%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW187+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 : n014.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 03:10:03 PM UTC 2026
% Result : Theorem 150.98s 22.60s
% Output : CNFRefutation 173.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 44
% Syntax : Number of formulae : 185 ( 74 unt; 0 def)
% Number of atoms : 391 ( 204 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 363 ( 157 ~; 141 |; 19 &)
% ( 13 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 5 con; 0-3 aty)
% Number of variables : 350 ( 38 sgn 200 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_gr0__conv__Suc,axiom,
! [X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25)
<=> ? [X62] : X25 = c_Nat_OSuc(X62) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_Suc__eq__plus1,axiom,
! [X19] : c_Nat_OSuc(X19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_Zero__neq__Suc,axiom,
! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_add__eq__self__zero,axiom,
! [X19,X24] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X19) = X24
=> X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_nat__add__commute,axiom,
! [X19,X24] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_nat__neq__iff,axiom,
! [X25,X26] :
( X26 != X25
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X26)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_less__zeroE,axiom,
! [X19] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(conj_1,conjecture,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact_nat__add__assoc,axiom,
! [X30,X19,X24] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X19),X30) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_less__le__not__le,axiom,
! [X21,X22,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X22,X21)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X21,X22)
& c_Orderings_Oord__class_Oless__eq(X8,X22,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_le__diff__conv,axiom,
! [X85,X34,X86] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X86,X34),X85)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X86,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X85,X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(fact_order__refl,axiom,
! [X16,X11] :
( class_Orderings_Opreorder(X11)
=> c_Orderings_Oord__class_Oless__eq(X11,X16,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_smult__0__left,axiom,
! [X13,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> c_Polynomial_Osmult(X11,c_Groups_Ozero__class_Ozero(X11),X13) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X21,X22,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X22,X21)
<=> ( X22 = X21
| c_Orderings_Oord__class_Oless(X8,X21,X22) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X20,X18,X10,X11] :
( class_Groups_Ocancel__semigroup__add(X11)
=> ( c_Groups_Oplus__class_Oplus(X11,X10,X18) = c_Groups_Oplus__class_Oplus(X11,X10,X20)
=> X18 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(fact_diff__add__0,axiom,
! [X24,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X24)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(fact_diff__diff__left,axiom,
! [X30,X32,X33] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X32),X30) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_degree__smult__le,axiom,
! [X13,X10,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X11,c_Polynomial_Osmult(X11,X10,X13)),c_Polynomial_Odegree(X11,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__smult__le) ).
fof(fact_synthetic__div__unique__lemma,axiom,
! [X10,X13,X20,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> ( c_Polynomial_Osmult(X11,X20,X13) = c_Polynomial_OpCons(X11,X10,X13)
=> X13 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
fof(tfree_0,hypothesis,
class_Rings_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
fof(fact_pCons__cases,axiom,
! [X13,X11] :
( class_Groups_Ozero(X11)
=> ~ ! [X14,X15] : X13 != c_Polynomial_OpCons(X11,X14,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__cases) ).
fof(fact_offset__poly__pCons,axiom,
! [X9,X13,X10,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X11,c_Polynomial_OpCons(X11,X10,X13),X9) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X11),c_Polynomial_Osmult(X11,X9,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X11,X13,X9)),c_Polynomial_OpCons(X11,X10,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X11,X13,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
fof(fact_degree__add__eq__right,axiom,
! [X17,X13,X11] :
( class_Groups_Ocomm__monoid__add(X11)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X11,X13),c_Polynomial_Odegree(X11,X17))
=> c_Polynomial_Odegree(X11,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X11),X13,X17)) = c_Polynomial_Odegree(X11,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__add__eq__right) ).
fof(fact_degree__pCons__eq,axiom,
! [X10,X13,X11] :
( class_Groups_Ozero(X11)
=> ( X13 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))
=> c_Polynomial_Odegree(X11,c_Polynomial_OpCons(X11,X10,X13)) = c_Nat_OSuc(c_Polynomial_Odegree(X11,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pCons__eq) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X24] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X24,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_diff__is__0__eq,axiom,
! [X25,X26] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(conj_0,hypothesis,
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',conj_0) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X20,X10,X11] :
( class_Rings_Ocomm__semiring__1(X11)
=> c_Groups_Oplus__class_Oplus(X11,X10,X20) = c_Groups_Oplus__class_Oplus(X11,X20,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_le__iff__add,axiom,
! [X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
<=> ? [X35] : X25 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(clrel_Rings_Ocomm__semiring__0__Groups_Ozero,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__0(X90)
=> class_Groups_Ozero(X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ozero) ).
fof(clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__0(X90)
=> class_Groups_Ocomm__monoid__add(X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(fact_pCons__eq__0__iff,axiom,
! [X6,X7,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_OpCons(X8,X7,X6) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> ( X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
& X7 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(fact_synthetic__div__unique,axiom,
! [X39,X17,X20,X13,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X11),X13,c_Polynomial_Osmult(X11,X20,X17)) = c_Polynomial_OpCons(X11,X39,X17)
=> ( X17 = c_Polynomial_Osynthetic__div(X11,X13,X20)
& X39 = hAPP(c_Polynomial_Opoly(X11,X13),X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
fof(fact_add__poly__code_I2_J,axiom,
! [X13,X11] :
( class_Groups_Ocomm__monoid__add(X11)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X11),X13,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(fact_add__poly__code_I1_J,axiom,
! [X17,X11] :
( class_Groups_Ocomm__monoid__add(X11)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X11),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)),X17) = X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(fact_offset__poly__eq__0__iff,axiom,
! [X12,X6,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X8,X6,X12) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
fof(fact_offset__poly__single,axiom,
! [X9,X10,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X11,c_Polynomial_OpCons(X11,X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))),X9) = c_Polynomial_OpCons(X11,X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__single) ).
fof(fact_smult__0__right,axiom,
! [X10,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> c_Polynomial_Osmult(X11,X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(fact_synthetic__div__eq__0__iff,axiom,
! [X23,X6,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Polynomial_Osynthetic__div(X8,X6,X23) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> c_Polynomial_Odegree(X8,X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__eq__0__iff) ).
fof(c_0_44,plain,
! [X1594,X1596,X1597] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1596)
| X1596 != c_Nat_OSuc(X1597) )
& ( X1594 = c_Nat_OSuc(esk11_1(X1594))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1594) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc])])])])])]) ).
fof(c_0_45,plain,
! [X998] : c_Nat_OSuc(X998) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X998,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(c_0_46,plain,
! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X24),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_47,plain,
! [X275,X276] :
( X275 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X276,X275) != X276 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
fof(c_0_48,plain,
! [X494,X495] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X495,X494) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X494,X495),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
cnf(c_0_49,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 = c_Nat_OSuc(esk11_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,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_45]) ).
fof(c_0_51,plain,
! [X25,X26] :
( X26 != X25
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X26)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__neq__iff]) ).
fof(c_0_52,plain,
! [X19] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(c_0_53,plain,
! [X422] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X422),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_46])]) ).
fof(c_0_54,negated_conjecture,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
inference(assume_negation,[status(cth)],[conj_1]) ).
cnf(c_0_55,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_57,plain,
! [X499,X500,X501] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X501,X500),X499) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X501,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X500,X499)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
cnf(c_0_58,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk11_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
fof(c_0_59,plain,
! [X1874,X1875] :
( ( X1875 != X1874
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1874,X1875) )
& ( X1875 != X1874
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1875,X1874) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1874,X1875)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1875,X1874)
| X1875 = X1874 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])]) ).
fof(c_0_60,plain,
! [X1158] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1158,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_52])]) ).
cnf(c_0_61,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_62,plain,
! [X21,X22,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X22,X21)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X21,X22)
& c_Orderings_Oord__class_Oless__eq(X8,X22,X21) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_63,plain,
! [X2710,X2711,X2712] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2712,X2711),X2710)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2712,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2710,X2711)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2712,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2710,X2711))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2712,X2711),X2710) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])])]) ).
fof(c_0_64,plain,
! [X468,X469] :
( c_Orderings_Oord__class_Oless__eq(X469,X468,X468)
| ~ class_Orderings_Opreorder(X469) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])])]) ).
fof(c_0_65,plain,
! [X154,X155] :
( c_Polynomial_Osmult(X155,c_Groups_Ozero__class_Ozero(X155),X154) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X155))
| ~ class_Rings_Ocomm__semiring__0(X155) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__left])])]) ).
fof(c_0_66,negated_conjecture,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_67,plain,
! [X21,X22,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X22,X21)
<=> ( X22 = X21
| c_Orderings_Oord__class_Oless(X8,X21,X22) ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
cnf(c_0_68,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X2
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_69,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_70,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),esk11_1(X1)) = X1 ),
inference(rw,[status(thm)],[c_0_58,c_0_56]) ).
cnf(c_0_71,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_72,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_60]) ).
fof(c_0_73,plain,
! [X259,X260,X261,X262] :
( X260 = X259
| c_Groups_Oplus__class_Oplus(X262,X261,X260) != c_Groups_Oplus__class_Oplus(X262,X261,X259)
| ~ class_Groups_Ocancel__semigroup__add(X262) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])])]) ).
cnf(c_0_74,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[c_0_61,c_0_50]) ).
fof(c_0_75,plain,
! [X1320,X1321,X1322] :
( ( ~ class_Orderings_Opreorder(X1322)
| c_Orderings_Oord__class_Oless(X1322,X1321,X1320)
| c_Orderings_Oord__class_Oless__eq(X1322,X1320,X1321)
| ~ c_Orderings_Oord__class_Oless__eq(X1322,X1321,X1320) )
& ( ~ class_Orderings_Opreorder(X1322)
| ~ c_Orderings_Oord__class_Oless(X1322,X1321,X1320)
| ~ c_Orderings_Oord__class_Oless__eq(X1322,X1320,X1321) )
& ( ~ class_Orderings_Opreorder(X1322)
| ~ c_Orderings_Oord__class_Oless(X1322,X1321,X1320)
| c_Orderings_Oord__class_Oless__eq(X1322,X1321,X1320) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).
cnf(c_0_76,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_77,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_78,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
fof(c_0_79,plain,
! [X2827,X2828] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2828,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2828,X2827)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).
fof(c_0_80,plain,
! [X2862,X2863,X2864] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2864,X2863),X2862) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2864,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2863,X2862)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
fof(c_0_81,plain,
! [X138,X139,X140] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X140,c_Polynomial_Osmult(X140,X139,X138)),c_Polynomial_Odegree(X140,X138))
| ~ class_Rings_Ocomm__semiring__0(X140) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__smult__le])])]) ).
fof(c_0_82,plain,
! [X212,X213,X214,X215] :
( X213 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X215))
| c_Polynomial_Osmult(X215,X214,X213) != c_Polynomial_OpCons(X215,X212,X213)
| ~ class_Rings_Ocomm__semiring__0(X215) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique__lemma])])]) ).
cnf(c_0_83,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_84,hypothesis,
class_Rings_Ocomm__semiring__0(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]) ).
fof(c_0_85,plain,
! [X13,X11] :
( class_Groups_Ozero(X11)
=> ~ ! [X14,X15] : X13 != c_Polynomial_OpCons(X11,X14,X15) ),
inference(fof_simplification,[status(thm)],[fact_pCons__cases]) ).
fof(c_0_86,negated_conjecture,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
inference(fof_nnf,[status(thm)],[c_0_66]) ).
fof(c_0_87,plain,
! [X109,X110,X111,X112] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X112,c_Polynomial_OpCons(X112,X111,X110),X109) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X112),c_Polynomial_Osmult(X112,X109,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X112,X110,X109)),c_Polynomial_OpCons(X112,X111,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X112,X110,X109)))
| ~ class_Rings_Ocomm__semiring__0(X112) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__pCons])])]) ).
fof(c_0_88,plain,
! [X1671,X1672,X1673] :
( c_Polynomial_Odegree(X1673,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1673),X1672,X1671)) = c_Polynomial_Odegree(X1673,X1671)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1673,X1672),c_Polynomial_Odegree(X1673,X1671))
| ~ class_Groups_Ocomm__monoid__add(X1673) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__add__eq__right])])]) ).
fof(c_0_89,plain,
! [X1185,X1186,X1187] :
( ( ~ class_Orderings_Olinorder(X1187)
| ~ c_Orderings_Oord__class_Oless(X1187,X1186,X1185)
| X1186 != X1185 )
& ( ~ class_Orderings_Olinorder(X1187)
| ~ c_Orderings_Oord__class_Oless(X1187,X1186,X1185)
| ~ c_Orderings_Oord__class_Oless(X1187,X1185,X1186) )
& ( ~ class_Orderings_Olinorder(X1187)
| X1186 = X1185
| c_Orderings_Oord__class_Oless(X1187,X1185,X1186)
| c_Orderings_Oord__class_Oless(X1187,X1186,X1185) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])]) ).
fof(c_0_90,plain,
! [X10,X13,X11] :
( class_Groups_Ozero(X11)
=> ( X13 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))
=> c_Polynomial_Odegree(X11,c_Polynomial_OpCons(X11,X10,X13)) = c_Nat_OSuc(c_Polynomial_Odegree(X11,X13)) ) ),
inference(fof_simplification,[status(thm)],[fact_degree__pCons__eq]) ).
cnf(c_0_91,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) != X3
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_92,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),esk11_1(X1)) = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_93,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4)
| ~ class_Groups_Ocancel__semigroup__add(X1)
| X3 = X4 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_94,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).
cnf(c_0_95,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(spm,[status(thm)],[c_0_74,c_0_56]) ).
cnf(c_0_96,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_97,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_56]),c_0_78])]) ).
cnf(c_0_98,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_99,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
fof(c_0_100,plain,
! [X279] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X279,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X279,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_101,plain,
! [X2689,X2690] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2690,X2689) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2690,X2689) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2690,X2689)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2690,X2689) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])])]) ).
cnf(c_0_102,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X1,c_Polynomial_Osmult(X1,X2,X3)),c_Polynomial_Odegree(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_103,hypothesis,
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),
inference(split_conjunct,[status(thm)],[conj_0]) ).
cnf(c_0_104,plain,
( c_Polynomial_Osmult(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X3)
| ~ class_Rings_Ocomm__semiring__0(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_105,hypothesis,
c_Polynomial_Osmult(t_a,c_Groups_Ozero__class_Ozero(t_a),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
fof(c_0_106,plain,
! [X115,X116] :
( X115 = c_Polynomial_OpCons(X116,esk2_2(X115,X116),esk3_2(X115,X116))
| ~ class_Groups_Ozero(X116) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])])]) ).
cnf(c_0_107,negated_conjecture,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_108,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4)),c_Polynomial_OpCons(X1,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_109,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X3))
| ~ class_Groups_Ocomm__monoid__add(X1)
| c_Polynomial_Odegree(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)) = c_Polynomial_Odegree(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_110,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_111,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
fof(c_0_112,plain,
! [X119,X120,X121] :
( c_Polynomial_Odegree(X121,c_Polynomial_OpCons(X121,X119,X120)) = c_Nat_OSuc(c_Polynomial_Odegree(X121,X120))
| X120 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X121))
| ~ class_Groups_Ozero(X121) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_90])])]) ).
cnf(c_0_113,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != esk11_1(X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_74]) ).
cnf(c_0_114,plain,
esk11_1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) = X1,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_92]),c_0_94])])]),c_0_95]) ).
fof(c_0_115,plain,
! [X571,X572,X573] :
( c_Groups_Oplus__class_Oplus(X573,X572,X571) = c_Groups_Oplus__class_Oplus(X573,X571,X572)
| ~ class_Rings_Ocomm__semiring__1(X573) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])]) ).
fof(c_0_116,plain,
! [X338,X339,X341,X342,X343] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X342,X341)
| X341 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X342,X343) )
& ( X338 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X339,esk4_2(X338,X339))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X339,X338) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__add])])])])])]) ).
cnf(c_0_117,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_78])]) ).
cnf(c_0_118,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_119,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_120,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_121,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,v_p)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_84])]) ).
fof(c_0_122,plain,
! [X280] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X280) = X280,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
cnf(c_0_123,hypothesis,
( c_Polynomial_OpCons(t_a,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_84])]) ).
cnf(c_0_124,plain,
( ~ class_Groups_Ozero(X1)
| X2 = c_Polynomial_OpCons(X1,esk2_2(X2,X1),esk3_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
fof(c_0_125,plain,
! [X2991] :
( class_Groups_Ozero(X2991)
| ~ class_Rings_Ocomm__semiring__0(X2991) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__semiring__0__Groups_Ozero])])]) ).
cnf(c_0_126,negated_conjecture,
c_Polynomial_Odegree(t_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_84])]) ).
cnf(c_0_127,plain,
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X1,X2))
| c_Polynomial_Odegree(X1,X2) = c_Polynomial_Odegree(X1,X3)
| c_Polynomial_Odegree(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)) = c_Polynomial_Odegree(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111])]) ).
fof(c_0_128,plain,
! [X2985] :
( class_Groups_Ocomm__monoid__add(X2985)
| ~ class_Rings_Ocomm__semiring__0(X2985) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add])])]) ).
cnf(c_0_129,plain,
( ~ class_Groups_Ozero(X1)
| c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X3,X2)) = c_Nat_OSuc(c_Polynomial_Odegree(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_130,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) != X2,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_95]) ).
cnf(c_0_131,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_132,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).
cnf(c_0_133,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk4_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_134,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]) ).
cnf(c_0_135,hypothesis,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,v_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_136,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_137,hypothesis,
( ~ class_Groups_Ozero(t_a)
| esk3_2(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124])]) ).
cnf(c_0_138,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_139,negated_conjecture,
( ~ class_Groups_Ocomm__monoid__add(t_a)
| c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_140,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_141,plain,
( ~ class_Groups_Ozero(X1)
| c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X3,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(rw,[status(thm)],[c_0_129,c_0_50]) ).
cnf(c_0_142,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_69]),c_0_132])]) ).
cnf(c_0_143,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),esk4_2(c_Polynomial_Odegree(t_a,v_p),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))) = c_Polynomial_Odegree(t_a,v_p),
inference(spm,[status(thm)],[c_0_133,c_0_121]) ).
cnf(c_0_144,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,v_p),X1),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]) ).
cnf(c_0_145,hypothesis,
esk3_2(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_84])]) ).
cnf(c_0_146,negated_conjecture,
( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_84])]) ).
cnf(c_0_147,plain,
( ~ class_Groups_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X1,X3)) ),
inference(rw,[status(thm)],[c_0_141,c_0_56]) ).
cnf(c_0_148,hypothesis,
c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_149,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Polynomial_Odegree(t_a,v_p)),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_131]),c_0_132])]) ).
fof(c_0_150,plain,
! [X186,X187,X188] :
( ( ~ class_Groups_Ozero(X188)
| c_Polynomial_OpCons(X188,X187,X186) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X188))
| X186 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X188))
| X187 != c_Groups_Ozero__class_Ozero(X188) )
& ( ~ class_Groups_Ozero(X188)
| c_Polynomial_OpCons(X188,X187,X186) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X188))
| X186 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X188)) )
& ( ~ class_Groups_Ozero(X188)
| c_Polynomial_OpCons(X188,X187,X186) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X188))
| X187 = c_Groups_Ozero__class_Ozero(X188) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__0__iff])])])]) ).
cnf(c_0_151,hypothesis,
( ~ class_Groups_Ozero(t_a)
| c_Polynomial_OpCons(t_a,esk2_2(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(spm,[status(thm)],[c_0_124,c_0_145]) ).
fof(c_0_152,plain,
! [X470,X471,X472,X473,X474] :
( ( ~ class_Rings_Ocomm__semiring__0(X474)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X474),X473,c_Polynomial_Osmult(X474,X472,X471)) != c_Polynomial_OpCons(X474,X470,X471)
| X471 = c_Polynomial_Osynthetic__div(X474,X473,X472) )
& ( ~ class_Rings_Ocomm__semiring__0(X474)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X474),X473,c_Polynomial_Osmult(X474,X472,X471)) != c_Polynomial_OpCons(X474,X470,X471)
| X470 = hAPP(c_Polynomial_Opoly(X474,X473),X472) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique])])])]) ).
cnf(c_0_153,negated_conjecture,
( ~ class_Groups_Ozero(t_a)
| c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_103]),c_0_103]),c_0_103]),c_0_148]),c_0_149]) ).
cnf(c_0_154,plain,
( ~ class_Groups_Ozero(X2)
| c_Polynomial_OpCons(X2,X1,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_Groups_Ozero__class_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_155,hypothesis,
c_Polynomial_OpCons(t_a,esk2_2(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_138]),c_0_84])]) ).
cnf(c_0_156,plain,
( ~ class_Rings_Ocomm__semiring__0(X2)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X3,c_Polynomial_Osmult(X2,X4,X1)) != c_Polynomial_OpCons(X2,X5,X1)
| X1 = c_Polynomial_Osynthetic__div(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
fof(c_0_157,plain,
! [X163,X164] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X164),X163,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X164))) = X163
| ~ class_Groups_Ocomm__monoid__add(X164) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J])])]) ).
cnf(c_0_158,negated_conjecture,
( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_138]),c_0_84])]) ).
cnf(c_0_159,hypothesis,
( ~ class_Groups_Ozero(t_a)
| esk2_2(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) = c_Groups_Ozero__class_Ozero(t_a) ),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
fof(c_0_160,plain,
! [X156,X157] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X157),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X157)),X156) = X156
| ~ class_Groups_Ocomm__monoid__add(X157) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J])])]) ).
cnf(c_0_161,hypothesis,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) != c_Polynomial_OpCons(t_a,X3,X1)
| X1 = c_Polynomial_Osynthetic__div(t_a,X2,c_Groups_Ozero__class_Ozero(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_105]),c_0_84])]) ).
cnf(c_0_162,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_157]) ).
fof(c_0_163,plain,
! [X106,X107,X108] :
( ( ~ class_Rings_Ocomm__semiring__0(X108)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X108,X107,X106) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X108))
| X107 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X108)) )
& ( ~ class_Rings_Ocomm__semiring__0(X108)
| X107 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X108))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X108,X107,X106) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X108)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__iff])])])]) ).
cnf(c_0_164,negated_conjecture,
( ~ class_Groups_Ozero(t_a)
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(spm,[status(thm)],[c_0_158,c_0_147]) ).
fof(c_0_165,plain,
! [X101,X102,X103] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X103,c_Polynomial_OpCons(X103,X102,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X103))),X101) = c_Polynomial_OpCons(X103,X102,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X103)))
| ~ class_Rings_Ocomm__semiring__0(X103) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__single])])]) ).
cnf(c_0_166,hypothesis,
esk2_2(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) = c_Groups_Ozero__class_Ozero(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_138]),c_0_84])]) ).
fof(c_0_167,plain,
! [X161,X162] :
( c_Polynomial_Osmult(X162,X161,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X162))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X162))
| ~ class_Rings_Ocomm__semiring__0(X162) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__right])])]) ).
cnf(c_0_168,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_160]) ).
fof(c_0_169,plain,
! [X608,X609,X610] :
( ( ~ class_Rings_Ocomm__semiring__0(X610)
| c_Polynomial_Osynthetic__div(X610,X609,X608) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X610))
| c_Polynomial_Odegree(X610,X609) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ class_Rings_Ocomm__semiring__0(X610)
| c_Polynomial_Odegree(X610,X609) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Osynthetic__div(X610,X609,X608) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X610)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__eq__0__iff])])])]) ).
cnf(c_0_170,hypothesis,
( ~ class_Groups_Ocomm__monoid__add(t_a)
| c_Polynomial_Osynthetic__div(t_a,c_Polynomial_OpCons(t_a,X1,X2),c_Groups_Ozero__class_Ozero(t_a)) = X2 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162])]) ).
cnf(c_0_171,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3) != 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_163]) ).
cnf(c_0_172,negated_conjecture,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_138]),c_0_84])]) ).
cnf(c_0_173,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X3) = c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_165]) ).
cnf(c_0_174,hypothesis,
c_Polynomial_OpCons(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(rw,[status(thm)],[c_0_155,c_0_166]) ).
cnf(c_0_175,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_167]) ).
cnf(c_0_176,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2 ),
inference(spm,[status(thm)],[c_0_168,c_0_140]) ).
cnf(c_0_177,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osynthetic__div(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Odegree(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_178,hypothesis,
c_Polynomial_Osynthetic__div(t_a,c_Polynomial_OpCons(t_a,X1,X2),c_Groups_Ozero__class_Ozero(t_a)) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_140]),c_0_84])]) ).
cnf(c_0_179,negated_conjecture,
v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_84])]) ).
cnf(c_0_180,hypothesis,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_84])]) ).
cnf(c_0_181,hypothesis,
c_Polynomial_Osmult(t_a,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(spm,[status(thm)],[c_0_175,c_0_84]) ).
cnf(c_0_182,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X1) = X1,
inference(spm,[status(thm)],[c_0_176,c_0_84]) ).
cnf(c_0_183,hypothesis,
c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_84])])]) ).
cnf(c_0_184,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_179]),c_0_180]),c_0_181]),c_0_180]),c_0_182]),c_0_183]),c_0_183])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW187+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 09:40:04 UTC 2026
% 0.16/0.39 % CPUTime :
% 0.16/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 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
% 150.98/22.60 % Version: 3.5.1
% 150.98/22.60 % Preprocessing class: FMLMSMSMSSSNFFN.
% 150.98/22.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 150.98/22.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 150.98/22.60 % Starting new_bool_3 with 300s (1) cores
% 150.98/22.60 % Starting new_bool_1 with 300s (1) cores
% 150.98/22.60 % Starting sh5l with 300s (1) cores
% 150.98/22.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3754129 completed with status 0
% 150.98/22.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 150.98/22.60 % Preprocessing class: FMLMSMSMSSSNFFN.
% 150.98/22.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 150.98/22.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 150.98/22.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 150.98/22.60 % No SInE strategy applied
% 150.98/22.60 % Search class: FGHSM-SSLM32-DFFFFFNN
% 150.98/22.60 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 150.98/22.60 % Starting SubtermCWHack with 136s (1) cores
% 150.98/22.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 150.98/22.60 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 150.98/22.60 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 150.98/22.60 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 150.98/22.60 % G-E--_208_B07_F1_SE_CS_SP_PS_S4d with pid 3754139 completed with status 0
% 150.98/22.60 % Result found by G-E--_208_B07_F1_SE_CS_SP_PS_S4d
% 150.98/22.60 % Preprocessing class: FMLMSMSMSSSNFFN.
% 150.98/22.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 150.98/22.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 150.98/22.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 150.98/22.60 % No SInE strategy applied
% 150.98/22.60 % Search class: FGHSM-SSLM32-DFFFFFNN
% 150.98/22.60 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 150.98/22.60 % Starting SubtermCWHack with 136s (1) cores
% 150.98/22.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 150.98/22.60 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 150.98/22.60 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 150.98/22.60 % Preprocessing time : 0.025 s
% 150.98/22.60 % Presaturation interreduction done
% 150.98/22.60
% 150.98/22.60 % Proof found!
% 150.98/22.60 % SZS status Theorem
% 150.98/22.60 % SZS output start CNFRefutation
% See solution above
% 173.10/22.60 % Parsed axioms : 1187
% 173.10/22.60 % Removed by relevancy pruning/SinE : 0
% 173.10/22.60 % Initial clauses : 1576
% 173.10/22.60 % Removed in clause preprocessing : 77
% 173.10/22.60 % Initial clauses in saturation : 1499
% 173.10/22.60 % Processed clauses : 78922
% 173.10/22.60 % ...of these trivial : 962
% 173.10/22.60 % ...subsumed : 69460
% 173.10/22.60 % ...remaining for further processing : 8500
% 173.10/22.60 % Other redundant clauses eliminated : 13648
% 173.10/22.60 % Clauses deleted for lack of memory : 0
% 173.10/22.60 % Backward-subsumed : 419
% 173.10/22.60 % Backward-rewritten : 527
% 173.10/22.60 % Generated clauses : 821517
% 173.10/22.60 % ...of the previous two non-redundant : 727538
% 173.10/22.60 % ...aggressively subsumed : 0
% 173.10/22.60 % Contextual simplify-reflections : 53
% 173.10/22.60 % Paramodulations : 807814
% 173.10/22.60 % Factorizations : 20
% 173.10/22.60 % NegExts : 0
% 173.10/22.60 % Equation resolutions : 13711
% 173.10/22.60 % Disequality decompositions : 0
% 173.10/22.60 % Total rewrite steps : 826941
% 173.10/22.60 % ...of those cached : 780696
% 173.10/22.60 % Propositional unsat checks : 0
% 173.10/22.60 % Propositional check models : 0
% 173.10/22.60 % Propositional check unsatisfiable : 0
% 173.10/22.60 % Propositional clauses : 0
% 173.10/22.60 % Propositional clauses after purity: 0
% 173.10/22.60 % Propositional unsat core size : 0
% 173.10/22.60 % Propositional preprocessing time : 0.000
% 173.10/22.60 % Propositional encoding time : 0.000
% 173.10/22.60 % Propositional solver time : 0.000
% 173.10/22.60 % Success case prop preproc time : 0.000
% 173.10/22.60 % Success case prop encoding time : 0.000
% 173.10/22.60 % Success case prop solver time : 0.000
% 173.10/22.60 % Current number of processed clauses : 6222
% 173.10/22.60 % Positive orientable unit clauses : 791
% 173.10/22.60 % Positive unorientable unit clauses: 82
% 173.10/22.60 % Negative unit clauses : 611
% 173.10/22.60 % Non-unit-clauses : 4738
% 173.10/22.60 % Current number of unprocessed clauses: 648995
% 173.10/22.60 % ...number of literals in the above : 1594618
% 173.10/22.60 % Current number of archived formulas : 0
% 173.10/22.60 % Current number of archived clauses : 2141
% 173.10/22.60 % Clause-clause subsumption calls (NU) : 1850836
% 173.10/22.60 % Rec. Clause-clause subsumption calls : 1384462
% 173.10/22.60 % Non-unit clause-clause subsumptions : 22317
% 173.10/22.60 % Unit Clause-clause subsumption calls : 92505
% 173.10/22.60 % Rewrite failures with RHS unbound : 0
% 173.10/22.60 % BW rewrite match attempts : 31694
% 173.10/22.60 % BW rewrite match successes : 679
% 173.10/22.60 % Condensation attempts : 0
% 173.10/22.60 % Condensation successes : 0
% 173.10/22.60 % Termbank termtop insertions : 18058108
% 173.10/22.60 % Search garbage collected termcells : 20700
% 173.10/22.60
% 173.10/22.60 % -------------------------------------------------
% 173.10/22.60 % User time : 20.923 s
% 173.10/22.60 % System time : 0.580 s
% 173.10/22.60 % Total time : 21.503 s
% 173.10/22.60 % Maximum resident set size: 9624 pages
% 173.10/22.60
% 173.10/22.60 % -------------------------------------------------
% 173.10/22.60 % User time : 103.503 s
% 173.10/22.60 % System time : 3.366 s
% 173.10/22.60 % Total time : 106.869 s
% 173.10/22.60 % Maximum resident set size: 5888 pages
% 173.10/22.60 % E exiting
%------------------------------------------------------------------------------