TSTP Solution File: ALG419-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG419-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 16:10:11 EDT 2022
% Result : Unsatisfiable 0.55s 0.67s
% Output : Proof 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 117
% Syntax : Number of formulae : 231 ( 66 unt; 25 typ; 0 def)
% Number of atoms : 1019 ( 402 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1401 ( 642 ~; 663 |; 0 &)
% ( 96 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 54 ( 54 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 20 >; 14 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 453 ( 409 !; 0 ?; 453 :)
% 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_Odegree_type,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(v_pa_____type,type,
v_pa____: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Polynomial_Oorder_type,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(v_s_____type,type,
v_s____: $i ).
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_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(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_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $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(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
tff(5,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)],[4,3]) ).
tff(6,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)],[5]) ).
tff(7,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)],[6,2]) ).
tff(8,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(9,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
tff(10,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,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(12,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(13,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)],[12,11]) ).
tff(14,plain,
class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,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/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
tff(19,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)],[18,17]) ).
tff(20,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)],[19]) ).
tff(21,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)],[20,16]) ).
tff(22,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(23,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(24,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)],[23,22]) ).
tff(25,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[24,10,21]) ).
tff(26,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(27,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)],[26]) ).
tff(28,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(29,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/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
tff(30,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)],[29,28]) ).
tff(31,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)],[30]) ).
tff(32,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)],[31,27]) ).
tff(33,plain,
( class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
tff(35,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,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(37,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(38,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)],[37,36]) ).
tff(39,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[38,35,32]) ).
tff(40,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(41,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)],[40]) ).
tff(42,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(43,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/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
tff(44,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)],[43,42]) ).
tff(45,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)],[44]) ).
tff(46,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)],[45,41]) ).
tff(47,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(48,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
tff(49,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,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(51,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(52,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)],[51,50]) ).
tff(53,plain,
class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[52,49,46]) ).
tff(54,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(55,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
tff(56,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
tff(61,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)],[60,59]) ).
tff(62,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)],[61]) ).
tff(63,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)],[62,58]) ).
tff(64,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(65,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(66,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)],[65,64]) ).
tff(67,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[66,63,56]) ).
tff(68,plain,
( class_HOL_Ozero(tc_Complex_Ocomplex)
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(69,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
tff(70,plain,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,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(72,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)],[71]) ).
tff(73,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(74,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(75,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)],[74]) ).
tff(76,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/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
tff(77,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)],[76,75]) ).
tff(78,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)],[77,73]) ).
tff(79,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)],[78]) ).
tff(80,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)],[79,72]) ).
tff(81,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(82,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(83,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)],[82,81]) ).
tff(84,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)],[83,80,70,67]) ).
tff(85,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(86,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)],[85]) ).
tff(87,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(88,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(89,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)],[88]) ).
tff(90,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/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
tff(91,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)],[90,89]) ).
tff(92,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)],[91,87]) ).
tff(93,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)],[92]) ).
tff(94,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)],[93,86]) ).
tff(95,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(96,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(97,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)],[96,95]) ).
tff(98,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)],[97,94,70,84]) ).
tff(99,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(100,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)],[99]) ).
tff(101,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(102,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(103,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)],[102]) ).
tff(104,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/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
tff(105,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)],[104,103]) ).
tff(106,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)],[105,101]) ).
tff(107,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)],[106]) ).
tff(108,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)],[107,100]) ).
tff(109,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(110,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(111,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)],[110,109]) ).
tff(112,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)],[111,108]) ).
tff(113,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)],[112,98,53,39,25,14]) ).
tff(114,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(115,axiom,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sne_0) ).
tff(116,plain,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,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(118,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)],[117]) ).
tff(119,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(120,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(121,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)],[120]) ).
tff(122,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/sandbox2/benchmark/theBenchmark.p',cls_degree__mult__eq_0) ).
tff(123,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)],[122,121]) ).
tff(124,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)],[123,119]) ).
tff(125,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)],[124]) ).
tff(126,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)],[125,118]) ).
tff(127,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(128,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(129,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)],[128]) ).
tff(130,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)],[129,127]) ).
tff(131,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(132,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)],[131,130]) ).
tff(133,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)],[132,126,116,35]) ).
tff(134,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)],[133,113]) ).
tff(135,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(136,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/sandbox2/benchmark/theBenchmark.p',cls_s_0) ).
tff(137,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)],[136,135]) ).
tff(138,plain,
c_Polynomial_Odegree(v_pa____,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(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
c_Polynomial_Odegree(v_pa____,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)],[138,134]) ).
tff(140,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(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),tc_nat),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(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),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
^ [V_n: $i] :
refl(
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n )
<=> ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ) )),
inference(bind,[status(th)],]) ).
tff(143,plain,
( ! [V_n: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n )
<=> ! [V_n: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,plain,
( ! [V_n: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n )
<=> ! [V_n: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ) ),
inference(rewrite,[status(thm)],]) ).
tff(145,axiom,
! [V_n: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
tff(146,plain,
! [V_n: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
! [V_n: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ),
inference(skolemize,[status(sab)],[146]) ).
tff(148,plain,
! [V_n: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ),
inference(modus_ponens,[status(thm)],[147,143]) ).
tff(149,plain,
( ~ ! [V_n: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n )
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(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),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(quant_inst,[status(thm)],]) ).
tff(150,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(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),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(unit_resolution,[status(thm)],[149,148]) ).
tff(151,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_HOL_Ozero__class_Ozero(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),tc_nat),
inference(symmetry,[status(thm)],[150]) ).
tff(152,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(153,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)],[152]) ).
tff(154,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(155,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/sandbox2/benchmark/theBenchmark.p',cls_degree__linear__power_0) ).
tff(156,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)],[155,154]) ).
tff(157,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)],[156]) ).
tff(158,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)],[157,153]) ).
tff(159,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(160,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(161,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)],[160,159]) ).
tff(162,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)],[161,158,10]) ).
tff(163,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)],[162]) ).
tff(164,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)],[163]) ).
tff(165,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(166,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
tff(167,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,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(169,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)],[168]) ).
tff(170,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(171,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
tff(172,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)],[171,170]) ).
tff(173,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)],[172]) ).
tff(174,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)],[173,169]) ).
tff(175,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(176,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(177,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)],[176,175]) ).
tff(178,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)],[177,174,167]) ).
tff(179,plain,
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_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)],[178]) ).
tff(180,plain,
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_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat),
inference(transitivity,[status(thm)],[179,164,151,141]) ).
tff(181,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(v_pa____,tc_Complex_Ocomplex),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(182,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(183,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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(184,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)],[183,182]) ).
tff(185,plain,
~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat),
inference(modus_ponens,[status(thm)],[184,181]) ).
tff(186,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat)
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(187,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(188,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
^ [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
refl(
( ( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) )
<=> ( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) ) )),
inference(bind,[status(th)],]) ).
tff(190,plain,
( ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) )
<=> ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[189]) ).
tff(191,plain,
( ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) )
<=> ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(192,plain,
^ [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
trans(
monotonicity(
rewrite(
( ( ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) )
| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) )
<=> ( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) ) )),
( ( ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) )
| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) )
<=> ( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) )
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) )),
rewrite(
( ( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) )
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) )
<=> ( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) ) )),
( ( ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) )
| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) )
<=> ( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) ) )),
inference(bind,[status(th)],]) ).
tff(193,plain,
( ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) )
| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) )
<=> ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[192]) ).
tff(194,axiom,
! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) )
| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
tff(195,plain,
! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) ),
inference(modus_ponens,[status(thm)],[194,193]) ).
tff(196,plain,
! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) ),
inference(modus_ponens,[status(thm)],[195,191]) ).
tff(197,plain,
! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) ),
inference(skolemize,[status(sab)],[196]) ).
tff(198,plain,
! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) ),
inference(modus_ponens,[status(thm)],[197,190]) ).
tff(199,plain,
( ( ~ ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,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) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat) ) )
<=> ( ~ ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,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) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(200,plain,
( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_pa____,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) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat) ) )
<=> ( c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,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) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(201,plain,
( ( ~ ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_pa____,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) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat) ) )
<=> ( ~ ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,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) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat) ) ) ),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
( ( ~ ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_pa____,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) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat) ) )
<=> ( ~ ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,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) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat) ) ) ),
inference(transitivity,[status(thm)],[201,199]) ).
tff(203,plain,
( ~ ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_pa____,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) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(204,plain,
( ~ ! [V_n: $i,V_l: $i,V_m: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ) )
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Oorder(v_a____,v_pa____,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) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
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_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat),
inference(unit_resolution,[status(thm)],[204,198,188,185]) ).
tff(206,plain,
$false,
inference(unit_resolution,[status(thm)],[205,180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG419-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 17:03:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.55/0.67 % SZS status Unsatisfiable
% 0.55/0.67 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------