%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV627-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:35:50 AM UTC 2025
% Result : Unsatisfiable 0.57s 0.73s
% Output : Proof 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 64
% Syntax : Number of formulae : 146 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 675 ( 269 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 901 ( 414 ~; 420 |; 0 &)
% ( 67 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 303 ( 275 !; 0 ?; 303 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $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(c_FFT__Mirabelle_Oroot_type,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
tff(v_n_type,type,
v_n: $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
tff(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(class_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(class_Ring__and__Field_Odivision__by__zero_type,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(1,plain,
( class_Int_Onumber__ring(tc_Complex_Ocomplex)
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
tff(3,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
tff(6,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_x: $i,T_a: $i] :
refl(( ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [V_x: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(( ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_x: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
tff(13,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),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(18,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),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(19,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),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)],[18,17]) ).
tff(20,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),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)],[19,16,6,3]) ).
tff(21,plain,
( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
tff(23,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(( ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
trans(monotonicity(rewrite(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Int_Onumber__ring(T_a) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ) )),
rewrite(( ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).
tff(30,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[36,33,23,3]) ).
tff(38,plain,
( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
tff(40,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
^ [V_n: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [V_n: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_n: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [V_n: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_n: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
! [V_n: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
tff(45,plain,
! [V_n: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [V_n: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [V_n: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ( ~ ! [V_n: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_n: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [V_n: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [V_n: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[50,47,40]) ).
tff(52,plain,
( class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
tff(54,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
^ [T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
tff(59,plain,
! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ( ~ ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [T_a: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[64,61,54]) ).
tff(66,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
tff(68,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
^ [V_a: $i,T_a: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
rewrite(( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
tff(75,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[84,78,68,23,65]) ).
tff(86,plain,
^ [V_n: $i] :
refl(( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,axiom,
! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__unity_0) ).
tff(90,plain,
! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
( ~ ! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) )
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[93,92]) ).
tff(95,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ) )),
rewrite(( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).
tff(102,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[108,105,68,23]) ).
tff(110,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[110,95,85]) ).
tff(112,plain,
c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[112,51]) ).
tff(114,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[118,33,23,3]) ).
tff(120,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[120,115,37]) ).
tff(122,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
( class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
tff(126,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
^ [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) )
<=> ( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(128,plain,
( ! [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) )
<=> ! [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,plain,
( ! [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) )
<=> ! [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,axiom,
! [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
tff(131,plain,
! [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[132,128]) ).
tff(134,plain,
( ( ~ ! [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ~ ! [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [V_a_H: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[136,133,126]) ).
tff(138,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[140,33,23,3]) ).
tff(142,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[141,137,123,20]) ).
tff(143,plain,
( ( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,axiom,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(145,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
$false,
inference(unit_resolution,[status(thm)],[145,142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV627-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 : Fri Jun 20 10:30:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.57/0.73 % SZS status Unsatisfiable
% 0.57/0.73 % SZS output start Proof
% See solution above
% 0.60/0.78 % E exiting
%------------------------------------------------------------------------------