%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG401-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:59:03 AM UTC 2025
% Result : Unsatisfiable 8.77s 8.94s
% Output : Proof 8.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 111
% Syntax : Number of formulae : 278 ( 118 unt; 0 typ; 0 def)
% Number of atoms : 933 ( 495 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1157 ( 530 ~; 537 |; 0 &)
% ( 90 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 651 ( 603 !; 0 ?; 651 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(v_k_____type,type,
v_k____: $i ).
tff(v_w_____type,type,
v_w____: $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(v_q_____type,type,
v_q____: $i ).
tff(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(v_s_____type,type,
v_s____: $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__0_type,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(class_Ring__and__Field_Osemiring_type,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(class_HOL_Ozero_type,type,
class_HOL_Ozero: $i > $o ).
tff(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(class_Ring__and__Field_Oring_type,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(1,plain,
( ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
<=> ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
tff(3,plain,
c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r01_0) ).
tff(7,plain,
c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
tff(12,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [V_c: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
tff(17,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[22,19,12]) ).
tff(24,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
tff(28,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[33,30,12]) ).
tff(35,plain,
( ( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
tff(37,plain,
v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex) = c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
tff(43,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
^ [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
<=> ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
<=> ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
tff(48,plain,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[53,50,43]) ).
tff(55,plain,
c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[55,40]) ).
tff(57,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[57,34]) ).
tff(59,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
tff(62,plain,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
refl(( ( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
<=> ( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
tff(67,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[72,69,62]) ).
tff(74,plain,
^ [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) )
<=> ! [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) )
<=> ! [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,axiom,
! [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
tff(78,plain,
! [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ( ~ ! [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [V_c: $i,V_d: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[83,80,12]) ).
tff(85,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[87,19,12]) ).
tff(89,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
tff(92,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
( ( v_a____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( v_a____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,axiom,
v_a____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_kas_I1_J_0) ).
tff(95,plain,
v_a____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
^ [V_c: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
^ [V_c: $i,V_a: $i,T_a: $i] :
rewrite(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
tff(102,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( v_a____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( v_a____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( v_a____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( v_a____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[108,105,95,92]) ).
tff(110,plain,
( ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[112,50,43]) ).
tff(114,plain,
( class_HOL_Ozero(tc_Complex_Ocomplex)
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
tff(116,plain,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
^ [T_a: $i] :
refl(( ( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
( ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,axiom,
! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
tff(121,plain,
! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
( ( ~ ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( ~ ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [T_a: $i] :
( ~ class_HOL_Ozero(T_a)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_HOL_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[126,123,116]) ).
tff(128,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
( class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
tff(132,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(134,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[133]) ).
tff(135,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).
tff(137,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[137]) ).
tff(139,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[138,134]) ).
tff(140,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[142,139,132]) ).
tff(144,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[144,129,113]) ).
tff(146,plain,
( class_Int_Onumber__ring(tc_Complex_Ocomplex)
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
tff(148,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
^ [V_x: $i,V_a: $i,T_a: $i] :
refl(( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(150,plain,
( ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
<=> ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,plain,
( ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
<=> ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
^ [V_x: $i,V_a: $i,T_a: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ) )),
rewrite(( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(153,plain,
( ! [V_x: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,axiom,
! [V_x: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
tff(155,plain,
! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[155,151]) ).
tff(157,plain,
! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[156]) ).
tff(158,plain,
! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[157,150]) ).
tff(159,plain,
( ( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,plain,
( ( ( c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,plain,
( ( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ( c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ( c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(transitivity,[status(thm)],[161,159]) ).
tff(163,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ( c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[164,158,132,148,145]) ).
tff(166,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[165,109]) ).
tff(167,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[166]) ).
tff(168,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
tff(170,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
^ [V_b: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(172,plain,
( ! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[171]) ).
tff(173,plain,
( ! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,axiom,
! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
tff(175,plain,
! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[175]) ).
tff(177,plain,
! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[176,172]) ).
tff(178,plain,
( ( ~ ! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(179,plain,
( ~ ! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
( ~ ! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[180,177,170]) ).
tff(182,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(186,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[185]) ).
tff(187,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
tff(189,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[189]) ).
tff(191,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[190,186]) ).
tff(192,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(193,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[193,192]) ).
tff(195,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[194,191,12]) ).
tff(196,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[109]) ).
tff(198,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[56,197]) ).
tff(199,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[198,34]) ).
tff(200,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[58]) ).
tff(201,plain,
( class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(202,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
tff(203,plain,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) )
<=> ( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(205,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ) ),
inference(quant_intro,[status(thm)],[204]) ).
tff(206,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
tff(208,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ),
inference(skolemize,[status(sab)],[208]) ).
tff(210,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[209,205]) ).
tff(211,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) )
| ~ class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) )
| ~ class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(212,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) )
| ~ class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) )
| ~ class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[213,210,203]) ).
tff(215,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[197]) ).
tff(217,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[216,215,200]) ).
tff(218,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[217,199]) ).
tff(219,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
( ( ~ ! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(221,plain,
( ~ ! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(222,plain,
( ~ ! [V_b: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[222,177,170]) ).
tff(224,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[224,219,196,184,167]) ).
tff(226,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_w____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[225,89]) ).
tff(227,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[8]) ).
tff(228,plain,
c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
^ [V_z: $i] :
refl(( ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_z,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
<=> ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_z,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )),
inference(bind,[status(th)],[]) ).
tff(230,plain,
( ! [V_z: $i] : ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_z,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
<=> ! [V_z: $i] : ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_z,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_intro,[status(thm)],[229]) ).
tff(231,plain,
( ! [V_z: $i] : ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_z,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
<=> ! [V_z: $i] : ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_z,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(232,axiom,
! [V_z: $i] : ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_z,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_kas_I4_J_0) ).
tff(233,plain,
! [V_z: $i] : ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_z,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[232,231]) ).
tff(234,plain,
! [V_z: $i] : ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_z,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(skolemize,[status(sab)],[233]) ).
tff(235,plain,
! [V_z: $i] : ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_z,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[234,230]) ).
tff(236,plain,
( ~ ! [V_z: $i] : ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_z,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
| ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(237,plain,
c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[236,235]) ).
tff(238,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[8,237,228]) ).
tff(239,plain,
( ( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(240,plain,
( ( ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(241,plain,
( ( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
( ( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(transitivity,[status(thm)],[241,239]) ).
tff(243,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(244,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[243,242]) ).
tff(245,plain,
( ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(unit_resolution,[status(thm)],[244,158,132,148]) ).
tff(246,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[245,238]) ).
tff(247,plain,
c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[38]) ).
tff(248,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[247]) ).
tff(249,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[249,246]) ).
tff(251,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(253,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[253,252]) ).
tff(255,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[254,19,12]) ).
tff(256,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[249]) ).
tff(258,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[88,257]) ).
tff(259,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(260,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[259]) ).
tff(261,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(262,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
tff(263,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[262,261]) ).
tff(264,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[263]) ).
tff(265,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[264,260]) ).
tff(266,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(267,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(268,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[267,266]) ).
tff(269,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[268,265,12]) ).
tff(270,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[269]) ).
tff(271,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[238]) ).
tff(272,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[89,271,270,258,256,251,226,84,73,59,23,9,4]) ).
tff(273,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
( ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
<=> ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(276,axiom,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(277,plain,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[276,275]) ).
tff(278,plain,
$false,
inference(unit_resolution,[status(thm)],[277,274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG401-1 : TPTP v9.0.0. Released v4.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 11:17:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 8.77/8.94 % SZS status Unsatisfiable
% 8.77/8.94 % SZS output start Proof
% See solution above
% 8.83/9.03 % E exiting
%------------------------------------------------------------------------------