TSTP Solution File: SWW285+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW285+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 20:58:12 EDT 2022
% Result : Theorem 0.72s 0.76s
% Output : Proof 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 76
% Syntax : Number of formulae : 147 ( 35 unt; 19 typ; 0 def)
% Number of atoms : 747 ( 218 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 980 ( 402 ~; 337 |; 100 &)
% ( 117 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 41 ( 41 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 14 >; 2 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 194 ( 171 !; 0 ?; 194 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(v_q_type,type,
v_q: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(v_r_____type,type,
v_r____: $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(v_p_type,type,
v_p: $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(class_Rings_Ozero__neq__one_type,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(class_Rings_Omult__zero_type,type,
class_Rings_Omult__zero: $i > $o ).
tff(class_Rings_Ono__zero__divisors_type,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
tff(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
tff(1,plain,
( class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
<=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
tff(3,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_q: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [V_q: $i,T_a: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_q: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_q: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
tff(10,plain,
! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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(16,plain,
( ~ ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(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(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____) )
<=> ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_r____) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____) )
<=> ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r) ).
tff(21,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_r____),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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)],[22,17]) ).
tff(24,plain,
^ [T_1: $i] :
refl(
( ( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [T_1: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__1(T_1)
=> class_Power_Opower(tc_Polynomial_Opoly(T_1)) )
<=> ( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Power_Opower(tc_Polynomial_Opoly(T_1)) )
<=> ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Power_Opower(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
tff(30,plain,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
tff(36,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ( ~ ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[39,36,33]) ).
tff(41,plain,
^ [T_1: $i] :
refl(
( ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
^ [T_1: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) )
<=> ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) )
<=> ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
tff(47,plain,
! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ~ ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
( ~ ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[53,36,50]) ).
tff(55,plain,
^ [T_1: $i] :
refl(
( ( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) )
<=> ( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
^ [T_1: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) )
<=> ( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [T_1: $i] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) )
<=> ! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,axiom,
! [T_1: $i] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
tff(61,plain,
! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
( ( ~ ! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) )
| class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) )
| class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ~ ! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) )
| class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [T_1: $i] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) )
| class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[67,3,64]) ).
tff(69,plain,
^ [T_1: $i] :
refl(
( ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
<=> ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
^ [T_1: $i] :
rewrite(
( ( class_Rings_Oidom(T_1)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) )
<=> ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [T_1: $i] :
( class_Rings_Oidom(T_1)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) )
<=> ! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [T_1: $i] :
( class_Rings_Oidom(T_1)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
tff(75,plain,
! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( class_Rings_Oidom(tc_Complex_Ocomplex)
<=> class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
tff(81,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
( ( ~ ! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ~ ! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
( ~ ! [T_1: $i] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) )
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[84,81,78]) ).
tff(86,plain,
^ [V_n_2: $i,V_a_2: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
^ [V_n_2: $i,V_a_2: $i,T_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
<=> ~ ( ~ class_Power_Opower(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Ozero__neq__one(T_a) ) )),
( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
<=> ~ ~ ( ~ class_Power_Opower(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Ozero__neq__one(T_a) ) )),
rewrite(
( ~ ~ ( ~ class_Power_Opower(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Ozero__neq__one(T_a) )
<=> ( ~ class_Power_Opower(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Ozero__neq__one(T_a) ) )),
( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
<=> ( ~ class_Power_Opower(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Ozero__neq__one(T_a) ) )),
rewrite(
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
<=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )),
( ( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ( ~ class_Power_Opower(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) )),
rewrite(
( ( ~ class_Power_Opower(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) )),
( ( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
^ [V_n_2: $i,V_a_2: $i,T_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a) )
<=> ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a) ) )),
( ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
<=> ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) ) )),
rewrite(
( ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
<=> ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) ) )),
( ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
<=> ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) ) )),
( ( ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ( ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) )),
rewrite(
( ( ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) )),
( ( ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,axiom,
! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
=> ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
tff(94,plain,
! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ ( class_Power_Opower(T_a)
& class_Rings_Omult__zero(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Ozero__neq__one(T_a) )
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ),
inference(modus_ponens,[status(thm)],[96,89]) ).
tff(98,plain,
! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ),
inference(modus_ponens,[status(thm)],[97,87]) ).
tff(99,plain,
( ( ~ ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ( ~ ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ( ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ( ~ ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ( ~ ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ~ ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
<=> ( ~ ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( ~ ! [V_n_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Power_Opower(T_a)
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ~ ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
( ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ),
inference(unit_resolution,[status(thm)],[104,98]) ).
tff(106,plain,
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(unit_resolution,[status(thm)],[105,85,68,54,40]) ).
tff(107,plain,
( class_Groups_Ozero(tc_Complex_Ocomplex)
<=> class_Groups_Ozero(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(108,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
tff(109,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
^ [T_a: $i] :
refl(
( ( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )),
inference(bind,[status(th)],]) ).
tff(111,plain,
( ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
( ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
^ [T_a: $i] :
rewrite(
( ( class_Groups_Ozero(T_a)
=> ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [T_a: $i] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,axiom,
! [T_a: $i] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__0) ).
tff(116,plain,
! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(modus_ponens,[status(thm)],[118,111]) ).
tff(120,plain,
( ( ~ ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ( ~ ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ~ ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(unit_resolution,[status(thm)],[122,119,109]) ).
tff(124,plain,
( ( v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(tautology,[status(thm)],]) ).
tff(125,plain,
( ( v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(unit_resolution,[status(thm)],[124,123]) ).
tff(126,plain,
( ~ ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(127,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(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)],[126,125,106]) ).
tff(128,plain,
$false,
inference(unit_resolution,[status(thm)],[127,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW285+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 13:53:42 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.72/0.76 % SZS status Theorem
% 0.72/0.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------