%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG360-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:58:58 AM UTC 2025
% Result : Unsatisfiable 1.18s 1.33s
% Output : Proof 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 63
% Syntax : Number of formulae : 142 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 636 ( 333 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 839 ( 366 ~; 410 |; 0 &)
% ( 63 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 288 ( 265 !; 0 ?; 288 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
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_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(v_b_type,type,
v_b: $i ).
tff(c_RealVector_Oof__real_type,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(v_na_____type,type,
v_na____: $i ).
tff(v_v_____type,type,
v_v____: $i ).
tff(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
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(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(class_RealVector_Oreal__algebra__1_type,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(1,plain,
( ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
<=> ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__is__one_1) ).
tff(3,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
<=> ( c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_th0_0) ).
tff(6,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(transitivity,[status(thm)],[7,3]) ).
tff(9,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
tff(11,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
tff(16,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[21,18,11]) ).
tff(23,plain,
( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
tff(25,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,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(27,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
tff(28,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ( v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
tff(31,plain,
v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [V_c: $i,V_b: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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)
| ( V_c = c_HOL_Ozero__class_Ozero(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 ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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 ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,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)
| ( V_c = c_HOL_Ozero__class_Ozero(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)
| ( V_c = c_HOL_Ozero__class_Ozero(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 ) ) )),
inference(bind,[status(th)],[]) ).
tff(36,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)
| ( V_c = c_HOL_Ozero__class_Ozero(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 ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,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/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
tff(38,plain,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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 ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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 ) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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 ) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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 ) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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(tc_Complex_Ocomplex)
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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(tc_Complex_Ocomplex)
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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(tc_Complex_Ocomplex)
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[47,41,31,28,25]) ).
tff(49,plain,
c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,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(52,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
tff(53,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,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(55,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)],[54]) ).
tff(56,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(57,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
tff(58,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)],[57,56]) ).
tff(59,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)],[58]) ).
tff(60,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)],[59,55]) ).
tff(61,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_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),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_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,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_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,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_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[63,60,53]) ).
tff(65,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
tff(67,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
^ [V_x: $i,T_a: $i] :
refl(( ( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
^ [V_x: $i,T_a: $i] :
rewrite(( ( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
tff(74,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) )
| ( c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[83,77,31,67]) ).
tff(85,plain,
( class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
tff(87,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
^ [V_x: $i,T_a: $i] :
refl(( ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) )
<=> ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) )
<=> ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) )
<=> ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
^ [V_x: $i,T_a: $i] :
rewrite(( ( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(92,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,axiom,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).
tff(94,plain,
! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) ),
inference(modus_ponens,[status(thm)],[96,89]) ).
tff(98,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ( ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) )
<=> ( ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(transitivity,[status(thm)],[100,98]) ).
tff(102,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__algebra__1(T_a) )
| ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[103,97,87,84]) ).
tff(105,plain,
( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) )
<=> ( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ) ),
inference(transitivity,[status(thm)],[107,105]) ).
tff(109,plain,
( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( V_c = c_HOL_Ozero__class_Ozero(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(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
( ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) ) ),
inference(unit_resolution,[status(thm)],[110,41,28,25]) ).
tff(112,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[111,104]) ).
tff(113,plain,
c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[113,64,50,22]) ).
tff(115,plain,
( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
tff(117,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
<=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
tff(122,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[127,124,117]) ).
tff(129,plain,
c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[129,114]) ).
tff(131,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(monotonicity,[status(thm)],[132,8]) ).
tff(134,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,axiom,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_v_0) ).
tff(137,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[137,134]) ).
tff(139,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,axiom,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(141,plain,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
$false,
inference(unit_resolution,[status(thm)],[141,138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG360-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 11:09:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.18/1.33 % SZS status Unsatisfiable
% 1.18/1.33 % SZS output start Proof
% See solution above
% 1.22/1.40 % E exiting
%------------------------------------------------------------------------------