%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW261+1 : TPTP v9.0.0. Released v5.2.0.
% 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 05:36:43 AM UTC 2025
% Result : Theorem 0.54s 0.76s
% Output : Proof 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 60
% Syntax : Number of formulae : 138 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 736 ( 95 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 977 ( 421 ~; 417 |; 0 &)
% ( 75 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 311 ( 281 !; 0 ?; 311 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(v_w_____type,type,
v_w____: $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_RealVector_Oof__real_type,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(v_t_____type,type,
v_t____: $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Groups_Oabs__class_Oabs_type,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(class_RealVector_Oreal__normed__algebra__1_type,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(class_Groups_Oordered__ab__group__add__abs_type,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(class_RealVector_Oreal__normed__div__algebra_type,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
tff(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(1,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
tff(3,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_r: $i,T_a: $i] :
refl(( ( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) )
<=> ( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) )
<=> ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) )
<=> ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_r: $i,T_a: $i] :
rewrite(( ( class_RealVector_Oreal__normed__algebra__1(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) )
<=> ( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_r: $i,T_a: $i] :
( class_RealVector_Oreal__normed__algebra__1(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) )
<=> ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_r: $i,T_a: $i] :
( class_RealVector_Oreal__normed__algebra__1(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__of__real) ).
tff(10,plain,
! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) )
| ~ class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) ) )
<=> ( ~ ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) )
| ~ class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) )
| ~ class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_r: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) )
| ~ class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
<=> class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
tff(21,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) )
<=> ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
^ [V_a: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )),
( ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )
<=> ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ) )),
rewrite(( ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )
<=> ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ) )),
( ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )
<=> ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [V_a: $i,T_a: $i] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [V_a: $i,T_a: $i] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__pos) ).
tff(28,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_t_I1_J) ).
tff(34,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = v_t____ )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = v_t____ )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = v_t____ )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) )
<=> ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = v_t____ )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) )
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = v_t____ )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = v_t____ )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) )
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = v_t____ )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = v_t____ )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) )
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = v_t____ )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = v_t____ )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = v_t____,
inference(unit_resolution,[status(thm)],[40,34,31,21]) ).
tff(42,plain,
v_t____ = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
v_t____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),
inference(transitivity,[status(thm)],[42,18]) ).
tff(44,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
tff(49,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
refl(( ( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
<=> ( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
rewrite(( ( class_RealVector_Oreal__normed__div__algebra(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
<=> ( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult) ).
tff(56,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
| ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
| ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
| ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) )
| ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(unit_resolution,[status(thm)],[62,59,49]) ).
tff(64,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(transitivity,[status(thm)],[63,46]) ).
tff(65,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( class_Orderings_Opreorder(tc_RealDef_Oreal)
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
tff(69,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
refl(( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )),
( ( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
<=> ( class_Orderings_Opreorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) )),
rewrite(( ( class_Orderings_Opreorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) )),
( ( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
tff(76,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(modus_ponens,[status(thm)],[78,71]) ).
tff(80,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_t_I2_J) ).
tff(82,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(transitivity,[status(thm)],[85,83]) ).
tff(87,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(unit_resolution,[status(thm)],[88,82,79,69]) ).
tff(90,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
tff(92,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
^ [V_x: $i,T_a: $i] :
refl(( ( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
<=> ( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
^ [V_x: $i,T_a: $i] :
rewrite(( ( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
<=> ( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [V_x: $i,T_a: $i] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [V_x: $i,T_a: $i] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
tff(99,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(unit_resolution,[status(thm)],[105,102,92]) ).
tff(107,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____) ) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____) ) ),
inference(transitivity,[status(thm)],[109,107]) ).
tff(111,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
inference(unit_resolution,[status(thm)],[112,34,79,69]) ).
tff(114,plain,
( class_Rings_Olinordered__idom(tc_RealDef_Oreal)
<=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
tff(116,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
refl(( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) )),
rewrite(( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) ) ) )),
rewrite(( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) ) )),
( ( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) )
<=> ( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) ) ) )),
rewrite(( ( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ) )),
( ( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(121,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
tff(123,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(modus_ponens,[status(thm)],[125,118]) ).
tff(127,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(transitivity,[status(thm)],[129,127]) ).
tff(131,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(unit_resolution,[status(thm)],[132,126,116,113,106,89]) ).
tff(134,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(modus_ponens,[status(thm)],[133,66]) ).
tff(135,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(137,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
$false,
inference(unit_resolution,[status(thm)],[137,134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW261+1 : TPTP v9.0.0. Released v5.2.0.
% 0.00/0.12 % 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 : Fri Jun 20 11:20:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.54/0.76 % SZS status Theorem
% 0.54/0.76 % SZS output start Proof
% See solution above
% 0.60/0.85 % E exiting
%------------------------------------------------------------------------------