TSTP Solution File: SWW270+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW270+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 20:58:09 EDT 2022
% Result : Theorem 116.86s 74.67s
% Output : Proof 116.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 150
% Syntax : Number of formulae : 311 ( 89 unt; 27 typ; 0 def)
% Number of atoms : 1378 ( 466 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1676 ( 651 ~; 662 |; 0 &)
% ( 256 <=>; 107 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 69 ( 69 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 21 >; 11 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 635 ( 568 !; 0 ?; 635 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(v_x_____type,type,
v_x____: $i ).
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(c_RealVector_Oof__real_type,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(class_RealVector_Oreal__algebra__1_type,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(c_Rings_Oinverse__class_Odivide_type,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(class_Rings_Odivision__ring_type,type,
class_Rings_Odivision__ring: $i > $o ).
tff(c_Groups_Osgn__class_Osgn_type,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(class_RealVector_Oreal__normed__algebra__1_type,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(class_Groups_Omonoid__mult_type,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(class_RealVector_Oreal__normed__div__algebra_type,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(v_m_____type,type,
v_m____: $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(v_ds_____type,type,
v_ds____: $i ).
tff(v_d_____type,type,
v_d____: $i ).
tff(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
tff(class_Rings_Oordered__semiring_type,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(1,plain,
( class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
tff(3,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_y_2: $i,V_xa_2: $i,T_b: $i] :
refl(
( ( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) )
<=> ( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) )
<=> ! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) )
<=> ! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [V_y_2: $i,V_xa_2: $i,T_b: $i] :
rewrite(
( ( class_RealVector_Oreal__algebra__1(T_b)
=> ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) )
<=> ( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( class_RealVector_Oreal__algebra__1(T_b)
=> ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) )
<=> ! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( class_RealVector_Oreal__algebra__1(T_b)
=> ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__eq__iff) ).
tff(10,plain,
! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) )
<=> ( v_x____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) ) ) )
<=> ( ~ ! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) )
<=> ( v_x____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) )
<=> ( v_x____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_y_2: $i,V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_RealVector_Oof__real(T_b,V_y_2) )
<=> ( V_xa_2 = V_y_2 ) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) )
<=> ( v_x____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) )
<=> ( v_x____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) ) ),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [V_xa_2: $i,T_b: $i] :
refl(
( ( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [V_xa_2: $i,T_b: $i] :
rewrite(
( ( class_RealVector_Oreal__algebra__1(T_b)
=> ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [V_xa_2: $i,T_b: $i] :
( class_RealVector_Oreal__algebra__1(T_b)
=> ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [V_xa_2: $i,T_b: $i] :
( class_RealVector_Oreal__algebra__1(T_b)
=> ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__eq__0__iff) ).
tff(24,plain,
! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ( ~ ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_b)
| ( ( c_RealVector_Oof__real(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(T_b) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(unit_resolution,[status(thm)],[30,27,3]) ).
tff(32,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
tff(34,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
^ [V_xa_2: $i,T_b: $i] :
refl(
( ( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) )
<=> ( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) )
<=> ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) )
<=> ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
^ [V_xa_2: $i,T_b: $i] :
rewrite(
( ( class_RealVector_Oreal__normed__vector(T_b)
=> ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) )
<=> ( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [V_xa_2: $i,T_b: $i] :
( class_RealVector_Oreal__normed__vector(T_b)
=> ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) )
<=> ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [V_xa_2: $i,T_b: $i] :
( class_RealVector_Oreal__normed__vector(T_b)
=> ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
tff(41,plain,
! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) )
<=> ( ~ ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ~ ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [V_xa_2: $i,T_b: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ( ( c_RealVector_Onorm__class_Onorm(T_b,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(unit_resolution,[status(thm)],[47,44,34]) ).
tff(49,plain,
( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cx_I1_J) ).
tff(51,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ ( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(tautology,[status(thm)],]) ).
tff(53,plain,
( ~ ( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[53,48]) ).
tff(55,plain,
( ~ ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(tautology,[status(thm)],]) ).
tff(56,plain,
( ~ ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[56,31]) ).
tff(58,plain,
( class_Rings_Odivision__ring(tc_Complex_Ocomplex)
<=> class_Rings_Odivision__ring(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
tff(60,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
^ [V_a_2: $i,V_b_2: $i,T_b: $i] :
refl(
( ( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) )
<=> ( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) )
<=> ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) )
<=> ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
^ [V_a_2: $i,V_b_2: $i,T_b: $i] :
trans(
monotonicity(
rewrite(
( ( ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b) )
=> ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) ) )
<=> ( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) ) ) )),
( ( class_Rings_Odivision__ring(T_b)
=> ( ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b) )
=> ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) ) ) )
<=> ( class_Rings_Odivision__ring(T_b)
=> ( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) ) ) ) )),
rewrite(
( ( class_Rings_Odivision__ring(T_b)
=> ( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) ) ) )
<=> ( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) ) )),
( ( class_Rings_Odivision__ring(T_b)
=> ( ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b) )
=> ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) ) ) )
<=> ( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( class_Rings_Odivision__ring(T_b)
=> ( ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b) )
=> ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) ) ) )
<=> ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,axiom,
! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( class_Rings_Odivision__ring(T_b)
=> ( ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b) )
=> ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
tff(67,plain,
! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
( ( ~ ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Rings_Odivision__ring(tc_Complex_Ocomplex)
| ( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) ) )
<=> ( ~ ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Rings_Odivision__ring(tc_Complex_Ocomplex)
| ( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) )
| ~ class_Rings_Odivision__ring(tc_Complex_Ocomplex) )
<=> ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Rings_Odivision__ring(tc_Complex_Ocomplex)
| ( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ( ~ ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) )
| ~ class_Rings_Odivision__ring(tc_Complex_Ocomplex) )
<=> ( ~ ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Rings_Odivision__ring(tc_Complex_Ocomplex)
| ( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) ) ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ( ~ ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) )
| ~ class_Rings_Odivision__ring(tc_Complex_Ocomplex) )
<=> ( ~ ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Rings_Odivision__ring(tc_Complex_Ocomplex)
| ( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) ) ) ),
inference(transitivity,[status(thm)],[73,71]) ).
tff(75,plain,
( ~ ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) )
| ~ class_Rings_Odivision__ring(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( ( c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_b) )
<=> ( V_a_2 = V_b_2 ) )
| ~ class_Rings_Odivision__ring(T_b) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Rings_Odivision__ring(tc_Complex_Ocomplex)
| ( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) ) ),
inference(unit_resolution,[status(thm)],[76,70,60]) ).
tff(78,plain,
( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) ),
inference(unit_resolution,[status(thm)],[77,57]) ).
tff(79,plain,
^ [T_a: $i] :
refl(
( ( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(80,plain,
( ! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
^ [T_a: $i] :
rewrite(
( ( class_RealVector_Oreal__algebra__1(T_a)
=> ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [T_a: $i] :
( class_RealVector_Oreal__algebra__1(T_a)
=> ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,axiom,
! [T_a: $i] :
( class_RealVector_Oreal__algebra__1(T_a)
=> ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__1) ).
tff(85,plain,
! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[87,80]) ).
tff(89,plain,
( ( ~ ! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ~ ! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[91,88,3]) ).
tff(93,plain,
( class_Rings_Olinordered__idom(tc_RealDef_Oreal)
<=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(94,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
tff(95,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
<=> ( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
<=> ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
<=> ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
^ [V_a: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) )),
( ( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) )
<=> ( class_Rings_Olinordered__idom(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) )),
rewrite(
( ( class_Rings_Olinordered__idom(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) )
<=> ( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
( ( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) )
<=> ( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [V_a: $i,T_a: $i] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [V_a: $i,T_a: $i] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__pos) ).
tff(102,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____) ),
inference(rewrite,[status(thm)],]) ).
tff(107,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_x_I1_J) ).
tff(108,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____) )
<=> ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[114,108,105,95]) ).
tff(116,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(118,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
tff(119,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
^ [V_r: $i,T_a: $i] :
refl(
( ( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) )
<=> ( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) )
<=> ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) )
<=> ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
^ [V_r: $i,T_a: $i] :
rewrite(
( ( class_RealVector_Oreal__normed__algebra__1(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) )
<=> ( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) ) )),
inference(bind,[status(th)],]) ).
tff(124,plain,
( ! [V_r: $i,T_a: $i] :
( class_RealVector_Oreal__normed__algebra__1(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) )
<=> ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,axiom,
! [V_r: $i,T_a: $i] :
( class_RealVector_Oreal__normed__algebra__1(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__of__real) ).
tff(126,plain,
! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) ),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) ),
inference(skolemize,[status(sab)],[127]) ).
tff(129,plain,
! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) ),
inference(modus_ponens,[status(thm)],[128,121]) ).
tff(130,plain,
( ( ~ ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) )
| ~ class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____)) ) )
<=> ( ~ ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) )
| ~ class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( ~ ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) )
| ~ class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
( ~ ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)) ) )
| ~ class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____)) ) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____)),
inference(unit_resolution,[status(thm)],[132,129,119]) ).
tff(134,plain,
^ [V_z: $i] :
refl(
( ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,V_z,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) )
<=> ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,V_z,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) ) )),
inference(bind,[status(th)],]) ).
tff(135,plain,
( ! [V_z: $i] : ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,V_z,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) )
<=> ! [V_z: $i] : ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,V_z,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) ) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,plain,
( ! [V_z: $i] : ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,V_z,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) )
<=> ! [V_z: $i] : ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,V_z,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,axiom,
! [V_z: $i] : ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,V_z,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__eq) ).
tff(138,plain,
! [V_z: $i] : ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,V_z,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
! [V_z: $i] : ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,V_z,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) ),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [V_z: $i] : ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,V_z,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) ),
inference(modus_ponens,[status(thm)],[139,135]) ).
tff(141,plain,
( ~ ! [V_z: $i] : ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,V_z,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) )
| ( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(142,plain,
c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),
inference(unit_resolution,[status(thm)],[141,140]) ).
tff(143,plain,
c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[143,133,116,92]) ).
tff(145,plain,
( ~ ( ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) )
| ( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ) ),
inference(tautology,[status(thm)],]) ).
tff(146,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),
inference(unit_resolution,[status(thm)],[145,144,78]) ).
tff(147,plain,
( ~ ( ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) )
<=> ( v_x____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) ) )
| ( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) != c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) )
| ( v_x____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) ) ),
inference(tautology,[status(thm)],]) ).
tff(148,plain,
v_x____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),
inference(unit_resolution,[status(thm)],[147,146,17]) ).
tff(149,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____) ),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
( class_Groups_Omonoid__mult(tc_Complex_Ocomplex)
<=> class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(152,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
tff(153,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
<=> ( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(155,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
^ [V_a: $i,T_a: $i] :
rewrite(
( ( class_Groups_Omonoid__mult(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
<=> ( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(158,plain,
( ! [V_a: $i,T_a: $i] :
( class_Groups_Omonoid__mult(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,axiom,
! [V_a: $i,T_a: $i] :
( class_Groups_Omonoid__mult(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
tff(160,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ),
inference(skolemize,[status(sab)],[161]) ).
tff(163,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ),
inference(modus_ponens,[status(thm)],[162,155]) ).
tff(164,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
| ~ class_Groups_Omonoid__mult(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
| ~ class_Groups_Omonoid__mult(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
| ~ class_Groups_Omonoid__mult(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) )
| ~ class_Groups_Omonoid__mult(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) ) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____),
inference(unit_resolution,[status(thm)],[166,163,153]) ).
tff(168,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
( class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(170,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
tff(171,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
refl(
( ( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
<=> ( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ) )),
inference(bind,[status(th)],]) ).
tff(173,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ) ),
inference(quant_intro,[status(thm)],[172]) ).
tff(174,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(175,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
rewrite(
( ( class_RealVector_Oreal__normed__div__algebra(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
<=> ( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ) )),
inference(bind,[status(th)],]) ).
tff(176,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ) ),
inference(quant_intro,[status(thm)],[175]) ).
tff(177,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult) ).
tff(178,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ),
inference(modus_ponens,[status(thm)],[178,174]) ).
tff(180,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ),
inference(skolemize,[status(sab)],[179]) ).
tff(181,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ),
inference(modus_ponens,[status(thm)],[180,173]) ).
tff(182,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
| ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
| ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(183,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
| ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(184,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
| ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) ) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
inference(unit_resolution,[status(thm)],[184,181,171]) ).
tff(186,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),
inference(transitivity,[status(thm)],[186,168]) ).
tff(188,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) ),
inference(monotonicity,[status(thm)],[168,187]) ).
tff(189,plain,
( class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(190,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
tff(191,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
refl(
( ( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) )
<=> ( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) )),
inference(bind,[status(th)],]) ).
tff(193,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ),
inference(quant_intro,[status(thm)],[192]) ).
tff(194,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
rewrite(
( ( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) )
<=> ( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) )),
inference(bind,[status(th)],]) ).
tff(196,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ),
inference(quant_intro,[status(thm)],[195]) ).
tff(197,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
tff(198,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ),
inference(modus_ponens,[status(thm)],[198,194]) ).
tff(200,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ),
inference(skolemize,[status(sab)],[199]) ).
tff(201,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ),
inference(modus_ponens,[status(thm)],[200,193]) ).
tff(202,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(203,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(204,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
inference(unit_resolution,[status(thm)],[204,201,191]) ).
tff(206,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),
inference(modus_ponens,[status(thm)],[205,188]) ).
tff(207,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____),
inference(modus_ponens,[status(thm)],[206,150]) ).
tff(208,plain,
( ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____) ) ),
inference(rewrite,[status(thm)],]) ).
tff(209,axiom,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cth) ).
tff(210,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
| ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) ) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
| ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(212,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
| ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(213,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
| ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) ) ),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),
inference(unit_resolution,[status(thm)],[213,181,171]) ).
tff(215,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____),
inference(transitivity,[status(thm)],[215,210]) ).
tff(217,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)) ),
inference(monotonicity,[status(thm)],[216]) ).
tff(218,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)) ),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)) ),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)) ),
inference(rewrite,[status(thm)],]) ).
tff(221,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)) ),
inference(rewrite,[status(thm)],]) ).
tff(222,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(223,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)),
inference(modus_ponens,[status(thm)],[222,221]) ).
tff(224,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)),
inference(modus_ponens,[status(thm)],[223,220]) ).
tff(225,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)),
inference(modus_ponens,[status(thm)],[224,219]) ).
tff(226,plain,
^ [V_x: $i,T_a: $i] :
refl(
( ( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
<=> ( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) )),
inference(bind,[status(th)],]) ).
tff(227,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) ),
inference(quant_intro,[status(thm)],[226]) ).
tff(228,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(229,plain,
^ [V_x: $i,T_a: $i] :
rewrite(
( ( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
<=> ( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) )),
inference(bind,[status(th)],]) ).
tff(230,plain,
( ! [V_x: $i,T_a: $i] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) ),
inference(quant_intro,[status(thm)],[229]) ).
tff(231,axiom,
! [V_x: $i,T_a: $i] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
tff(232,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
inference(modus_ponens,[status(thm)],[232,228]) ).
tff(234,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
inference(skolemize,[status(sab)],[233]) ).
tff(235,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
inference(modus_ponens,[status(thm)],[234,227]) ).
tff(236,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(237,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(238,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) ),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),
inference(unit_resolution,[status(thm)],[238,235,34]) ).
tff(240,plain,
( class_Orderings_Opreorder(tc_RealDef_Oreal)
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(241,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
tff(242,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[241,240]) ).
tff(243,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
refl(
( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(244,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) ),
inference(quant_intro,[status(thm)],[243]) ).
tff(245,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(246,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )),
( ( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
<=> ( class_Orderings_Opreorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) )),
rewrite(
( ( class_Orderings_Opreorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) )),
( ( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(247,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) ),
inference(quant_intro,[status(thm)],[246]) ).
tff(248,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
tff(249,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(modus_ponens,[status(thm)],[248,247]) ).
tff(250,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(modus_ponens,[status(thm)],[249,245]) ).
tff(251,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemize,[status(sab)],[250]) ).
tff(252,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(modus_ponens,[status(thm)],[251,244]) ).
tff(253,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____) ) ),
inference(rewrite,[status(thm)],]) ).
tff(254,plain,
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____) ) ),
inference(rewrite,[status(thm)],]) ).
tff(255,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____) ) ),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____) ) ),
inference(transitivity,[status(thm)],[255,253]) ).
tff(257,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(258,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____) ),
inference(modus_ponens,[status(thm)],[257,256]) ).
tff(259,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____),
inference(unit_resolution,[status(thm)],[258,108,252,242]) ).
tff(260,plain,
( class_Rings_Oordered__semiring(tc_RealDef_Oreal)
<=> class_Rings_Oordered__semiring(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(261,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
tff(262,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[261,260]) ).
tff(263,plain,
^ [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) )),
inference(bind,[status(th)],]) ).
tff(264,plain,
( ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) )
<=> ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) ),
inference(quant_intro,[status(thm)],[263]) ).
tff(265,plain,
( ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) )
<=> ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(266,plain,
^ [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) )),
rewrite(
( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) ) ) )),
rewrite(
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) ) )),
rewrite(
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) )),
( ( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) )
<=> ( class_Rings_Oordered__semiring(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) ) )),
rewrite(
( ( class_Rings_Oordered__semiring(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) )),
( ( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) )),
inference(bind,[status(th)],]) ).
tff(267,plain,
( ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) )
<=> ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) ),
inference(quant_intro,[status(thm)],[266]) ).
tff(268,axiom,
! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
tff(269,plain,
! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ),
inference(modus_ponens,[status(thm)],[268,267]) ).
tff(270,plain,
! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ),
inference(modus_ponens,[status(thm)],[269,265]) ).
tff(271,plain,
! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ),
inference(skolemize,[status(sab)],[270]) ).
tff(272,plain,
! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ),
inference(modus_ponens,[status(thm)],[271,264]) ).
tff(273,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____) ),
inference(rewrite,[status(thm)],]) ).
tff(274,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A_Ipoly_Ads_A_Icomplex__of__real_Ax_J_J_A_060_061_Am_096) ).
tff(275,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____),
inference(modus_ponens,[status(thm)],[274,273]) ).
tff(276,plain,
( ( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____)
| ~ class_Rings_Oordered__semiring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)) )
<=> ( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____)
| ~ class_Rings_Oordered__semiring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(277,plain,
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))))
| ~ class_Rings_Oordered__semiring(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____)
| ~ class_Rings_Oordered__semiring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(278,plain,
( ( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))))
| ~ class_Rings_Oordered__semiring(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____) )
<=> ( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____)
| ~ class_Rings_Oordered__semiring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)) ) ),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
( ( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))))
| ~ class_Rings_Oordered__semiring(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____) )
<=> ( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____)
| ~ class_Rings_Oordered__semiring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)) ) ),
inference(transitivity,[status(thm)],[278,276]) ).
tff(280,plain,
( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))))
| ~ class_Rings_Oordered__semiring(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____) ),
inference(quant_inst,[status(thm)],]) ).
tff(281,plain,
( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Rings_Oordered__semiring(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____)
| ~ class_Rings_Oordered__semiring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)) ),
inference(modus_ponens,[status(thm)],[280,279]) ).
tff(282,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)) ),
inference(unit_resolution,[status(thm)],[281,275,272,262,259,239]) ).
tff(283,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)),v_x____),
inference(unit_resolution,[status(thm)],[282,225]) ).
tff(284,plain,
$false,
inference(unit_resolution,[status(thm)],[283,207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWW270+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n021.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 13:41:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 116.86/74.67 % SZS status Theorem
% 116.86/74.67 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------