TSTP Solution File: ALG385-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG385-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Tue Sep 6 16:10:02 EDT 2022
% Result : Unsatisfiable 42.95s 27.94s
% Output : Proof 43.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 196
% Syntax : Number of formulae : 412 ( 124 unt; 33 typ; 0 def)
% Number of atoms : 1488 ( 481 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1929 ( 867 ~; 918 |; 0 &)
% ( 144 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 47 ( 47 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 26 >; 20 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 1111 (1018 !; 0 ?;1111 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(v_c_____type,type,
v_c____: $i ).
tff(v_z_____type,type,
v_z____: $i ).
tff(v_aa_____type,type,
v_aa____: $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_Ring__and__Field_Osemiring_type,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(class_Ring__and__Field_Odivision__by__zero_type,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__0_type,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(v_da_____type,type,
v_da____: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
tff(v_cs_____type,type,
v_cs____: $i ).
tff(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
tff(1,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
tff(3,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
tff(8,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
tff(17,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
<=> ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
tff(22,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = v_aa____ ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = v_aa____ ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = v_aa____ ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = v_aa____ ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = v_aa____,
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
tff(31,plain,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
tff(36,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[41,38,31]) ).
tff(43,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[14]) ).
tff(45,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
tff(47,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
tff(52,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[57,54,47]) ).
tff(59,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
tff(63,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[68,65,17]) ).
tff(70,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
tff(76,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[81,78,17]) ).
tff(83,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
tff(87,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[92,89,47]) ).
tff(94,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(96,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
tff(97,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) )
<=> ( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
tff(102,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[107,104,97]) ).
tff(109,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[108,94]) ).
tff(110,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[109,93]) ).
tff(111,plain,
^ [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(112,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,axiom,
! [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
tff(115,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[120,117,47]) ).
tff(122,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[125,78,17]) ).
tff(127,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
^ [V_x: $i,V_xa: $i,T_a: $i] :
refl(
( ( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) )
<=> ( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(129,plain,
( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) )
<=> ! [V_x: $i,V_xa: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) )
<=> ! [V_x: $i,V_xa: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
tff(132,plain,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,plain,
( ( ~ ! [V_x: $i,V_xa: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_xa: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( ~ ! [V_x: $i,V_xa: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
( ~ ! [V_x: $i,V_xa: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) )
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[137,134,97]) ).
tff(139,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(141,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
tff(144,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[144]) ).
tff(146,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[145,141]) ).
tff(147,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[149,146,47]) ).
tff(151,plain,
( class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(152,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
tff(153,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(155,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).
tff(158,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[157,156]) ).
tff(159,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[158]) ).
tff(160,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[159,155]) ).
tff(161,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[163,160,153]) ).
tff(165,plain,
c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[164,127]) ).
tff(166,plain,
c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[166,150,139,82,127]) ).
tff(168,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[168,122,110,82]) ).
tff(170,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = v_aa____,
inference(transitivity,[status(thm)],[170,71,58,44,43,28]) ).
tff(172,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[93,171]) ).
tff(173,plain,
( class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(174,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
tff(175,plain,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
refl(
( ( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
<=> ( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(177,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ) ),
inference(quant_intro,[status(thm)],[176]) ).
tff(178,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
tff(180,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ),
inference(skolemize,[status(sab)],[180]) ).
tff(182,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[181,177]) ).
tff(183,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(185,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i,V_e: $i] :
( ~ class_Ring__and__Field_Osemiring(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) )
| ~ class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[185,182,175]) ).
tff(187,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(189,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
tff(190,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,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(192,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
tff(193,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
( ( v_c____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( v_c____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,axiom,
v_c____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_c0_0) ).
tff(196,plain,
v_c____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,plain,
^ [V_c: $i,V_b: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) )),
inference(bind,[status(th)],]) ).
tff(198,plain,
( ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
<=> ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) ),
inference(quant_intro,[status(thm)],[197]) ).
tff(199,plain,
( ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
<=> ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(200,plain,
^ [V_c: $i,V_b: $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_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) )),
rewrite(
( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b )
| ( V_c = 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_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b )
| ( V_c = 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_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b )
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b )
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) )),
inference(bind,[status(th)],]) ).
tff(201,plain,
( ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b )
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ) ),
inference(quant_intro,[status(thm)],[200]) ).
tff(202,axiom,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b )
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
tff(203,plain,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ),
inference(modus_ponens,[status(thm)],[203,199]) ).
tff(205,plain,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ),
inference(skolemize,[status(sab)],[204]) ).
tff(206,plain,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) ),
inference(modus_ponens,[status(thm)],[205,198]) ).
tff(207,plain,
( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( v_c____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(v_aa____,v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex) = v_aa____ ) )
<=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( v_c____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(v_aa____,v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex) = v_aa____ ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(208,plain,
( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( v_c____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(v_aa____,v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex) = v_aa____ ) ),
inference(quant_inst,[status(thm)],]) ).
tff(209,plain,
( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( v_c____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(v_aa____,v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex) = v_aa____ ) ),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(v_aa____,v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex) = v_aa____,
inference(unit_resolution,[status(thm)],[209,206,196,193,190]) ).
tff(211,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(v_aa____,v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
v_aa____ = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(v_aa____,v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[210]) ).
tff(213,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(214,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
tff(215,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[214,213]) ).
tff(216,plain,
^ [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(217,plain,
( ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
<=> ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[216]) ).
tff(218,plain,
( ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
<=> ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(219,axiom,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
tff(220,plain,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[219,218]) ).
tff(221,plain,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
inference(skolemize,[status(sab)],[220]) ).
tff(222,plain,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[221,217]) ).
tff(223,plain,
( ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(224,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(225,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[224,223]) ).
tff(226,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[225,222,215]) ).
tff(227,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[226]) ).
tff(228,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(229,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(230,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[229,228]) ).
tff(231,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[230,89,47]) ).
tff(232,plain,
c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[232,227]) ).
tff(234,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(v_aa____,v_c____,tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[233,212]) ).
tff(235,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(236,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(237,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[236,235]) ).
tff(238,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[237,10,3]) ).
tff(239,plain,
c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_aa____,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
( ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(241,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(242,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[241,240]) ).
tff(243,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[242,222,215]) ).
tff(244,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[243,239,234,211,187,172,14]) ).
tff(245,plain,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
( class_Orderings_Olinorder(tc_RealDef_Oreal)
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(247,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
tff(248,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[247,246]) ).
tff(249,plain,
( ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
<=> ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(250,plain,
( ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
<=> ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(251,axiom,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(252,plain,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[251,250]) ).
tff(253,plain,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[252,249]) ).
tff(254,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(255,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[254]) ).
tff(256,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(257,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(258,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[257]) ).
tff(259,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
tff(260,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[259,258]) ).
tff(261,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[260,256]) ).
tff(262,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(skolemize,[status(sab)],[261]) ).
tff(263,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[262,255]) ).
tff(264,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(265,plain,
( ( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
<=> ( c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(266,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[266,264]) ).
tff(268,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(269,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[268,267]) ).
tff(270,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[269,263,253,248]) ).
tff(271,plain,
( class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
<=> class_Lattices_Olower__semilattice(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(272,axiom,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olower__semilattice) ).
tff(273,plain,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[272,271]) ).
tff(274,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
<=> ( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ) )),
inference(bind,[status(th)],]) ).
tff(275,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ) ),
inference(quant_intro,[status(thm)],[274]) ).
tff(276,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(277,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y )
| ~ c_lessequals(V_y,V_x,T_a) )
<=> ( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ) )),
inference(bind,[status(th)],]) ).
tff(278,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y )
| ~ c_lessequals(V_y,V_x,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ) ),
inference(quant_intro,[status(thm)],[277]) ).
tff(279,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y )
| ~ c_lessequals(V_y,V_x,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
tff(280,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[279,278]) ).
tff(281,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[280,276]) ).
tff(282,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ),
inference(skolemize,[status(sab)],[281]) ).
tff(283,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[282,275]) ).
tff(284,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(285,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(286,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[285,284]) ).
tff(287,plain,
c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[286,283,273,270]) ).
tff(288,plain,
( c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
<=> c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(289,axiom,
c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
tff(290,plain,
c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[289,288]) ).
tff(291,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) = v_da____ ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) = v_da____ ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(292,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) = v_da____ ) ),
inference(quant_inst,[status(thm)],]) ).
tff(293,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) = v_da____ ) ),
inference(modus_ponens,[status(thm)],[292,291]) ).
tff(294,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) = v_da____,
inference(unit_resolution,[status(thm)],[293,283,290,273]) ).
tff(295,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(monotonicity,[status(thm)],[294]) ).
tff(296,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
<=> ( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(297,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[296]) ).
tff(298,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(299,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
tff(300,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[299,298]) ).
tff(301,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[300]) ).
tff(302,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[301,297]) ).
tff(303,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(304,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(305,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[304,303]) ).
tff(306,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[305,302,273]) ).
tff(307,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[306]) ).
tff(308,plain,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[287]) ).
tff(309,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Lattices_Olower__semilattice__class_Oinf(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(monotonicity,[status(thm)],[308]) ).
tff(310,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[309,307,295,287]) ).
tff(311,plain,
( ( c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
<=> ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(monotonicity,[status(thm)],[310]) ).
tff(312,plain,
( ( c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
<=> ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(monotonicity,[status(thm)],[311]) ).
tff(313,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(314,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[313]) ).
tff(315,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(316,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(317,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[316]) ).
tff(318,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
tff(319,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[318,317]) ).
tff(320,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[319,315]) ).
tff(321,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(skolemize,[status(sab)],[320]) ).
tff(322,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[321,314]) ).
tff(323,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(324,plain,
( ( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
<=> ( c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(325,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[324]) ).
tff(326,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[325,323]) ).
tff(327,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(328,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a) )
| c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[327,326]) ).
tff(329,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[328,322,253,248]) ).
tff(330,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(331,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[330]) ).
tff(332,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(333,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
<=> ( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(334,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[333]) ).
tff(335,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
tff(336,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[335,334]) ).
tff(337,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[336,332]) ).
tff(338,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(skolemize,[status(sab)],[337]) ).
tff(339,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[338,331]) ).
tff(340,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(341,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(342,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[341,340]) ).
tff(343,plain,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[342,339,290,248]) ).
tff(344,plain,
( class_Orderings_Opreorder(tc_RealDef_Oreal)
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(345,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
tff(346,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[345,344]) ).
tff(347,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
refl(
( ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(348,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[347]) ).
tff(349,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(350,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
trans(
monotonicity(
rewrite(
( ( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) )
<=> ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ) )),
( ( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
rewrite(
( ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
( ( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(351,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[350]) ).
tff(352,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
tff(353,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[352,351]) ).
tff(354,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[353,349]) ).
tff(355,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(skolemize,[status(sab)],[354]) ).
tff(356,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[355,348]) ).
tff(357,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(358,plain,
( ( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
<=> ( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(359,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[358]) ).
tff(360,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[359,357]) ).
tff(361,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(362,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[361,360]) ).
tff(363,plain,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[362,356,346,343,329]) ).
tff(364,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) )
<=> ( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) ) )),
inference(bind,[status(th)],]) ).
tff(365,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) ) ),
inference(quant_intro,[status(thm)],[364]) ).
tff(366,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(367,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x )
| c_lessequals(V_x,V_y,T_a) )
<=> ( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) ) )),
inference(bind,[status(th)],]) ).
tff(368,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x )
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) ) ),
inference(quant_intro,[status(thm)],[367]) ).
tff(369,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x )
| c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
tff(370,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) ),
inference(modus_ponens,[status(thm)],[369,368]) ).
tff(371,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) ),
inference(modus_ponens,[status(thm)],[370,366]) ).
tff(372,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) ),
inference(skolemize,[status(sab)],[371]) ).
tff(373,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) ),
inference(modus_ponens,[status(thm)],[372,365]) ).
tff(374,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(375,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(376,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x ) )
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ( c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[375,374]) ).
tff(377,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[376,373,273,363]) ).
tff(378,plain,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[377,312]) ).
tff(379,plain,
$false,
inference(unit_resolution,[status(thm)],[378,245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG385-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 29 16:38:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 42.95/27.94 % SZS status Unsatisfiable
% 42.95/27.94 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------