TSTP Solution File: ALG346-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG346-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 16:09:52 EDT 2022
% Result : Unsatisfiable 137.19s 88.65s
% Output : Proof 137.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 84
% Syntax : Number of formulae : 184 ( 50 unt; 19 typ; 0 def)
% Number of atoms : 710 ( 223 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 951 ( 426 ~; 451 |; 0 &)
% ( 74 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 14 >; 13 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 408 ( 371 !; 0 ?; 408 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_pa_type,type,
v_pa: $i ).
tff(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(v_h_type,type,
v_h: $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(v_a_type,type,
v_a: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__0_type,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(class_HOL_Ozero_type,type,
class_HOL_Ozero: $i > $o ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
tff(1,plain,
( ( v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
<=> ( v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(3,plain,
v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( class_Ring__and__Field_Ocomm__semiring__0(t_a)
<=> class_Ring__and__Field_Ocomm__semiring__0(t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
class_Ring__and__Field_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tff(6,plain,
class_Ring__and__Field_Ocomm__semiring__0(t_a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [T_a: $i,V_p: $i,V_h: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [T_a: $i,V_p: $i,V_h: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_offset__poly__eq__0__iff_0) ).
tff(13,plain,
! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
^ [T: $i] :
refl(
( ( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
<=> ( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
<=> ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
<=> ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_HOL_Ozero(T) )
<=> ( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_HOL_Ozero(T) )
<=> ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_HOL_Ozero(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_HOL_Ozero) ).
tff(30,plain,
! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
| class_HOL_Ozero(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) )
<=> ( ~ ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
| class_HOL_Ozero(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
| class_HOL_Ozero(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [T: $i] :
( class_HOL_Ozero(T)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T) )
| class_HOL_Ozero(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
class_HOL_Ozero(t_a),
inference(unit_resolution,[status(thm)],[36,6,33]) ).
tff(38,plain,
^ [V_a: $i,T_a: $i,V_p: $i] :
refl(
( ( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
<=> ( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
^ [V_a: $i,T_a: $i,V_p: $i] :
rewrite(
( ( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__pCons__eq_0) ).
tff(44,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ~ class_HOL_Ozero(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ~ class_HOL_Ozero(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) )
<=> ( ~ class_HOL_Ozero(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ~ class_HOL_Ozero(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ~ class_HOL_Ozero(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ~ class_HOL_Ozero(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)),
inference(unit_resolution,[status(thm)],[53,47,37,23]) ).
tff(55,plain,
c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a) = c_Polynomial_Odegree(v_pa,t_a) )
<=> ( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a) = c_Polynomial_Odegree(v_pa,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a) = c_Polynomial_Odegree(v_pa,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(58,plain,
c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a) = c_Polynomial_Odegree(v_pa,t_a),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)) = c_Suc(c_Polynomial_Odegree(v_pa,t_a)),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
c_Suc(c_Polynomial_Odegree(v_pa,t_a)) = c_Suc(c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a)),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
c_Suc(c_Polynomial_Odegree(v_pa,t_a)) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),
inference(transitivity,[status(thm)],[60,55]) ).
tff(62,plain,
( c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
<=> c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),tc_nat) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),tc_nat)
<=> c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat) ),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),tc_nat)
<=> ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a) = c_Suc(c_Polynomial_Odegree(v_pa,t_a)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a) = c_Suc(c_Polynomial_Odegree(v_pa,t_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a) = c_Suc(c_Polynomial_Odegree(v_pa,t_a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a)) ) )
| ( v_pa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a) = c_Suc(c_Polynomial_Odegree(v_pa,t_a)) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ class_HOL_Ozero(t_a)
| ( c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a) = c_Suc(c_Polynomial_Odegree(v_pa,t_a)) ) ),
inference(unit_resolution,[status(thm)],[67,47,3]) ).
tff(69,plain,
c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a) = c_Suc(c_Polynomial_Odegree(v_pa,t_a)),
inference(unit_resolution,[status(thm)],[68,37]) ).
tff(70,plain,
c_Suc(c_Polynomial_Odegree(v_pa,t_a)) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a),
inference(transitivity,[status(thm)],[54,59,70]) ).
tff(72,plain,
^ [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
! [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_offset__poly__pCons_0) ).
tff(76,plain,
! [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i,V_h: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)),
inference(unit_resolution,[status(thm)],[81,78,6]) ).
tff(83,plain,
c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)),t_a) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a),t_a),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)),t_a) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) )
<=> ( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a),t_a) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a) ) ),
inference(monotonicity,[status(thm)],[84,71]) ).
tff(86,plain,
( ( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a),t_a) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a) )
<=> ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)),t_a) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) ) ),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
( ( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a),t_a) != c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a) )
<=> ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)),t_a) != c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( ( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a),t_a) != c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a) )
<=> ( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a),t_a) != c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,axiom,
c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a),t_a) != c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(90,plain,
c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(v_a,v_pa,t_a),v_h,t_a),t_a) != c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,v_pa,t_a),t_a),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)),t_a) != c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),
inference(modus_ponens,[status(thm)],[90,87]) ).
tff(92,plain,
^ [T: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_OrderedGroup_Ocomm__monoid__add) ).
tff(96,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| class_OrderedGroup_Ocomm__monoid__add(t_a) )
<=> ( class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| class_OrderedGroup_Ocomm__monoid__add(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| class_OrderedGroup_Ocomm__monoid__add(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| class_OrderedGroup_Ocomm__monoid__add(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T)
| class_OrderedGroup_Ocomm__monoid__add(T) )
| class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
class_OrderedGroup_Ocomm__monoid__add(t_a),
inference(unit_resolution,[status(thm)],[104,6,98]) ).
tff(106,plain,
^ [V_q: $i,T_a: $i,V_p: $i] :
refl(
( ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) )
<=> ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) )
<=> ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
^ [V_q: $i,T_a: $i,V_p: $i] :
rewrite(
( ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) )
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(110,plain,
( ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) )
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
<=> ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,axiom,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) )
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__add__eq__right_0) ).
tff(112,plain,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) ),
inference(modus_ponens,[status(thm)],[114,107]) ).
tff(116,plain,
( ( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)),t_a) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) ) )
<=> ( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)),t_a) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)),t_a) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)),t_a) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
( ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),tc_nat)
| ( c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_Polynomial_Opoly(t_a)),t_a) = c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) ) ),
inference(unit_resolution,[status(thm)],[118,115,105]) ).
tff(120,plain,
~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),tc_nat),
inference(unit_resolution,[status(thm)],[119,91]) ).
tff(121,plain,
~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat),
inference(modus_ponens,[status(thm)],[120,64]) ).
tff(122,plain,
c_Polynomial_Odegree(v_pa,t_a) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),
inference(symmetry,[status(thm)],[58]) ).
tff(123,plain,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat)
<=> c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_nat) ),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_nat)
<=> c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat) ),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
^ [V_a: $i,T_a: $i,V_p: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,axiom,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__smult__le_0) ).
tff(129,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) ),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_nat) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),tc_nat),
inference(unit_resolution,[status(thm)],[134,131,6]) ).
tff(136,plain,
c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat),
inference(modus_ponens,[status(thm)],[135,124]) ).
tff(137,plain,
^ [V_x: $i] :
refl(
( c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat)
<=> c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) )),
inference(bind,[status(th)],]) ).
tff(138,plain,
( ! [V_x: $i] : c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat)
<=> ! [V_x: $i] : c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ),
inference(quant_intro,[status(thm)],[137]) ).
tff(139,plain,
( ! [V_x: $i] : c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat)
<=> ! [V_x: $i] : c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(140,axiom,
! [V_x: $i] : c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
tff(141,plain,
! [V_x: $i] : c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [V_x: $i] : c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat),
inference(skolemize,[status(sab)],[141]) ).
tff(143,plain,
! [V_x: $i] : c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat),
inference(modus_ponens,[status(thm)],[142,138]) ).
tff(144,plain,
( ~ ! [V_x: $i] : c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa,t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa,t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat),
inference(unit_resolution,[status(thm)],[144,143]) ).
tff(146,plain,
( class_Orderings_Opreorder(tc_nat)
<=> class_Orderings_Opreorder(tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(147,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
tff(148,plain,
class_Orderings_Opreorder(tc_nat),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
refl(
( ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(150,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
trans(
monotonicity(
rewrite(
( ( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) )
<=> ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ) )),
( ( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
rewrite(
( ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
( ( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(153,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
tff(155,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[155,151]) ).
tff(157,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(skolemize,[status(sab)],[156]) ).
tff(158,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[157,150]) ).
tff(159,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa,t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa,t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,plain,
( ( c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa,t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat) )
<=> ( ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa,t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa,t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa,t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa,t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa,t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat) ) ),
inference(transitivity,[status(thm)],[161,159]) ).
tff(163,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa,t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa,t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Polynomial_Odegree(v_pa,t_a),tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Polynomial_Osmult(v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a),c_Suc(c_Polynomial_Odegree(v_pa,t_a)),tc_nat) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
$false,
inference(unit_resolution,[status(thm)],[164,158,148,145,136,121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG346-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 15:39:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 137.19/88.65 % SZS status Unsatisfiable
% 137.19/88.65 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------