%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG409-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:59:04 AM UTC 2025
% Result : Unsatisfiable 0.41s 0.57s
% Output : Proof 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 48 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 225 ( 20 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 317 ( 149 ~; 145 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 110 ( 100 !; 0 ?; 110 :)
% 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_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(v_k_____type,type,
v_k____: $i ).
tff(v_t_____type,type,
v_t____: $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_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(v_w_____type,type,
v_w____: $i ).
tff(c_RealVector_Oof__real_type,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(v_s_____type,type,
v_s____: $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(v_m_____type,type,
v_m____: $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(1,plain,
( class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
tff(3,plain,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,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(8,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)],[7,6]) ).
tff(9,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)],[8]) ).
tff(10,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)],[9,5]) ).
tff(11,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_RealDef_Oreal)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal) ) )
<=> ( ~ ! [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_RealDef_Oreal)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,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_RealDef_Oreal)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,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_RealDef_Oreal)
| ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),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_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( class_Orderings_Oorder(tc_RealDef_Oreal)
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
tff(20,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(23,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_th30_0) ).
tff(26,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
refl(( ( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) )
<=> ( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
trans(monotonicity(rewrite(( ( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a) )
<=> ( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) )),
( ( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
<=> ( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) )),
rewrite(( ( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
<=> ( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) )),
( ( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
<=> ( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
tff(33,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) )
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) )
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),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_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) )
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),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_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) )
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) )
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),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_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) )
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) )
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),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_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a) )
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[42,36,26,23,20]) ).
tff(44,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[43,17]) ).
tff(45,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(47,plain,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : ALG409-1 : TPTP v9.0.0. Released v4.1.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 11:13:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.41/0.57 % SZS status Unsatisfiable
% 0.41/0.57 % SZS output start Proof
% See solution above
% 0.41/0.61 % E exiting
%------------------------------------------------------------------------------