TSTP Solution File: SWW238+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW238+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Thu Sep 29 20:58:01 EDT 2022
% Result : Theorem 0.69s 0.83s
% Output : Proof 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 43
% Syntax : Number of formulae : 78 ( 22 unt; 13 typ; 0 def)
% Number of atoms : 329 ( 125 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 414 ( 168 ~; 162 |; 0 &)
% ( 57 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 203 ( 181 !; 0 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_c_____type,type,
v_c____: $i ).
tff(v_z_____type,type,
v_z____: $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(v_aa_____type,type,
v_aa____: $i ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(class_Groups_Ocancel__semigroup__add_type,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
tff(1,plain,
( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
tff(3,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_c: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [V_c: $i,V_a: $i,T_a: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_c: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(10,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal)
<=> class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
tff(22,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
^ [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
refl(
( ( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) )
<=> ( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) )
<=> ! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) )
<=> ! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
^ [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
rewrite(
( ( class_Groups_Ocancel__semigroup__add(T_a)
=> ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) )
<=> ( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) )
<=> ! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
tff(29,plain,
! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ~ ! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) )
| ~ class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal)
| ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))) ) ) )
<=> ( ~ ! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) )
| ~ class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal)
| ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) )
| ~ class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal)
| ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [V_ca_2: $i,V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Groups_Ocancel__semigroup__add(T_a)
| ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) )
<=> ( V_b_2 = V_ca_2 ) ) )
| ~ class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal)
| ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))) ) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))) ) ),
inference(unit_resolution,[status(thm)],[35,32,22]) ).
tff(37,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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
<=> ~ 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))) ),
inference(rewrite,[status(thm)],]) ).
tff(38,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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(39,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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( class_Orderings_Oord(tc_RealDef_Oreal)
<=> class_Orderings_Oord(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
tff(42,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) )
<=> ( ( V_b != V_c )
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( ( V_b != V_c )
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) )),
rewrite(
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( ( V_b != V_c )
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ( V_b != V_c ) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ( V_b != V_c ) ) )),
( ( class_Orderings_Oord(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) )
<=> ( class_Orderings_Oord(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ( V_b != V_c ) ) ) )),
rewrite(
( ( class_Orderings_Oord(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ( V_b != V_c ) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) ) )),
( ( class_Orderings_Oord(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( class_Orderings_Oord(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( class_Orderings_Oord(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
tff(49,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
<=> 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))) ),
inference(rewrite,[status(thm)],]) ).
tff(54,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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A_Iz_A_K_Ac_J_A_060_061_Acmod_A_Iz_A_K_Ac_A_L_Aa_J_A_L_Acmod_Aa_096) ).
tff(55,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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) )
| 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
| ~ class_Orderings_Oord(tc_RealDef_Oreal)
| ~ 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) )
| 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
| ~ class_Orderings_Oord(tc_RealDef_Oreal)
| ~ 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ~ class_Orderings_Oord(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) ) )
<=> ( 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
| ~ class_Orderings_Oord(tc_RealDef_Oreal)
| ~ 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) )
| ~ 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ~ class_Orderings_Oord(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) )
| 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
| ~ class_Orderings_Oord(tc_RealDef_Oreal)
| ~ 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) )
| ~ 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ~ class_Orderings_Oord(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) )
| 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
| ~ class_Orderings_Oord(tc_RealDef_Oreal)
| ~ 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) )
| ~ 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ~ class_Orderings_Oord(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ class_Orderings_Oord(T_a)
| ( V_b != V_c ) )
| 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
| ~ class_Orderings_Oord(tc_RealDef_Oreal)
| ~ 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),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),
inference(unit_resolution,[status(thm)],[61,55,52,42,39]) ).
tff(63,plain,
( ~ ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
<=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))) ) )
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)) )
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))) ) ),
inference(tautology,[status(thm)],]) ).
tff(64,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(unit_resolution,[status(thm)],[63,62,36]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15 % Problem : SWW238+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.16 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.36 % Computer : n020.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 4 13:12:29 EDT 2022
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.36 Usage: tptp [options] [-file:]file
% 0.12/0.36 -h, -? prints this message.
% 0.12/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.36 -m, -model generate model.
% 0.12/0.36 -p, -proof generate proof.
% 0.12/0.36 -c, -core generate unsat core of named formulas.
% 0.12/0.36 -st, -statistics display statistics.
% 0.12/0.36 -t:timeout set timeout (in second).
% 0.12/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.36 -<param>:<value> configuration parameter and value.
% 0.12/0.36 -o:<output-file> file to place output in.
% 0.69/0.83 % SZS status Theorem
% 0.69/0.83 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------