TSTP Solution File: SWW276+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW276+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 : Thu Sep 29 20:58:10 EDT 2022
% Result : Theorem 0.87s 0.91s
% Output : Proof 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 103
% Syntax : Number of formulae : 209 ( 64 unt; 25 typ; 0 def)
% Number of atoms : 824 ( 468 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 947 ( 349 ~; 419 |; 0 &)
% ( 121 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 18 >; 13 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 389 ( 348 !; 0 ?; 389 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(v_pa_____type,type,
v_pa____: $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $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(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(class_Rings_Oring__1__no__zero__divisors_type,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
tff(v_r_____type,type,
v_r____: $i ).
tff(class_Rings_Oring__no__zero__divisors_type,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(v_qa_____type,type,
v_qa____: $i ).
tff(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
tff(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(1,plain,
^ [T_1: $i] :
refl(
( ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
<=> ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [T_1: $i] :
rewrite(
( ( class_Rings_Oidom(T_1)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) )
<=> ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [T_1: $i] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) )
<=> ! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [T_1: $i] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
tff(7,plain,
! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( class_Rings_Oidom(tc_Complex_Ocomplex)
<=> class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
tff(13,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [T_1: $i] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [T_1: $i] :
refl(
( ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
<=> ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [T_1: $i] :
rewrite(
( ( class_Rings_Oidom(T_1)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) )
<=> ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [T_1: $i] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) )
<=> ! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [T_1: $i] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
tff(24,plain,
! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [T_1: $i] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[30,13,27]) ).
tff(32,plain,
^ [V_b_2: $i,V_aa_2: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
<=> ( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
<=> ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
<=> ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
^ [V_b_2: $i,V_aa_2: $i,T_a: $i] :
rewrite(
( ( class_Rings_Oring__no__zero__divisors(T_a)
=> ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
<=> ( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( class_Rings_Oring__no__zero__divisors(T_a)
=> ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
<=> ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( class_Rings_Oring__no__zero__divisors(T_a)
=> ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
tff(38,plain,
! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
| ~ class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) )
<=> ( ~ ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
| ~ class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ~ class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) )
<=> ( ~ class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ~ ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
| ~ class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) )
<=> ( ~ ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
| ~ class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
| ~ class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) )
<=> ( ~ ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
| ~ class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
| ~ class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
( ~ class_Rings_Oring__no__zero__divisors(T_a)
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )
| ~ class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ~ class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) ),
inference(unit_resolution,[status(thm)],[47,41]) ).
tff(49,plain,
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(unit_resolution,[status(thm)],[48,31]) ).
tff(50,plain,
( ( v_qa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( v_qa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( v_qa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
v_qa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q0) ).
tff(53,plain,
v_qa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[53,50]) ).
tff(55,plain,
( ~ ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(56,plain,
( ~ ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) )
| ~ ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
~ ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(unit_resolution,[status(thm)],[56,49]) ).
tff(58,plain,
( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(tautology,[status(thm)],]) ).
tff(59,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
refl(
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) )
<=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( ( V_a != c_Groups_Ozero__class_Ozero(T_a) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) )),
( ( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( ( V_a != c_Groups_Ozero__class_Ozero(T_a) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
rewrite(
( ( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ) )),
( ( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( ( V_a != c_Groups_Ozero__class_Ozero(T_a) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( ( V_a != c_Groups_Ozero__class_Ozero(T_a) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,axiom,
! [V_n: $i,V_a: $i,T_a: $i] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( ( V_a != c_Groups_Ozero__class_Ozero(T_a) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
tff(66,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(unit_resolution,[status(thm)],[75,69]) ).
tff(77,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[76,59,17]) ).
tff(78,plain,
^ [V_q: $i,V_p: $i,T_a: $i] :
refl(
( ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) )
<=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) )
<=> ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) )
<=> ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [V_q: $i,V_p: $i,T_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) )
<=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )),
( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )
<=> ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) )),
rewrite(
( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )
<=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )),
( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )
<=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )),
( ( class_Rings_Oidom(T_a)
=> ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) )
<=> ( class_Rings_Oidom(T_a)
=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) )),
rewrite(
( ( class_Rings_Oidom(T_a)
=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )
<=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) ) )),
( ( class_Rings_Oidom(T_a)
=> ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) )
<=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [V_q: $i,V_p: $i,T_a: $i] :
( class_Rings_Oidom(T_a)
=> ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) )
<=> ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [V_q: $i,V_p: $i,T_a: $i] :
( class_Rings_Oidom(T_a)
=> ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__mult__eq) ).
tff(84,plain,
! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( ( v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,axiom,
v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sne) ).
tff(90,plain,
v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
( ( ~ ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) )
| ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Rings_Oidom(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) ) )
<=> ( ~ ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) )
| ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Rings_Oidom(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ( ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) )
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) )
<=> ( ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Rings_Oidom(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ( ~ ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) )
| ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) )
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) )
<=> ( ~ ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) )
| ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Rings_Oidom(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) ) ) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ( ~ ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) )
| ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) )
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) )
<=> ( ~ ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) )
| ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Rings_Oidom(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) ) ) ),
inference(transitivity,[status(thm)],[93,91]) ).
tff(95,plain,
( ~ ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) )
| ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) )
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
( ~ ! [V_q: $i,V_p: $i,T_a: $i] :
( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
| ~ class_Rings_Oidom(T_a) )
| ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Rings_Oidom(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) ) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) ) ),
inference(unit_resolution,[status(thm)],[96,90,87,13]) ).
tff(98,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)),
inference(unit_resolution,[status(thm)],[97,77]) ).
tff(99,plain,
( ( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____) )
<=> ( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,axiom,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s) ).
tff(101,plain,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)),
inference(transitivity,[status(thm)],[102,98]) ).
tff(104,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
^ [V_n: $i] :
refl(
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n )
<=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [V_n: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n )
<=> ! [V_n: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [V_n: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n )
<=> ! [V_n: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
! [V_n: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
tff(110,plain,
! [V_n: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [V_n: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [V_n: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
( ~ ! [V_n: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) ),
inference(rewrite,[status(thm)],]) ).
tff(117,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(118,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
^ [V_n: $i] :
refl(
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) )
<=> ! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) )
<=> ! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
^ [V_n: $i] :
rewrite(
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [V_n: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) )
<=> ! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,axiom,
! [V_n: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
tff(125,plain,
! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(modus_ponens,[status(thm)],[127,120]) ).
tff(129,plain,
( ( ~ ! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) )
<=> ( ~ ! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ~ ! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
( ~ ! [V_n: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(unit_resolution,[status(thm)],[131,128,118]) ).
tff(133,plain,
c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(135,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
tff(136,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ) )),
inference(bind,[status(th)],]) ).
tff(138,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ) ),
inference(quant_intro,[status(thm)],[137]) ).
tff(139,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ) )),
inference(bind,[status(th)],]) ).
tff(141,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,axiom,
! [V_n: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__linear__power) ).
tff(143,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ),
inference(modus_ponens,[status(thm)],[143,139]) ).
tff(145,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ),
inference(skolemize,[status(sab)],[144]) ).
tff(146,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ),
inference(modus_ponens,[status(thm)],[145,138]) ).
tff(147,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) ) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),
inference(unit_resolution,[status(thm)],[149,146,136]) ).
tff(151,plain,
c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) = c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)),
inference(monotonicity,[status(thm)],[151,133]) ).
tff(153,plain,
^ [V_n: $i,V_m: $i] :
refl(
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) )
<=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ) )),
inference(bind,[status(th)],]) ).
tff(154,plain,
( ! [V_n: $i,V_m: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) )
<=> ! [V_n: $i,V_m: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ) ),
inference(quant_intro,[status(thm)],[153]) ).
tff(155,plain,
( ! [V_n: $i,V_m: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) )
<=> ! [V_n: $i,V_m: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,axiom,
! [V_n: $i,V_m: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
tff(157,plain,
! [V_n: $i,V_m: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
! [V_n: $i,V_m: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ),
inference(skolemize,[status(sab)],[157]) ).
tff(159,plain,
! [V_n: $i,V_m: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ),
inference(modus_ponens,[status(thm)],[158,154]) ).
tff(160,plain,
( ~ ! [V_n: $i,V_m: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(unit_resolution,[status(thm)],[160,159]) ).
tff(162,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)),
inference(monotonicity,[status(thm)],[132]) ).
tff(163,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)),
inference(transitivity,[status(thm)],[162,161,152,115,105]) ).
tff(164,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____))
<=> ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)) ),
inference(rewrite,[status(thm)],]) ).
tff(165,axiom,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(166,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) ),
inference(rewrite,[status(thm)],]) ).
tff(168,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(169,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
^ [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
refl(
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) )
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) ) )),
inference(bind,[status(th)],]) ).
tff(171,plain,
( ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) )
<=> ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) ) ),
inference(quant_intro,[status(thm)],[170]) ).
tff(172,plain,
( ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) )
<=> ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
^ [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
trans(
monotonicity(
rewrite(
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) )
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) )
<=> ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) )),
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) )
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) )
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) )),
rewrite(
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) )
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) ) )),
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) )
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) )
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) ) )),
inference(bind,[status(th)],]) ).
tff(174,plain,
( ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) )
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) )
<=> ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) ) ),
inference(quant_intro,[status(thm)],[173]) ).
tff(175,axiom,
! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) )
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
tff(176,plain,
! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) ),
inference(modus_ponens,[status(thm)],[176,172]) ).
tff(178,plain,
! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) ),
inference(skolemize,[status(sab)],[177]) ).
tff(179,plain,
! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) ),
inference(modus_ponens,[status(thm)],[178,171]) ).
tff(180,plain,
( ( ~ ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)) ) )
<=> ( ~ ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(181,plain,
( ~ ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
( ~ ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)) ) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)),
inference(unit_resolution,[status(thm)],[182,179,169,166]) ).
tff(184,plain,
$false,
inference(unit_resolution,[status(thm)],[183,163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW276+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 19:33:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.87/0.91 % SZS status Theorem
% 0.87/0.91 % SZS output start Proof
% See solution above
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