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__pCons])])]) ).
cnf(c_0_137,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_138,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_139,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
fof(c_0_140,plain,
! [X620,X621,X622] :
( hAPP(c_Polynomial_Ocoeff(X622,c_Polynomial_OpCons(X622,X621,X620)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X621
| ~ class_Groups_Ozero(X622) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__pCons__0])])]) ).
fof(c_0_141,plain,
! [X1624,X1625,X1626,X1627] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1627),c_Polynomial_Osmult(X1627,X1626,X1625),X1624) = c_Polynomial_Osmult(X1627,X1626,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1627),X1625,X1624))
| ~ class_Fields_Ofield(X1627) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__smult__left])])]) ).
cnf(c_0_142,plain,
( ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Fields_Ofield(X1)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,X3) = X5 ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_143,plain,
c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133]),c_0_134])]),c_0_135]) ).
cnf(c_0_144,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,X2,c_Polynomial_OpCons(X1,X3,X4)) = c_Polynomial_OpCons(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Polynomial_Osmult(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_145,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = X1,
inference(spm,[status(thm)],[c_0_137,c_0_68]) ).
cnf(c_0_146,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_147,plain,
( ~ class_Groups_Ozero(X1)
| hAPP(c_Polynomial_Ocoeff(X1,c_Polynomial_OpCons(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_148,plain,
v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex,v_k____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(split_conjunct,[status(thm)],[fact_k_I1_J]) ).
fof(c_0_149,plain,
! [X18,X17,X6] :
( class_Fields_Ofield(X6)
=> ( X17 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X6,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),X18,X17)),c_Polynomial_Odegree(X6,X17))
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),X18,X17) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_degree__mod__less]) ).
fof(c_0_150,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(fof_simplification,[status(thm)],[fact_pe]) ).
fof(c_0_151,plain,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
cnf(c_0_152,plain,
( ~ class_Fields_Ofield(X1)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) = c_Polynomial_Osmult(X1,X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_153,plain,
c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_134])]) ).
cnf(c_0_154,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_93]),c_0_145]),c_0_146]),c_0_139])]) ).
cnf(c_0_155,plain,
v_k____ = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_94])]) ).
fof(c_0_156,plain,
! [X878,X879] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X879),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X879)),X878) = X878
| ~ class_Groups_Ocomm__monoid__add(X879) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J])])]) ).
fof(c_0_157,negated_conjecture,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_k____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_158,plain,
! [X18,X17,X6] :
( class_Fields_Ofield(X6)
=> ( X17 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> c_Polynomial_Opoly__gcd(X6,X18,X17) = c_Polynomial_Opoly__gcd(X6,X17,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),X18,X17)) ) ),
inference(fof_simplification,[status(thm)],[fact_poly__gcd_Osimps_I2_J]) ).
fof(c_0_159,plain,
! [X1769,X1770,X1771] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1771,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1771),X1769,X1770)),c_Polynomial_Odegree(X1771,X1770))
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1771),X1769,X1770) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1771))
| X1770 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1771))
| ~ class_Fields_Ofield(X1771) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])]) ).
fof(c_0_160,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(fof_nnf,[status(thm)],[c_0_150]) ).
fof(c_0_161,plain,
! [X1546] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1546,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_151])]) ).
fof(c_0_162,plain,
! [X2665,X2666,X2667] :
( c_Groups_Oplus__class_Oplus(X2667,c_Divides_Odiv__class_Omod(X2667,X2666,X2665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2667),c_Divides_Odiv__class_Odiv(X2667,X2666,X2665)),X2665)) = X2666
| ~ class_Divides_Osemiring__div(X2667) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H])])]) ).
cnf(c_0_163,plain,
c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_146]),c_0_154]),c_0_134])]) ).
cnf(c_0_164,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = v_p,
inference(rw,[status(thm)],[c_0_148,c_0_155]) ).
cnf(c_0_165,plain,
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
fof(c_0_166,negated_conjecture,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_k____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_167,plain,
! [X1953,X1954,X1955] :
( c_Polynomial_Opoly__gcd(X1955,X1953,X1954) = c_Polynomial_Opoly__gcd(X1955,X1954,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1955),X1953,X1954))
| X1954 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1955))
| ~ class_Fields_Ofield(X1955) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_158])])]) ).
cnf(c_0_168,plain,
( ~ class_Fields_Ofield(X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X3,X2)),c_Polynomial_Odegree(X1,X2))
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X3,X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_169,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_dp]) ).
cnf(c_0_170,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[c_0_160]) ).
cnf(c_0_171,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
cnf(c_0_172,plain,
( ~ class_Divides_Osemiring__div(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),X3)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_162]) ).
cnf(c_0_173,plain,
c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_174,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1) = X1,
inference(spm,[status(thm)],[c_0_165,c_0_122]) ).
fof(c_0_175,plain,
! [X3008] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X3008))
| ~ class_Fields_Ofield(X3008) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Osemiring__div])])]) ).
fof(c_0_176,negated_conjecture,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_k____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(fof_nnf,[status(thm)],[c_0_166]) ).
cnf(c_0_177,plain,
( ~ class_Fields_Ofield(X1)
| c_Polynomial_Opoly__gcd(X1,X3,X2) = c_Polynomial_Opoly__gcd(X1,X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X3,X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_178,plain,
c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,v_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_134])]),c_0_170]),c_0_171]) ).
cnf(c_0_179,plain,
( ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = v_p ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_174]) ).
cnf(c_0_180,plain,
( ~ class_Fields_Ofield(X1)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_175]) ).
fof(c_0_181,plain,
! [X2532,X2533] :
( c_Divides_Odiv__class_Odiv(X2533,X2532,c_Groups_Oone__class_Oone(X2533)) = X2532
| ~ class_Divides_Osemiring__div(X2533) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])])]) ).
cnf(c_0_182,negated_conjecture,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_k____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
fof(c_0_183,plain,
! [X901,X902] :
( c_Polynomial_Opoly__gcd(X902,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X902)),X901) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X902))
| ~ class_Fields_Ofield(X902) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__1__left])])]) ).
cnf(c_0_184,plain,
c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,X1,v_p) = c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,v_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_134])]),c_0_170]) ).
cnf(c_0_185,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = v_p,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_134])]) ).
cnf(c_0_186,plain,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_181]) ).
cnf(c_0_187,negated_conjecture,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_k____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rw,[status(thm)],[c_0_182,c_0_169]) ).
fof(c_0_188,plain,
! [X218,X219] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X219),X218),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X219)
| ~ class_Rings_Ocomm__semiring__1(X219) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])])]) ).
fof(c_0_189,plain,
! [X758,X759,X760] :
( c_Polynomial_Opoly__gcd(X760,X759,X758) = c_Polynomial_Opoly__gcd(X760,X758,X759)
| ~ class_Fields_Ofield(X760) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd_Ocommute])])]) ).
cnf(c_0_190,plain,
( ~ class_Fields_Ofield(X1)
| c_Polynomial_Opoly__gcd(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_183]) ).
cnf(c_0_191,plain,
c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,X1,v_p) = c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,X2,v_p),
inference(spm,[status(thm)],[c_0_184,c_0_184]) ).
fof(c_0_192,plain,
! [X1792,X1793] :
( c_Rings_Oinverse__class_Oinverse(X1793,X1792) = c_Rings_Oinverse__class_Odivide(X1793,c_Groups_Oone__class_Oone(X1793),X1792)
| ~ class_Rings_Odivision__ring(X1793) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__divide])])]) ).
fof(c_0_193,plain,
! [X1292,X1293,X1294,X1295] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1295)),X1294),c_Polynomial_Osmult(X1295,X1293,X1292)) = c_Polynomial_Osmult(X1295,X1293,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1295)),X1294),X1292))
| ~ class_Rings_Ocomm__semiring__0(X1295) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__right])])]) ).
cnf(c_0_194,plain,
( ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = v_p ),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_195,negated_conjecture,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(spm,[status(thm)],[c_0_187,c_0_155]) ).
cnf(c_0_196,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
fof(c_0_197,plain,
! [X3006] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X3006))
| ~ class_Rings_Ocomm__semiring__1(X3006) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1])])]) ).
fof(c_0_198,plain,
! [X1544,X1545] :
( c_Polynomial_Opoly__gcd(X1545,X1544,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1545))) = c_Polynomial_Osmult(X1545,c_Rings_Oinverse__class_Oinverse(X1545,hAPP(c_Polynomial_Ocoeff(X1545,X1544),c_Polynomial_Odegree(X1545,X1544))),X1544)
| ~ class_Fields_Ofield(X1545) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd_Osimps_I1_J])])]) ).
cnf(c_0_199,plain,
( ~ class_Fields_Ofield(X1)
| c_Polynomial_Opoly__gcd(X1,X2,X3) = c_Polynomial_Opoly__gcd(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_200,plain,
c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,X1,v_p) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_134])]) ).
cnf(c_0_201,plain,
( ~ class_Rings_Odivision__ring(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_202,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]) ).
cnf(c_0_203,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_204,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = v_p,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_180]),c_0_134])]) ).
cnf(c_0_205,negated_conjecture,
( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_206,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_197]) ).
cnf(c_0_207,plain,
( ~ class_Fields_Ofield(X1)
| c_Polynomial_Opoly__gcd(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Osmult(X1,c_Rings_Oinverse__class_Oinverse(X1,hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2))),X2) ),
inference(split_conjunct,[status(thm)],[c_0_198]) ).
cnf(c_0_208,plain,
c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,v_p,X1) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_134])]) ).
cnf(c_0_209,plain,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1),
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_210,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,v_p) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_154]),c_0_139])]) ).
cnf(c_0_211,negated_conjecture,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_68])]) ).
cnf(c_0_212,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_208]),c_0_169]),c_0_209]),c_0_134])]),c_0_210]),c_0_211]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW286+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n007.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 09:43:35 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.93/3.75 % Version: 3.5.1
% 19.93/3.75 % Preprocessing class: FMLMSMSSSSSNFFN.
% 19.93/3.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.93/3.75 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 19.93/3.75 % Starting new_bool_3 with 300s (1) cores
% 19.93/3.75 % Starting new_bool_1 with 300s (1) cores
% 19.93/3.75 % Starting sh5l with 300s (1) cores
% 19.93/3.75 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 773470 completed with status 0
% 19.93/3.75 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 19.93/3.75 % Preprocessing class: FMLMSMSSSSSNFFN.
% 19.93/3.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.93/3.75 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 19.93/3.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 19.93/3.75 % No SInE strategy applied
% 19.93/3.75 % Search class: FGHSM-SSLM32-DFFFFFNN
% 19.93/3.75 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 19.93/3.75 % Starting SubtermCWHack with 136s (1) cores
% 19.93/3.75 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 19.93/3.75 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 19.93/3.75 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 19.93/3.75 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 19.93/3.75 % G-E--_208_B07_F1_SE_CS_SP_PS_S4d with pid 773480 completed with status 0
% 19.93/3.75 % Result found by G-E--_208_B07_F1_SE_CS_SP_PS_S4d
% 19.93/3.75 % Preprocessing class: FMLMSMSSSSSNFFN.
% 19.93/3.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.93/3.75 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 19.93/3.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 19.93/3.75 % No SInE strategy applied
% 19.93/3.75 % Search class: FGHSM-SSLM32-DFFFFFNN
% 19.93/3.75 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 19.93/3.75 % Starting SubtermCWHack with 136s (1) cores
% 19.93/3.75 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 19.93/3.75 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 19.93/3.75 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 19.93/3.75 % Preprocessing time : 0.040 s
% 19.93/3.75 % Presaturation interreduction done
% 19.93/3.75
% 19.93/3.75 % Proof found!
% 19.93/3.75 % SZS status Theorem
% 19.93/3.75 % SZS output start CNFRefutation
% See solution above
% 19.93/3.75 % Parsed axioms : 1170
% 19.93/3.75 % Removed by relevancy pruning/SinE : 0
% 19.93/3.75 % Initial clauses : 1597
% 19.93/3.75 % Removed in clause preprocessing : 79
% 19.93/3.75 % Initial clauses in saturation : 1518
% 19.93/3.75 % Processed clauses : 12136
% 19.93/3.75 % ...of these trivial : 262
% 19.93/3.75 % ...subsumed : 6728
% 19.93/3.75 % ...remaining for further processing : 5145
% 19.93/3.75 % Other redundant clauses eliminated : 1695
% 19.93/3.75 % Clauses deleted for lack of memory : 0
% 19.93/3.75 % Backward-subsumed : 210
% 19.93/3.75 % Backward-rewritten : 408
% 19.93/3.75 % Generated clauses : 93841
% 19.93/3.75 % ...of the previous two non-redundant : 80649
% 19.93/3.75 % ...aggressively subsumed : 0
% 19.93/3.75 % Contextual simplify-reflections : 7
% 19.93/3.75 % Paramodulations : 92102
% 19.93/3.75 % Factorizations : 7
% 19.93/3.75 % NegExts : 0
% 19.93/3.75 % Equation resolutions : 1761
% 19.93/3.75 % Disequality decompositions : 0
% 19.93/3.75 % Total rewrite steps : 72536
% 19.93/3.75 % ...of those cached : 65912
% 19.93/3.75 % Propositional unsat checks : 0
% 19.93/3.75 % Propositional check models : 0
% 19.93/3.75 % Propositional check unsatisfiable : 0
% 19.93/3.75 % Propositional clauses : 0
% 19.93/3.75 % Propositional clauses after purity: 0
% 19.93/3.75 % Propositional unsat core size : 0
% 19.93/3.75 % Propositional preprocessing time : 0.000
% 19.93/3.75 % Propositional encoding time : 0.000
% 19.93/3.75 % Propositional solver time : 0.000
% 19.93/3.75 % Success case prop preproc time : 0.000
% 19.93/3.75 % Success case prop encoding time : 0.000
% 19.93/3.75 % Success case prop solver time : 0.000
% 19.93/3.75 % Current number of processed clauses : 3097
% 19.93/3.75 % Positive orientable unit clauses : 708
% 19.93/3.75 % Positive unorientable unit clauses: 14
% 19.93/3.75 % Negative unit clauses : 183
% 19.93/3.75 % Non-unit-clauses : 2192
% 19.93/3.75 % Current number of unprocessed clauses: 70935
% 19.93/3.75 % ...number of literals in the above : 202811
% 19.93/3.75 % Current number of archived formulas : 0
% 19.93/3.75 % Current number of archived clauses : 1885
% 19.93/3.75 % Clause-clause subsumption calls (NU) : 534789
% 19.93/3.75 % Rec. Clause-clause subsumption calls : 347418
% 19.93/3.75 % Non-unit clause-clause subsumptions : 3244
% 19.93/3.75 % Unit Clause-clause subsumption calls : 17389
% 19.93/3.75 % Rewrite failures with RHS unbound : 12
% 19.93/3.75 % BW rewrite match attempts : 5882
% 19.93/3.75 % BW rewrite match successes : 478
% 19.93/3.75 % Condensation attempts : 0
% 19.93/3.75 % Condensation successes : 0
% 19.93/3.75 % Termbank termtop insertions : 2279512
% 19.93/3.75 % Search garbage collected termcells : 20247
% 19.93/3.75
% 19.93/3.75 % -------------------------------------------------
% 19.93/3.75 % User time : 2.831 s
% 19.93/3.75 % System time : 0.111 s
% 19.93/3.75 % Total time : 2.942 s
% 19.93/3.75 % Maximum resident set size: 9880 pages
% 19.93/3.75
% 19.93/3.75 % -------------------------------------------------
% 19.93/3.75 % User time : 13.037 s
% 19.93/3.75 % System time : 0.478 s
% 19.93/3.75 % Total time : 13.514 s
% 19.93/3.75 % Maximum resident set size: 5888 pages
% 19.93/3.75 % E exiting
%------------------------------------------------------------------------------