%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG419-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 04:59:05 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.63s
% Output : Proof 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 112
% Syntax : Number of formulae : 250 ( 69 unt; 0 typ; 0 def)
% Number of atoms : 1290 ( 467 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 1751 ( 775 ~; 858 |; 0 &)
% ( 118 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 64 ( 64 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 551 ( 498 !; 0 ?; 551 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Polynomial_Oorder_type,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(v_pa_____type,type,
v_pa____: $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(v_s_____type,type,
v_s____: $i ).
tff(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
tff(class_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(class_Ring__and__Field_Ono__zero__divisors_type,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_Ring__and__Field_Omult__zero_type,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
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_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Ring__and__Field_Odvd__class_Odvd_type,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(1,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
tff(3,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
tff(8,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| ( c_HOL_Oplus__class_Oplus(c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| ( c_HOL_Oplus__class_Oplus(c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| ( c_HOL_Oplus__class_Oplus(c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| ( c_HOL_Oplus__class_Oplus(c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_HOL_Oplus__class_Oplus(c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
tff(17,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__linear__power_0) ).
tff(22,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
c_HOL_Oplus__class_Oplus(c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) = c_HOL_Oplus__class_Oplus(c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
^ [T_1: $i] :
refl(( ( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
<=> ( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
tff(36,plain,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ( ~ ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[41,17,38]) ).
tff(43,plain,
^ [T_1: $i] :
refl(( ( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
<=> ( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [T_1: $i] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [T_1: $i] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
! [T_1: $i] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
tff(47,plain,
! [T_1: $i] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [T_1: $i] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [T_1: $i] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[52,17,49]) ).
tff(54,plain,
^ [T_1: $i] :
refl(( ( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) )
<=> ( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [T_1: $i] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) )
<=> ! [T_1: $i] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [T_1: $i] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) )
<=> ! [T_1: $i] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
! [T_1: $i] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
tff(58,plain,
! [T_1: $i] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [T_1: $i] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [T_1: $i] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
tff(63,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) )
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) )
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) )
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) )
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[66,63,60]) ).
tff(68,plain,
^ [T_1: $i] :
refl(( ( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) )
<=> ( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [T_1: $i] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) )
<=> ! [T_1: $i] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [T_1: $i] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) )
<=> ! [T_1: $i] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
! [T_1: $i] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
tff(72,plain,
! [T_1: $i] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [T_1: $i] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [T_1: $i] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
tff(77,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ( ~ ! [T_1: $i] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) )
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) )
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [T_1: $i] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) )
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [T_1: $i] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) )
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[80,77,74]) ).
tff(82,plain,
( class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
tff(84,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
^ [T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
tff(89,plain,
! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( ( ~ ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[94,91,84]) ).
tff(96,plain,
( class_HOL_Ozero(tc_Complex_Ocomplex)
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
tff(98,plain,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
^ [V_a: $i,T_a: $i,V_p: $i] :
refl(( ( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
^ [V_a: $i,T_a: $i,V_p: $i] :
rewrite(( ( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(103,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,axiom,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
tff(105,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[107,100]) ).
tff(109,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[111,108,98,95]) ).
tff(113,plain,
^ [V_a: $i,T_a: $i,V_p: $i] :
refl(( ( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
^ [V_a: $i,T_a: $i,V_p: $i] :
rewrite(( ( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(V_a,V_p,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_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,axiom,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(V_a,V_p,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/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
tff(119,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[121,114]) ).
tff(123,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_HOL_Ozero(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[125,122,98,112]) ).
tff(127,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
refl(( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(128,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) )
<=> ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) ) )),
rewrite(( ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) )
<=> ( ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) )
<=> ( ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) )
<=> ( ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a) ) )),
rewrite(( ( ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a) )
<=> ( ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) )
<=> ( ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(( ( ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(( ( ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,axiom,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
tff(133,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[135,128]) ).
tff(137,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
( ( c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(unit_resolution,[status(thm)],[139,136]) ).
tff(141,plain,
c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[140,126,81,67,53,42]) ).
tff(142,plain,
( ( v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,axiom,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sne_0) ).
tff(144,plain,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
^ [V_q: $i,T_a: $i,V_p: $i] :
refl(( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ) )),
inference(bind,[status(th)],[]) ).
tff(146,plain,
( ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(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_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,plain,
( ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(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_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
^ [V_q: $i,T_a: $i,V_p: $i] :
trans(monotonicity(rewrite(( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
| ( V_q = 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_Oidom(T_a)
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
rewrite(( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
| ( V_q = 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_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ) )),
inference(bind,[status(th)],[]) ).
tff(149,plain,
( ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[148]) ).
tff(150,axiom,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
| ( V_q = 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/sandbox/benchmark/theBenchmark.p',cls_degree__mult__eq_0) ).
tff(151,plain,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[151,147]) ).
tff(153,plain,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ),
inference(skolemize,[status(sab)],[152]) ).
tff(154,plain,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[153,146]) ).
tff(155,plain,
( ( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )
| ( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) ) )
<=> ( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )
| ( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,plain,
( ( ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) ) )
<=> ( ( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,plain,
( ( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) ) )
<=> ( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )
| ( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) ) ) ),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
( ( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) ) )
<=> ( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )
| ( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) ) ) ),
inference(transitivity,[status(thm)],[157,155]) ).
tff(159,plain,
( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )
| ( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
( ( c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) ) ),
inference(unit_resolution,[status(thm)],[160,154,144,63]) ).
tff(162,plain,
c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat),
inference(unit_resolution,[status(thm)],[161,141]) ).
tff(163,plain,
^ [T_1: $i] :
refl(( ( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
<=> ( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(164,plain,
( ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[163]) ).
tff(165,plain,
( ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,axiom,
! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
tff(167,plain,
! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
inference(skolemize,[status(sab)],[167]) ).
tff(169,plain,
! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[168,164]) ).
tff(170,plain,
( ( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,plain,
( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[172,17,169]) ).
tff(174,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(175,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[174]) ).
tff(176,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
tff(178,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ),
inference(skolemize,[status(sab)],[178]) ).
tff(180,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[179,175]) ).
tff(181,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_s____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_s____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(182,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_s____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(183,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_s____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_s____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(unit_resolution,[status(thm)],[183,180]) ).
tff(185,plain,
c_Ring__and__Field_Odvd__class_Odvd(v_s____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[184,173]) ).
tff(186,plain,
( ( v_pa____ = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( v_pa____ = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,axiom,
v_pa____ = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_s_0) ).
tff(188,plain,
v_pa____ = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_pa____,
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
( ( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
( ( v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
( ( v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(194,axiom,
v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pne_0) ).
tff(195,plain,
v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[194,193]) ).
tff(196,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[195,192]) ).
tff(197,plain,
^ [V_q: $i,T_a: $i,V_p: $i] :
refl(( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(198,plain,
( ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(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_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ),
inference(quant_intro,[status(thm)],[197]) ).
tff(199,plain,
( ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(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_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(200,plain,
^ [V_q: $i,T_a: $i,V_p: $i] :
trans(monotonicity(rewrite(( ( ~ class_Ring__and__Field_Oidom(T_a)
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) ) )),
rewrite(( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(201,plain,
( ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) )
<=> ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ),
inference(quant_intro,[status(thm)],[200]) ).
tff(202,axiom,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__degree__le_0) ).
tff(203,plain,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[203,199]) ).
tff(205,plain,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ),
inference(skolemize,[status(sab)],[204]) ).
tff(206,plain,
! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[205,198]) ).
tff(207,plain,
( ( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_s____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) )
<=> ( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_s____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(208,plain,
( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_s____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
( ~ ! [V_q: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_s____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) ),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat),
inference(unit_resolution,[status(thm)],[209,206,63,196,185]) ).
tff(211,plain,
( class_Orderings_Oorder(tc_nat)
<=> class_Orderings_Oorder(tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(212,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
tff(213,plain,
class_Orderings_Oorder(tc_nat),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
( ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat)
<=> ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(215,axiom,
~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(216,plain,
~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat),
inference(modus_ponens,[status(thm)],[215,214]) ).
tff(217,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(( ( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
<=> ( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(218,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[217]) ).
tff(219,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(220,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
trans(monotonicity(rewrite(( ( ~ class_Orderings_Oorder(T_a)
| ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
<=> ( ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) )),
( ( ~ class_Orderings_Oorder(T_a)
| ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
rewrite(( ( ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) )),
( ( ~ class_Orderings_Oorder(T_a)
| ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(221,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[220]) ).
tff(222,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
tff(223,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[222,221]) ).
tff(224,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[223,219]) ).
tff(225,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ),
inference(skolemize,[status(sab)],[224]) ).
tff(226,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[225,218]) ).
tff(227,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
| ~ c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
| ~ c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(228,plain,
( ( ~ c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat)
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
| ~ class_Orderings_Oorder(tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) )
<=> ( c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
| ~ c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(229,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
| ~ c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat)
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
| ~ class_Orderings_Oorder(tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
| ~ c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) ) ),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
| ~ c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat)
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
| ~ class_Orderings_Oorder(tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
| ~ c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) ) ),
inference(transitivity,[status(thm)],[229,227]) ).
tff(231,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
| ~ c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat)
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
| ~ class_Orderings_Oorder(tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) ),
inference(quant_inst,[status(thm)],[]) ).
tff(232,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_x,V_y,T_a)
| ( V_x = V_y )
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
| ~ c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) ),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
( ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
| ~ c_lessequals(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat) ),
inference(unit_resolution,[status(thm)],[232,226,216,213]) ).
tff(234,plain,
c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[233,210]) ).
tff(235,plain,
c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat),
inference(transitivity,[status(thm)],[234,162,31,14]) ).
tff(236,plain,
( ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) )
<=> ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(237,axiom,
c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_oa_0) ).
tff(238,plain,
c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
^ [V_x: $i,V_a: $i] :
refl(( ( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ) )),
inference(bind,[status(th)],[]) ).
tff(240,plain,
( ! [V_x: $i,V_a: $i] :
( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ! [V_x: $i,V_a: $i] :
( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[239]) ).
tff(241,plain,
( ! [V_x: $i,V_a: $i] :
( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ! [V_x: $i,V_a: $i] :
( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(242,axiom,
! [V_x: $i,V_a: $i] :
( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
tff(243,plain,
! [V_x: $i,V_a: $i] :
( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[242,241]) ).
tff(244,plain,
! [V_x: $i,V_a: $i] :
( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(skolemize,[status(sab)],[243]) ).
tff(245,plain,
! [V_x: $i,V_a: $i] :
( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[244,240]) ).
tff(246,plain,
( ( ~ ! [V_x: $i,V_a: $i] :
( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( ~ ! [V_x: $i,V_a: $i] :
( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(247,plain,
( ~ ! [V_x: $i,V_a: $i] :
( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(248,plain,
( ~ ! [V_x: $i,V_a: $i] :
( ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) )
| ( V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[247,246]) ).
tff(249,plain,
c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat),
inference(unit_resolution,[status(thm)],[248,245,238]) ).
tff(250,plain,
$false,
inference(unit_resolution,[status(thm)],[249,235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG419-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 11:14:49 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.48/0.63 % SZS status Unsatisfiable
% 0.48/0.63 % SZS output start Proof
% See solution above
% 0.48/0.70 % E exiting
%------------------------------------------------------------------------------