%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW261+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:29:58 PM UTC 2026
% Result : Theorem 29.40s 4.86s
% Output : Refutation 29.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 32
% Syntax : Number of formulae : 143 ( 40 unt; 11 def)
% Number of atoms : 330 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 339 ( 152 ~; 144 |; 10 &)
% ( 19 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 12 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 113 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),c_RealVector_Onorm__class_Onorm(X2,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
fof(f5,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_t_I1_J) ).
fof(f11,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(f12,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(f14,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_t_I2_J) ).
fof(f29,axiom,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(f40,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
fof(f84,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
& X1 != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(f107,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(f165,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(f486,axiom,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(f650,axiom,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(f679,axiom,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra__1(X1)
=> c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__of__real) ).
fof(f691,axiom,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__def) ).
fof(f697,axiom,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(f1127,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(f1132,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(f1152,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(f1188,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(f1189,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1288,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1289,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(negated_conjecture,[status(cth)],[f1288]) ).
fof(f1291,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(flattening,[],[f1289]) ).
fof(f1296,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),c_RealVector_Onorm__class_Onorm(X2,X0)))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(ennf_transformation,[],[f3]) ).
fof(f1301,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f1302,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(flattening,[],[f1301]) ).
fof(f1328,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f1443,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f107]) ).
fof(f1444,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(flattening,[],[f1443]) ).
fof(f1543,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) )
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f165]) ).
fof(f1544,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) )
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(flattening,[],[f1543]) ).
fof(f1853,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f486]) ).
fof(f2062,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(ennf_transformation,[],[f679]) ).
fof(f2078,plain,
! [X0] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(ennf_transformation,[],[f691]) ).
fof(f2437,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(nnf_transformation,[],[f1328]) ).
fof(f2450,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X0 = X1 )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
& X1 != X0 )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f84]) ).
fof(f2451,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X0 = X1 )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
& X1 != X0 )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(flattening,[],[f2450]) ).
fof(f2475,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(nnf_transformation,[],[f1544]) ).
fof(f2595,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f1853]) ).
fof(f2758,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1)),c_RealVector_Onorm__class_Onorm(X2,X0)))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(cnf_transformation,[],[f1296]) ).
fof(f2760,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
inference(cnf_transformation,[],[f5]) ).
fof(f2767,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f2768,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(cnf_transformation,[],[f1302]) ).
fof(f2770,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f14]) ).
fof(f2790,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),
inference(cnf_transformation,[],[f29]) ).
fof(f2809,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(cnf_transformation,[],[f2437]) ).
fof(f2866,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2451]) ).
fof(f2897,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f1444]) ).
fof(f2984,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f2475]) ).
fof(f3421,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f2595]) ).
fof(f3647,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f650]) ).
fof(f3685,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X0))
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(cnf_transformation,[],[f2062]) ).
fof(f3701,plain,
! [X0] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f2078]) ).
fof(f3709,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),
inference(cnf_transformation,[],[f697]) ).
fof(f4239,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1127]) ).
fof(f4244,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1132]) ).
fof(f4264,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1152]) ).
fof(f4300,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1188]) ).
fof(f4301,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1189]) ).
fof(f4400,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(cnf_transformation,[],[f1291]) ).
fof(f4588,definition,
( spl48_1
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
introduced(definition,[new_symbols(definition,[spl48_1])],[avatar_definition]) ).
fof(f4590,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| spl48_1 ),
inference(avatar_component_clause,[],[f4588]) ).
fof(f4591,plain,
~ spl48_1,
inference(avatar_split_clause,[],[f4400,f4588]) ).
fof(f4593,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))
| spl48_1 ),
inference(resolution,[],[f4590,f2767]) ).
fof(f4594,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),X0) )
| spl48_1 ),
inference(resolution,[],[f4590,f2768]) ).
fof(f4620,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) )
| spl48_1 ),
inference(resolution,[],[f4590,f2984]) ).
fof(f4654,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
| spl48_1 ),
inference(forward_subsumption_resolution,[],[f4620,f4244]) ).
fof(f4764,definition,
( spl48_3
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),X0) ) ),
introduced(definition,[new_symbols(definition,[spl48_3])],[avatar_definition]) ).
fof(f4765,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
| ~ spl48_3 ),
inference(avatar_component_clause,[],[f4764]) ).
fof(f4766,plain,
( spl48_3
| spl48_1 ),
inference(avatar_split_clause,[],[f4594,f4588,f4764]) ).
fof(f4810,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ~ spl48_3 ),
inference(resolution,[],[f4765,f2758]) ).
fof(f4886,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ spl48_3 ),
inference(forward_subsumption_resolution,[],[f4810,f4301]) ).
fof(f4927,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ spl48_3 ),
inference(forward_demodulation,[],[f4886,f2790]) ).
fof(f5595,definition,
( spl48_14
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
introduced(definition,[new_symbols(definition,[spl48_14])],[avatar_definition]) ).
fof(f5597,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| spl48_14 ),
inference(avatar_component_clause,[],[f5595]) ).
fof(f5598,plain,
( ~ spl48_14
| ~ spl48_3 ),
inference(avatar_split_clause,[],[f4927,f4764,f5595]) ).
fof(f5798,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| spl48_14 ),
inference(resolution,[],[f5597,f2897]) ).
fof(f5871,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| spl48_14 ),
inference(forward_subsumption_resolution,[],[f5798,f4264]) ).
fof(f7380,definition,
( spl48_35
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
introduced(definition,[new_symbols(definition,[spl48_35])],[avatar_definition]) ).
fof(f7382,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| spl48_35 ),
inference(avatar_component_clause,[],[f7380]) ).
fof(f7384,definition,
( spl48_36
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))) ),
introduced(definition,[new_symbols(definition,[spl48_36])],[avatar_definition]) ).
fof(f7386,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))
| spl48_36 ),
inference(avatar_component_clause,[],[f7384]) ).
fof(f7388,definition,
( spl48_37
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[spl48_37])],[avatar_definition]) ).
fof(f7390,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| spl48_37 ),
inference(avatar_component_clause,[],[f7388]) ).
fof(f7391,plain,
( ~ spl48_35
| ~ spl48_36
| ~ spl48_37
| spl48_14 ),
inference(avatar_split_clause,[],[f5871,f5595,f7388,f7384,f7380]) ).
fof(f7411,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)
| spl48_35 ),
inference(resolution,[],[f7382,f3421]) ).
fof(f7631,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)
| spl48_35 ),
inference(forward_subsumption_resolution,[],[f7411,f3709]) ).
fof(f7662,plain,
( $false
| spl48_35 ),
inference(forward_subsumption_resolution,[],[f7631,f4239]) ).
fof(f7663,plain,
spl48_35,
inference(avatar_contradiction_clause,[],[f7662]) ).
fof(f7723,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))
| ~ class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)
| spl48_36 ),
inference(resolution,[],[f7386,f3421]) ).
fof(f7945,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)
| spl48_36 ),
inference(forward_subsumption_resolution,[],[f7723,f3709]) ).
fof(f7977,plain,
( $false
| spl48_36 ),
inference(forward_subsumption_resolution,[],[f7945,f4239]) ).
fof(f7978,plain,
spl48_36,
inference(avatar_contradiction_clause,[],[f7977]) ).
fof(f7990,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| spl48_37 ),
inference(resolution,[],[f7390,f2866]) ).
fof(f11757,definition,
( spl48_58
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(definition,[new_symbols(definition,[spl48_58])],[avatar_definition]) ).
fof(f11758,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
| ~ spl48_58 ),
inference(avatar_component_clause,[],[f11757]) ).
fof(f11759,plain,
( spl48_58
| spl48_1 ),
inference(avatar_split_clause,[],[f4654,f4588,f11757]) ).
fof(f11760,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
| ~ spl48_58 ),
inference(resolution,[],[f11758,f2809]) ).
fof(f11916,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
| spl48_1
| ~ spl48_58 ),
inference(forward_subsumption_resolution,[],[f11760,f4593]) ).
fof(f12688,definition,
( spl48_61
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
introduced(definition,[new_symbols(definition,[spl48_61])],[avatar_definition]) ).
fof(f12689,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
| ~ spl48_61 ),
inference(avatar_component_clause,[],[f12688]) ).
fof(f12690,plain,
( spl48_61
| spl48_1
| ~ spl48_58 ),
inference(avatar_split_clause,[],[f11916,f11757,f4588,f12688]) ).
fof(f12693,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl48_61 ),
inference(resolution,[],[f12689,f2760]) ).
fof(f25705,definition,
( spl48_148
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[spl48_148])],[avatar_definition]) ).
fof(f25707,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| spl48_148 ),
inference(avatar_component_clause,[],[f25705]) ).
fof(f25708,plain,
( ~ spl48_148
| ~ spl48_61 ),
inference(avatar_split_clause,[],[f12693,f12688,f25705]) ).
fof(f25710,plain,
( v_t____ = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____)
| spl48_148 ),
inference(resolution,[],[f25707,f3701]) ).
fof(f25989,plain,
( v_t____ = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_t____)
| spl48_148 ),
inference(forward_demodulation,[],[f25710,f3647]) ).
fof(f26015,definition,
( spl48_149
<=> v_t____ = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_t____) ),
introduced(definition,[new_symbols(definition,[spl48_149])],[avatar_definition]) ).
fof(f26017,plain,
( v_t____ = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_t____)
| ~ spl48_149 ),
inference(avatar_component_clause,[],[f26015]) ).
fof(f26018,plain,
( spl48_149
| spl48_148 ),
inference(avatar_split_clause,[],[f25989,f25705,f26015]) ).
fof(f42641,definition,
( spl48_246
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[spl48_246])],[avatar_definition]) ).
fof(f42643,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| spl48_246 ),
inference(avatar_component_clause,[],[f42641]) ).
fof(f42644,plain,
( ~ spl48_246
| spl48_37 ),
inference(avatar_split_clause,[],[f7990,f7388,f42641]) ).
fof(f42710,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| spl48_246 ),
inference(superposition,[],[f42643,f3685]) ).
fof(f42715,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| spl48_246 ),
inference(forward_subsumption_resolution,[],[f42710,f4300]) ).
fof(f42745,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_t____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| spl48_246 ),
inference(forward_demodulation,[],[f42715,f3647]) ).
fof(f42753,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl48_149
| spl48_246 ),
inference(forward_demodulation,[],[f42745,f26017]) ).
fof(f42755,plain,
( $false
| ~ spl48_149
| spl48_246 ),
inference(forward_subsumption_resolution,[],[f42753,f2770]) ).
fof(f42756,plain,
( ~ spl48_149
| spl48_246 ),
inference(avatar_contradiction_clause,[],[f42755]) ).
cnf(s1,plain,
~ spl48_1,
inference(sat_conversion,[],[f4591]) ).
cnf(s3,plain,
( spl48_1
| spl48_3 ),
inference(sat_conversion,[],[f4766]) ).
cnf(s14,plain,
( ~ spl48_3
| ~ spl48_14 ),
inference(sat_conversion,[],[f5598]) ).
cnf(s34,plain,
( spl48_14
| ~ spl48_35
| ~ spl48_36
| ~ spl48_37 ),
inference(sat_conversion,[],[f7391]) ).
cnf(s36,plain,
spl48_35,
inference(sat_conversion,[],[f7663]) ).
cnf(s38,plain,
spl48_36,
inference(sat_conversion,[],[f7978]) ).
cnf(s59,plain,
( spl48_1
| spl48_58 ),
inference(sat_conversion,[],[f11759]) ).
cnf(s62,plain,
( spl48_1
| ~ spl48_58
| spl48_61 ),
inference(sat_conversion,[],[f12690]) ).
cnf(s149,plain,
( ~ spl48_61
| ~ spl48_148 ),
inference(sat_conversion,[],[f25708]) ).
cnf(s150,plain,
( spl48_148
| spl48_149 ),
inference(sat_conversion,[],[f26018]) ).
cnf(s257,plain,
( spl48_37
| ~ spl48_246 ),
inference(sat_conversion,[],[f42644]) ).
cnf(s258,plain,
( ~ spl48_149
| spl48_246 ),
inference(sat_conversion,[],[f42756]) ).
cnf(s262,plain,
( spl48_14
| ~ spl48_37 ),
inference(rat,[],[s34,s38,s36]) ).
cnf(s268,plain,
spl48_58,
inference(rat,[],[s59,s1]) ).
cnf(s273,plain,
spl48_3,
inference(rat,[],[s3,s1]) ).
cnf(s285,plain,
spl48_61,
inference(rat,[],[s62,s1,s268]) ).
cnf(s307,plain,
~ spl48_14,
inference(rat,[],[s14,s273]) ).
cnf(s324,plain,
~ spl48_148,
inference(rat,[],[s149,s285]) ).
cnf(s357,plain,
~ spl48_37,
inference(rat,[],[s262,s307]) ).
cnf(s408,plain,
spl48_149,
inference(rat,[],[s150,s324]) ).
cnf(s463,plain,
~ spl48_246,
inference(rat,[],[s257,s357]) ).
cnf(s474,plain,
$false,
inference(rat,[],[s258,s463,s408]) ).
fof(f42757,plain,
$false,
inference(avatar_sat_refutation,[],[s474]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW261+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 13:26:20 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.76/2.71 % (158831)Detected formulas, will run a generic FOF schedule.
% 13.76/2.71 % (158836)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1680453988:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 13.76/2.71 % (158837)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1174022812:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 13.76/2.71 % (158840)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1902243778:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 13.76/2.71 % (158838)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2964702767:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 13.76/2.71 % (158839)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4256395240:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 13.76/2.71 % (158841)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=508455263:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 13.76/2.71 % (158842)dis-21_1_sil=8000:lcm=predicate:random_seed=3370403806:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 13.76/2.71 % (158840)Instruction limit reached!
% 13.76/2.71 % (158840)------------------------------
% 13.76/2.71 % (158840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.76/2.71 % (158840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.76/2.71 % (158840)CaDiCaL version: 2.1.3
% 13.76/2.71 % (158840)Termination reason: Instruction limit
% 13.76/2.71 % (158840)Termination phase: Saturation
% 13.76/2.71 % (158840)Time elapsed: 0.070 s
% 13.76/2.71 % (158840)Peak memory usage: 89 MB
% 13.76/2.71 % (158840)Instructions burned: 119 (million)
% 13.76/2.71 % (158839)Instruction limit reached!
% 13.76/2.71 % (158839)------------------------------
% 13.76/2.71 % (158839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.76/2.71 % (158839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.76/2.71 % (158839)CaDiCaL version: 2.1.3
% 13.76/2.71 % (158839)Termination reason: Instruction limit
% 13.76/2.71 % (158839)Termination phase: Saturation
% 13.76/2.71 % (158839)Time elapsed: 0.061 s
% 13.76/2.71 % (158839)Peak memory usage: 89 MB
% 13.76/2.71 % (158839)Instructions burned: 110 (million)
% 13.76/2.71 % (158842)Instruction limit reached!
% 13.76/2.71 % (158842)------------------------------
% 13.76/2.71 % (158842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.76/2.71 % (158842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.76/2.71 % (158842)CaDiCaL version: 2.1.3
% 13.76/2.71 % (158842)Termination reason: Instruction limit
% 13.76/2.71 % (158842)Termination phase: Saturation
% 13.76/2.71 % (158842)Time elapsed: 0.067 s
% 13.76/2.71 % (158842)Peak memory usage: 91 MB
% 13.76/2.71 % (158842)Instructions burned: 129 (million)
% 13.76/2.71 % (158841)Instruction limit reached!
% 13.76/2.71 % (158841)------------------------------
% 13.76/2.71 % (158841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.76/2.71 % (158841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.76/2.71 % (158841)CaDiCaL version: 2.1.3
% 13.76/2.71 % (158841)Termination reason: Instruction limit
% 13.76/2.71 % (158841)Termination phase: Saturation
% 13.76/2.71 % (158841)Time elapsed: 0.076 s
% 13.76/2.71 % (158841)Peak memory usage: 91 MB
% 13.76/2.71 % (158841)Instructions burned: 140 (million)
% 13.76/2.71 % (158850)lrs+10_1_sil=8000:sp=occurrence:random_seed=137160345:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 13.76/2.71 % (158851)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3677639698:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 13.76/2.71 % (158852)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2825224354:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 13.76/2.71 % (158853)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2990528736:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 13.76/2.71 % (158851)Instruction limit reached!
% 13.76/2.71 % (158851)------------------------------
% 13.76/2.71 % (158851)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.61/3.58 % (158851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.61/3.58 % (158851)CaDiCaL version: 2.1.3
% 19.61/3.58 % (158851)Termination reason: Instruction limit
% 19.61/3.58 % (158851)Termination phase: Saturation
% 19.61/3.58 % (158851)Time elapsed: 0.082 s
% 19.61/3.58 % (158851)Peak memory usage: 90 MB
% 19.61/3.58 % (158851)Instructions burned: 157 (million)
% 19.61/3.58 % (158853)Instruction limit reached!
% 19.61/3.58 % (158853)------------------------------
% 19.61/3.58 % (158853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.61/3.58 % (158853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.61/3.58 % (158853)CaDiCaL version: 2.1.3
% 19.61/3.58 % (158853)Termination reason: Instruction limit
% 19.61/3.58 % (158853)Termination phase: Saturation
% 19.61/3.58 % (158853)Time elapsed: 0.138 s
% 19.61/3.58 % (158853)Peak memory usage: 92 MB
% 19.61/3.58 % (158853)Instructions burned: 249 (million)
% 19.61/3.58 % (158850)Instruction limit reached!
% 19.61/3.58 % (158850)------------------------------
% 19.61/3.58 % (158850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.61/3.58 % (158850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.61/3.58 % (158850)CaDiCaL version: 2.1.3
% 19.61/3.58 % (158850)Termination reason: Instruction limit
% 19.61/3.58 % (158850)Termination phase: Saturation
% 19.61/3.58 % (158850)Time elapsed: 0.182 s
% 19.61/3.58 % (158850)Peak memory usage: 92 MB
% 19.61/3.58 % (158850)Instructions burned: 285 (million)
% 19.61/3.58 % (158852)Instruction limit reached!
% 19.61/3.58 % (158852)------------------------------
% 19.61/3.58 % (158852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.61/3.58 % (158852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.61/3.58 % (158852)CaDiCaL version: 2.1.3
% 19.61/3.58 % (158852)Termination reason: Instruction limit
% 19.61/3.58 % (158852)Termination phase: Saturation
% 19.61/3.58 % (158852)Time elapsed: 0.191 s
% 19.61/3.58 % (158852)Peak memory usage: 92 MB
% 19.61/3.58 % (158852)Instructions burned: 326 (million)
% 19.61/3.58 % (158858)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1850324908:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 19.61/3.58 % (158859)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4246030339:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 19.61/3.58 % (158860)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2366302935:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 19.61/3.58 % (158861)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=510708128:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 19.61/3.58 % (158860)Instruction limit reached!
% 19.61/3.58 % (158860)------------------------------
% 19.61/3.58 % (158860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.61/3.58 % (158860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.61/3.58 % (158860)CaDiCaL version: 2.1.3
% 19.61/3.58 % (158860)Termination reason: Instruction limit
% 19.61/3.58 % (158860)Termination phase: Saturation
% 19.61/3.58 % (158860)Time elapsed: 0.062 s
% 19.61/3.58 % (158860)Peak memory usage: 91 MB
% 19.61/3.58 % (158860)Instructions burned: 113 (million)
% 19.61/3.58 % (158858)Instruction limit reached!
% 19.61/3.58 % (158858)------------------------------
% 19.61/3.58 % (158858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.61/3.58 % (158858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.61/3.58 % (158858)CaDiCaL version: 2.1.3
% 19.61/3.58 % (158858)Termination reason: Instruction limit
% 19.61/3.58 % (158858)Termination phase: Saturation
% 19.61/3.58 % (158858)Time elapsed: 0.175 s
% 19.61/3.58 % (158858)Peak memory usage: 92 MB
% 19.61/3.58 % (158858)Instructions burned: 294 (million)
% 19.61/3.58 % (158861)Instruction limit reached!
% 19.61/3.58 % (158861)------------------------------
% 19.61/3.58 % (158861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.61/3.58 % (158861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.61/3.58 % (158861)CaDiCaL version: 2.1.3
% 19.61/3.58 % (158861)Termination reason: Instruction limit
% 19.61/3.58 % (158861)Termination phase: Saturation
% 19.61/3.58 % (158861)Time elapsed: 0.061 s
% 19.61/3.58 % (158861)Peak memory usage: 90 MB
% 19.61/3.58 % (158861)Instructions burned: 129 (million)
% 29.40/4.86 % (158866)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3487947486:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 29.40/4.86 % (158867)lrs+10_1_sil=8000:sp=occurrence:random_seed=1276515206:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 29.40/4.86 % (158868)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3394089267:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 29.40/4.86 % (158866)Instruction limit reached!
% 29.40/4.86 % (158866)------------------------------
% 29.40/4.86 % (158866)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.40/4.86 % (158866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.40/4.86 % (158866)CaDiCaL version: 2.1.3
% 29.40/4.86 % (158866)Termination reason: Instruction limit
% 29.40/4.86 % (158866)Termination phase: Saturation
% 29.40/4.86 % (158866)Time elapsed: 0.057 s
% 29.40/4.86 % (158866)Peak memory usage: 89 MB
% 29.40/4.86 % (158866)Instructions burned: 115 (million)
% 29.40/4.86 % (158872)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=197108403:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 29.40/4.86 % (158868)Instruction limit reached!
% 29.40/4.86 % (158868)------------------------------
% 29.40/4.86 % (158868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.40/4.86 % (158868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.40/4.86 % (158868)CaDiCaL version: 2.1.3
% 29.40/4.86 % (158868)Termination reason: Instruction limit
% 29.40/4.86 % (158868)Termination phase: Saturation
% 29.40/4.86 % (158868)Time elapsed: 0.234 s
% 29.40/4.86 % (158868)Peak memory usage: 94 MB
% 29.40/4.86 % (158868)Instructions burned: 438 (million)
% 29.40/4.86 % (158874)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3533201818:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 29.40/4.86 % (158874)Instruction limit reached!
% 29.40/4.86 % (158874)------------------------------
% 29.40/4.86 % (158874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.40/4.86 % (158874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.40/4.86 % (158874)CaDiCaL version: 2.1.3
% 29.40/4.86 % (158874)Termination reason: Instruction limit
% 29.40/4.86 % (158874)Termination phase: Saturation
% 29.40/4.86 % (158874)Time elapsed: 0.069 s
% 29.40/4.86 % (158874)Peak memory usage: 92 MB
% 29.40/4.86 % (158874)Instructions burned: 134 (million)
% 29.40/4.86 % (158867)Instruction limit reached!
% 29.40/4.86 % (158867)------------------------------
% 29.40/4.86 % (158867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.40/4.86 % (158867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.40/4.86 % (158867)CaDiCaL version: 2.1.3
% 29.40/4.86 % (158867)Termination reason: Instruction limit
% 29.40/4.86 % (158867)Termination phase: Saturation
% 29.40/4.86 % (158867)Time elapsed: 0.568 s
% 29.40/4.86 % (158867)Peak memory usage: 98 MB
% 29.40/4.86 % (158867)Instructions burned: 908 (million)
% 29.40/4.86 % (158876)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1335751419:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 29.40/4.86 % (158877)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1427752440:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 29.40/4.86 % (158876)Instruction limit reached!
% 29.40/4.86 % (158876)------------------------------
% 29.40/4.86 % (158876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.40/4.86 % (158876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.40/4.86 % (158876)CaDiCaL version: 2.1.3
% 29.40/4.86 % (158876)Termination reason: Instruction limit
% 29.40/4.86 % (158876)Termination phase: Saturation
% 29.40/4.86 % (158876)Time elapsed: 0.327 s
% 29.40/4.86 % (158876)Peak memory usage: 94 MB
% 29.40/4.86 % (158876)Instructions burned: 593 (million)
% 29.40/4.86 % (158880)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=2714706411:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2981 on theBenchmark for (2981ds/125Mi)
% 29.40/4.86 % (158880)Instruction limit reached!
% 29.40/4.86 % (158880)------------------------------
% 29.40/4.86 % (158880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.40/4.86 % (158880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.40/4.86 % (158880)CaDiCaL version: 2.1.3
% 29.40/4.86 % (158880)Termination reason: Instruction limit
% 29.40/4.86 % (158880)Termination phase: Saturation
% 29.40/4.86 % (158880)Time elapsed: 0.070 s
% 29.40/4.86 % (158880)Peak memory usage: 91 MB
% 29.40/4.86 % (158880)Instructions burned: 126 (million)
% 29.40/4.86 % (158859)Instruction limit reached!
% 29.40/4.86 % (158859)------------------------------
% 29.40/4.86 % (158859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.40/4.86 % (158859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.40/4.86 % (158859)CaDiCaL version: 2.1.3
% 29.40/4.86 % (158859)Termination reason: Instruction limit
% 29.40/4.86 % (158859)Termination phase: Saturation
% 29.40/4.86 % (158859)Time elapsed: 1.453 s
% 29.40/4.86 % (158859)Peak memory usage: 149 MB
% 29.40/4.86 % (158859)Instructions burned: 2350 (million)
% 29.40/4.86 % (158882)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3779064496:i=134:gtgl=5:slsql=off:gtg=exists_sym_2979 on theBenchmark for (2979ds/134Mi)
% 29.40/4.86 % (158882)Instruction limit reached!
% 29.40/4.86 % (158882)------------------------------
% 29.40/4.86 % (158882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.40/4.86 % (158882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.40/4.86 % (158882)CaDiCaL version: 2.1.3
% 29.40/4.86 % (158882)Termination reason: Instruction limit
% 29.40/4.86 % (158882)Termination phase: Saturation
% 29.40/4.86 % (158882)Time elapsed: 0.066 s
% 29.40/4.86 % (158882)Peak memory usage: 90 MB
% 29.40/4.86 % (158882)Instructions burned: 135 (million)
% 29.40/4.86 % (158883)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=2503541821:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2978 on theBenchmark for (2978ds/141Mi)
% 29.40/4.86 % (158883)Instruction limit reached!
% 29.40/4.86 % (158883)------------------------------
% 29.40/4.86 % (158883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.40/4.86 % (158883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.40/4.86 % (158883)CaDiCaL version: 2.1.3
% 29.40/4.86 % (158883)Termination reason: Instruction limit
% 29.40/4.86 % (158883)Termination phase: Saturation
% 29.40/4.86 % (158883)Time elapsed: 0.061 s
% 29.40/4.86 % (158883)Peak memory usage: 89 MB
% 29.40/4.86 % (158883)Instructions burned: 142 (million)
% 29.40/4.86 % (158885)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=2292381761:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2977 on theBenchmark for (2977ds/431Mi)
% 29.40/4.86 % (158887)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=576182901:i=6060:aac=none:ins=25_2976 on theBenchmark for (2976ds/6060Mi)
% 29.40/4.86 % (158885)Instruction limit reached!
% 29.40/4.86 % (158885)------------------------------
% 29.40/4.86 % (158885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.40/4.86 % (158885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.40/4.86 % (158885)CaDiCaL version: 2.1.3
% 29.40/4.86 % (158885)Termination reason: Instruction limit
% 29.40/4.86 % (158885)Termination phase: Saturation
% 29.40/4.86 % (158885)Time elapsed: 0.189 s
% 29.40/4.86 % (158885)Peak memory usage: 91 MB
% 29.40/4.86 % (158885)Instructions burned: 433 (million)
% 29.40/4.86 % (158890)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=575713899:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2974 on theBenchmark for (2974ds/150Mi)
% 29.40/4.86 % (158890)Instruction limit reached!
% 29.40/4.86 % (158890)------------------------------
% 29.40/4.86 % (158890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.40/4.86 % (158890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.40/4.86 % (158890)CaDiCaL version: 2.1.3
% 29.40/4.86 % (158890)Termination reason: Instruction limit
% 29.40/4.86 % (158890)Termination phase: Saturation
% 29.40/4.86 % (158890)Time elapsed: 0.079 s
% 29.40/4.86 % (158890)Peak memory usage: 91 MB
% 29.40/4.86 % (158890)Instructions burned: 150 (million)
% 29.40/4.86 % (158892)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=375584253:i=14155:bd=all_2972 on theBenchmark for (2972ds/14155Mi)
% 29.40/4.86 % (158838)First to succeed.
% 29.40/4.86 % (158838)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-158831"
% 29.40/4.86 % (158872)Instruction limit reached!
% 29.40/4.86 % (158872)------------------------------
% 29.40/4.86 % (158872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.40/4.86 % (158872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.40/4.86 % (158872)CaDiCaL version: 2.1.3
% 29.40/4.86 % (158872)Termination reason: Instruction limit
% 29.40/4.86 % (158872)Termination phase: Saturation
% 29.40/4.86 % (158872)Time elapsed: 3.033 s
% 29.40/4.86 % (158872)Peak memory usage: 164 MB
% 29.40/4.86 % (158872)Instructions burned: 5202 (million)
% 29.40/4.86 % (158838)Refutation found. Thanks to Tanya!
% 29.40/4.86 % SZS status Theorem for theBenchmark
% 29.40/4.86 % SZS output start Proof for theBenchmark
% See solution above
% 29.99/5.06 % (158838)------------------------------
% 29.99/5.06 % (158838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.99/5.06 % (158838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.99/5.06 % (158838)CaDiCaL version: 2.1.3
% 29.99/5.06 % (158838)Termination reason: Refutation
% 29.99/5.06 % (158838)Time elapsed: 3.713 s
% 29.99/5.06 % (158838)Peak memory usage: 177 MB
% 29.99/5.06 % (158838)Instructions burned: 6135 (million)
% 29.99/5.06 % (158838)------------------------------
% 29.99/5.06 % (158838)------------------------------
% 29.99/5.06 % (158831)Success in time 4.194 s
% 29.99/5.06 % Vampire exiting
%------------------------------------------------------------------------------