TSTP Solution File: SWW234+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW234+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 20:58:00 EDT 2022
% Result : Theorem 275.31s 175.93s
% Output : Proof 276.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 101
% Syntax : Number of formulae : 207 ( 51 unt; 21 typ; 0 def)
% Number of atoms : 973 ( 236 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1278 ( 539 ~; 495 |; 0 &)
% ( 173 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 48 ( 48 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 17 >; 10 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 498 ( 446 !; 0 ?; 498 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Groups_Osgn__class_Osgn_type,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(v_r_____type,type,
v_r____: $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(c_Groups_Oabs__class_Oabs_type,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(class_Groups_Oordered__ab__group__add__abs_type,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
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_z_____type,type,
v_z____: $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_Groups_Oordered__comm__monoid__add_type,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(1,plain,
( class_Rings_Olinordered__idom(tc_RealDef_Oreal)
<=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
tff(3,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_k: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
<=> ( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
<=> ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
<=> ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [V_k: $i,T_a: $i] :
rewrite(
( ( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
<=> ( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_k: $i,T_a: $i] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
<=> ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_k: $i,T_a: $i] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__sgn) ).
tff(10,plain,
! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)) ) )
<=> ( ~ ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____))) ),
inference(symmetry,[status(thm)],[19]) ).
tff(21,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(22,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(23,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [V_ab_2: $i,T_a: $i] :
refl(
( ( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [V_ab_2: $i,T_a: $i] :
rewrite(
( ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).
tff(30,plain,
! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ 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),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))
<=> ( v_r____ != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ( ~ ! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ 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),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))
<=> ( v_r____ != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ 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),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))
<=> ( v_r____ != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [V_ab_2: $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),c_Groups_Oabs__class_Oabs(T_a,V_ab_2))
<=> ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ 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),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))
<=> ( v_r____ != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))
<=> ( v_r____ != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(unit_resolution,[status(thm)],[36,33,23]) ).
tff(38,plain,
^ [V_ab_2: $i,T_a: $i] :
refl(
( ( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
^ [V_ab_2: $i,T_a: $i] :
rewrite(
( ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [V_ab_2: $i,T_a: $i] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [V_ab_2: $i,T_a: $i] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__0) ).
tff(44,plain,
! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( v_r____ = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ( ~ ! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( v_r____ = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ ! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( v_r____ = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [V_ab_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( v_r____ = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( v_r____ = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(unit_resolution,[status(thm)],[50,47,23]) ).
tff(52,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
tff(54,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
^ [V_ab_2: $i,V_b_2: $i,T_a: $i] :
refl(
( ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
^ [V_ab_2: $i,V_b_2: $i,T_a: $i] :
rewrite(
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,axiom,
! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
tff(61,plain,
! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
( ( ~ ! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
| ( ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) )
<=> ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) )
<=> ( ~ ! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
| ( ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) )
<=> ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ~ ! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
| ( ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) )
<=> ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [V_ab_2: $i,V_b_2: $i,T_a: $i] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
| ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) )
<=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
| ( ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) )
<=> ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) )
<=> ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(unit_resolution,[status(thm)],[67,64,54]) ).
tff(69,plain,
( ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) )
<=> ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(commutativity,[status(thm)],]) ).
tff(70,plain,
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
<=> ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ) ),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
<=> ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(74,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
( class_Orderings_Oorder(tc_RealDef_Oreal)
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
tff(77,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
^ [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
refl(
( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
<=> ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
<=> ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) )
<=> ( ( V_b != V_c )
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( ( V_b != V_c )
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) )),
rewrite(
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( ( V_b != V_c )
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ( V_b != V_c ) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ( V_b != V_c ) ) )),
( ( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) )
<=> ( class_Orderings_Oorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ( V_b != V_c ) ) ) )),
rewrite(
( ( class_Orderings_Oorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ( V_b != V_c ) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ) )),
( ( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) )
<=> ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
tff(84,plain,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(rewrite,[status(thm)],]) ).
tff(89,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_h) ).
tff(90,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
( ( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
inference(transitivity,[status(thm)],[93,91]) ).
tff(95,plain,
( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[96,90,87,77,74]) ).
tff(98,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),
inference(modus_ponens,[status(thm)],[97,71]) ).
tff(99,plain,
( ~ ( ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) )
<=> ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) )
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(tautology,[status(thm)],]) ).
tff(100,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[99,98,68]) ).
tff(101,plain,
( ~ ( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( v_r____ = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( v_r____ != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(tautology,[status(thm)],]) ).
tff(102,plain,
v_r____ != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[101,100,51]) ).
tff(103,plain,
( ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))
<=> ( v_r____ != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))
| ( v_r____ = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(tautology,[status(thm)],]) ).
tff(104,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),
inference(unit_resolution,[status(thm)],[103,102,37]) ).
tff(105,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____))),
inference(modus_ponens,[status(thm)],[104,20]) ).
tff(106,plain,
( class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
<=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(107,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
tff(108,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,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(110,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)],[109]) ).
tff(111,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(112,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(113,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)],[112]) ).
tff(114,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/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(115,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)],[114,113]) ).
tff(116,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)],[115,111]) ).
tff(117,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)],[116]) ).
tff(118,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)],[117,110]) ).
tff(119,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_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ) )
<=> ( ~ ! [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_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,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_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,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_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),
inference(unit_resolution,[status(thm)],[121,118,108]) ).
tff(123,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(monotonicity,[status(thm)],[18]) ).
tff(124,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),
inference(transitivity,[status(thm)],[123,122]) ).
tff(125,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)))
<=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( class_Orderings_Olinorder(tc_RealDef_Oreal)
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(129,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
tff(130,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
^ [V_x: $i,V_y: $i,T_a: $i] :
refl(
( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
<=> ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
<=> ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
^ [V_x: $i,V_y: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) )),
( ( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) )
<=> ( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) )),
rewrite(
( ( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) )),
( ( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(135,plain,
( ! [V_x: $i,V_y: $i,T_a: $i] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) )
<=> ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,axiom,
! [V_x: $i,V_y: $i,T_a: $i] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
tff(137,plain,
! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[137,133]) ).
tff(139,plain,
! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[139,132]) ).
tff(141,plain,
( ( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))) )
<=> ( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
( ( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))) ) ),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( ( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))) ) ),
inference(transitivity,[status(thm)],[143,141]) ).
tff(145,plain,
( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))),
inference(unit_resolution,[status(thm)],[146,90,140,130]) ).
tff(148,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(modus_ponens,[status(thm)],[147,127]) ).
tff(149,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
refl(
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(150,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
rewrite(
( ( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(153,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
tff(155,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[155,151]) ).
tff(157,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemize,[status(sab)],[156]) ).
tff(158,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[157,150]) ).
tff(159,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,plain,
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(transitivity,[status(thm)],[161,159]) ).
tff(163,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(unit_resolution,[status(thm)],[164,158,130,74]) ).
tff(166,plain,
( class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
<=> class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(167,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
tff(168,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) )
<=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ) )),
inference(bind,[status(th)],]) ).
tff(170,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ) ),
inference(quant_intro,[status(thm)],[169]) ).
tff(171,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(172,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
| c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) )),
( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
| c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) )),
rewrite(
( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
| c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ) )),
( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ) )),
( ( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) )
<=> ( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ) ) )),
rewrite(
( ( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ) )),
( ( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ) )),
inference(bind,[status(th)],]) ).
tff(173,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ) ),
inference(quant_intro,[status(thm)],[172]) ).
tff(174,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
tff(175,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ),
inference(modus_ponens,[status(thm)],[175,171]) ).
tff(177,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ),
inference(skolemize,[status(sab)],[176]) ).
tff(178,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) ),
inference(modus_ponens,[status(thm)],[177,170]) ).
tff(179,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(180,plain,
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(181,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ),
inference(transitivity,[status(thm)],[181,179]) ).
tff(183,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(quant_inst,[status(thm)],]) ).
tff(184,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(unit_resolution,[status(thm)],[184,178,168,165]) ).
tff(186,plain,
$false,
inference(unit_resolution,[status(thm)],[185,148,105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW234+1 : TPTP v8.1.0. Released v5.2.0.
% 0.00/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.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 : Sun Sep 4 13:19:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 275.31/175.93 % SZS status Theorem
% 275.31/175.93 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------