%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW179+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 : n010.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 01:29:47 PM UTC 2026
% Result : Theorem 5.94s 1.68s
% Output : Refutation 7.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 30
% Syntax : Number of formulae : 163 ( 60 unt; 6 def)
% Number of atoms : 333 ( 65 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 316 ( 146 ~; 132 |; 12 &)
% ( 10 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 7 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 207 ( 0 sgn 207 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
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_c____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0960_A_060_061_Acmod_Ac_096) ).
fof(f3,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0960_A_060_061_Aabs_A_Ir_A_K_Am_J_096) ).
fof(f4,axiom,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(f14,axiom,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
fof(f21,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(f22,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(f69,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( X1 != X0
=> ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
=> c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(f116,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(f121,axiom,
! [X0,X1] :
( class_Rings_Olinordered__semidom(X1)
=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(f257,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(f258,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(f259,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f262,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(f382,axiom,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__diff__def) ).
fof(f470,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(f514,axiom,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
fof(f569,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oabs__class_Oabs(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0)
<=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ominus__class_Ominus(X3,X1,X0),X2)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).
fof(f1129,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f1137,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(f1147,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(f1148,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(f1160,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(f1163,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(f1275,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1276,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(negated_conjecture,[status(cth)],[f1275]) ).
fof(f1285,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(flattening,[],[f1276]) ).
fof(f1296,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f1377,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f69]) ).
fof(f1378,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| ~ class_Rings_Olinordered__idom(X2) ),
inference(flattening,[],[f1377]) ).
fof(f1437,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f116]) ).
fof(f1438,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f1437]) ).
fof(f1444,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(ennf_transformation,[],[f121]) ).
fof(f1649,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f257]) ).
fof(f1650,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f258]) ).
fof(f1651,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f259]) ).
fof(f1656,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f262]) ).
fof(f1657,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f1656]) ).
fof(f1876,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f470]) ).
fof(f1955,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oabs__class_Oabs(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0)
<=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ominus__class_Ominus(X3,X1,X0),X2)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ) )
| ~ class_Rings_Olinordered__idom(X3) ),
inference(ennf_transformation,[],[f569]) ).
fof(f2412,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,[],[f21]) ).
fof(f2413,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,[],[f2412]) ).
fof(f2586,plain,
! [X0,X1] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X0 != X1 )
& ( X1 = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) ) ),
inference(nnf_transformation,[],[f514]) ).
fof(f2620,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oabs__class_Oabs(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ominus__class_Ominus(X3,X1,X0),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) )
& ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ominus__class_Ominus(X3,X1,X0),X2)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oabs__class_Oabs(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) ) )
| ~ class_Rings_Olinordered__idom(X3) ),
inference(nnf_transformation,[],[f1955]) ).
fof(f2621,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oabs__class_Oabs(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ominus__class_Ominus(X3,X1,X0),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) )
& ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ominus__class_Ominus(X3,X1,X0),X2)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oabs__class_Oabs(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) ) )
| ~ class_Rings_Olinordered__idom(X3) ),
inference(flattening,[],[f2620]) ).
fof(f2798,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_c____)),
inference(cnf_transformation,[],[f2]) ).
fof(f2799,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))),
inference(cnf_transformation,[],[f3]) ).
fof(f2800,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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,X0))),
inference(cnf_transformation,[],[f4]) ).
fof(f2815,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f1296]) ).
fof(f2827,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2413]) ).
fof(f2828,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f22]) ).
fof(f2897,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1) ),
inference(cnf_transformation,[],[f1378]) ).
fof(f2960,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(cnf_transformation,[],[f1438]) ).
fof(f2967,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__semidom(X1)
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))) ),
inference(cnf_transformation,[],[f1444]) ).
fof(f3134,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1649]) ).
fof(f3135,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(cnf_transformation,[],[f1650]) ).
fof(f3136,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
inference(cnf_transformation,[],[f1651]) ).
fof(f3141,plain,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| c_Orderings_Oord__class_Oless(X3,X0,X1) ),
inference(cnf_transformation,[],[f1657]) ).
fof(f3326,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
inference(cnf_transformation,[],[f382]) ).
fof(f3445,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0 ),
inference(cnf_transformation,[],[f1876]) ).
fof(f3514,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f2586]) ).
fof(f3615,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__idom(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ominus__class_Ominus(X3,X1,X0),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
| c_Orderings_Oord__class_Oless(X3,c_Groups_Oabs__class_Oabs(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) ),
inference(cnf_transformation,[],[f2621]) ).
fof(f4375,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1129]) ).
fof(f4383,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1137]) ).
fof(f4393,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1147]) ).
fof(f4394,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1148]) ).
fof(f4406,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1160]) ).
fof(f4409,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1163]) ).
fof(f4521,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(cnf_transformation,[],[f1285]) ).
fof(f4782,plain,
! [X1] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),
inference(equality_resolution,[],[f3514]) ).
fof(f4986,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)) ),
inference(resolution,[],[f2827,f2799]) ).
fof(f4988,definition,
( spl73_5
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)) ),
introduced(definition,[new_symbols(definition,[spl73_5])],[avatar_definition]) ).
fof(f4989,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))
| ~ spl73_5 ),
inference(avatar_component_clause,[],[f4988]) ).
fof(f4991,definition,
( spl73_6
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))) ),
introduced(definition,[new_symbols(definition,[spl73_6])],[avatar_definition]) ).
fof(f4992,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))
| ~ spl73_6 ),
inference(avatar_component_clause,[],[f4991]) ).
fof(f4993,plain,
( spl73_5
| spl73_6 ),
inference(avatar_split_clause,[],[f4986,f4991,f4988]) ).
fof(f4998,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),
inference(resolution,[],[f4394,f3136]) ).
fof(f5047,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 = X1 ),
inference(resolution,[],[f4393,f2897]) ).
fof(f5051,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))) ),
inference(resolution,[],[f5047,f4521]) ).
fof(f5079,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2)),
inference(resolution,[],[f3135,f4394]) ).
fof(f5091,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)),
inference(superposition,[],[f5079,f4998]) ).
fof(f5112,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),X1),
inference(superposition,[],[f4998,f5079]) ).
fof(f5211,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____) ),
inference(resolution,[],[f2798,f2827]) ).
fof(f5213,definition,
( spl73_9
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____) ),
introduced(definition,[new_symbols(definition,[spl73_9])],[avatar_definition]) ).
fof(f5214,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)
| ~ spl73_9 ),
inference(avatar_component_clause,[],[f5213]) ).
fof(f5216,definition,
( spl73_10
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) ),
introduced(definition,[new_symbols(definition,[spl73_10])],[avatar_definition]) ).
fof(f5217,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))
| ~ spl73_10 ),
inference(avatar_component_clause,[],[f5216]) ).
fof(f5218,plain,
( spl73_9
| spl73_10 ),
inference(avatar_split_clause,[],[f5211,f5216,f5213]) ).
fof(f5219,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)),
inference(resolution,[],[f3134,f4394]) ).
fof(f5221,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2)),
inference(superposition,[],[f5219,f4998]) ).
fof(f5233,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))),
inference(superposition,[],[f4521,f5219]) ).
fof(f5264,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))
| ~ spl73_5 ),
inference(forward_demodulation,[],[f5233,f4989]) ).
fof(f5283,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))))
| ~ spl73_5 ),
inference(forward_demodulation,[],[f5264,f5091]) ).
fof(f5365,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1)),
inference(superposition,[],[f5079,f5091]) ).
fof(f5507,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))),
inference(superposition,[],[f4521,f5221]) ).
fof(f5547,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))),
inference(forward_demodulation,[],[f5507,f5079]) ).
fof(f5629,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)) = X1,
inference(resolution,[],[f3445,f4406]) ).
fof(f5630,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1)) = X1,
inference(forward_demodulation,[],[f5629,f5079]) ).
fof(f5632,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))) = X0,
inference(superposition,[],[f5630,f4998]) ).
fof(f5641,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))) = X0,
inference(superposition,[],[f5091,f5630]) ).
fof(f5667,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0,
inference(forward_demodulation,[],[f5641,f4782]) ).
fof(f5670,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) = X0,
inference(forward_demodulation,[],[f5632,f3326]) ).
fof(f5694,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) = X0,
inference(superposition,[],[f4998,f5667]) ).
fof(f5705,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)),
inference(superposition,[],[f5221,f5667]) ).
fof(f5792,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0,
inference(superposition,[],[f5694,f5670]) ).
fof(f5850,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(resolution,[],[f4383,f2967]) ).
fof(f5851,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1)) ),
inference(resolution,[],[f4383,f2960]) ).
fof(f5857,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(resolution,[],[f5850,f5851]) ).
fof(f5861,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)),
inference(superposition,[],[f5850,f4998]) ).
fof(f5872,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(forward_demodulation,[],[f5857,f5112]) ).
fof(f5874,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(forward_demodulation,[],[f5872,f5705]) ).
fof(f5877,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))
| ~ spl73_5 ),
inference(forward_demodulation,[],[f5283,f5705]) ).
fof(f6183,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(resolution,[],[f2815,f4375]) ).
fof(f6184,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f6183,f2828]) ).
fof(f8051,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),X2) ),
inference(resolution,[],[f3615,f4393]) ).
fof(f8055,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0) ),
inference(resolution,[],[f8051,f6184]) ).
fof(f8060,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0) ),
inference(forward_demodulation,[],[f8055,f5667]) ).
fof(f8061,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(forward_demodulation,[],[f8060,f5792]) ).
fof(f8076,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0),X0),
inference(resolution,[],[f8061,f5861]) ).
fof(f8109,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl73_10 ),
inference(resolution,[],[f5874,f5217]) ).
fof(f8125,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))
| ~ spl73_10 ),
inference(forward_demodulation,[],[f8109,f4998]) ).
fof(f8129,plain,
( $false
| ~ spl73_5
| ~ spl73_10 ),
inference(forward_subsumption_resolution,[],[f8125,f5877]) ).
fof(f8130,plain,
( ~ spl73_5
| ~ spl73_10 ),
inference(avatar_contradiction_clause,[],[f8129]) ).
fof(f8134,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))) ),
inference(forward_demodulation,[],[f5051,f5112]) ).
fof(f8137,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))))
| ~ spl73_9 ),
inference(forward_demodulation,[],[f5547,f5214]) ).
fof(f8139,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))) ),
inference(forward_demodulation,[],[f8134,f5365]) ).
fof(f8142,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))))
| ~ spl73_9 ),
inference(forward_demodulation,[],[f8137,f5079]) ).
fof(f8148,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))
| ~ spl73_9 ),
inference(forward_demodulation,[],[f8142,f5705]) ).
fof(f8153,plain,
( $false
| ~ spl73_9 ),
inference(forward_subsumption_resolution,[],[f8148,f2800]) ).
fof(f8154,plain,
~ spl73_9,
inference(avatar_contradiction_clause,[],[f8153]) ).
fof(f8169,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(forward_demodulation,[],[f8139,f5112]) ).
fof(f8171,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(forward_demodulation,[],[f8169,f5365]) ).
fof(f8174,definition,
( spl73_11
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[spl73_11])],[avatar_definition]) ).
fof(f8175,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl73_11 ),
inference(avatar_component_clause,[],[f8174]) ).
fof(f8177,definition,
( spl73_12
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))) ),
introduced(definition,[new_symbols(definition,[spl73_12])],[avatar_definition]) ).
fof(f8178,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))
| ~ spl73_12 ),
inference(avatar_component_clause,[],[f8177]) ).
fof(f8179,plain,
( spl73_11
| spl73_12 ),
inference(avatar_split_clause,[],[f8171,f8177,f8174]) ).
fof(f8193,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),X1)) )
| ~ spl73_6 ),
inference(resolution,[],[f4992,f5851]) ).
fof(f8226,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X2) ),
inference(resolution,[],[f4409,f3141]) ).
fof(f8235,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,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) ),
inference(resolution,[],[f8226,f2798]) ).
fof(f8766,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))
| ~ spl73_12 ),
inference(superposition,[],[f8076,f8178]) ).
fof(f9014,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))
| ~ spl73_6
| ~ spl73_10 ),
inference(resolution,[],[f8193,f5217]) ).
fof(f9025,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))
| ~ spl73_6
| ~ spl73_10 ),
inference(forward_demodulation,[],[f9014,f4998]) ).
fof(f9027,plain,
( $false
| ~ spl73_6
| ~ spl73_10
| ~ spl73_12 ),
inference(forward_subsumption_resolution,[],[f9025,f8766]) ).
fof(f9028,plain,
( ~ spl73_6
| ~ spl73_10
| ~ spl73_12 ),
inference(avatar_contradiction_clause,[],[f9027]) ).
fof(f9030,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))
| ~ spl73_11 ),
inference(resolution,[],[f8175,f8235]) ).
fof(f9052,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))
| ~ spl73_6
| ~ spl73_11 ),
inference(resolution,[],[f9030,f8193]) ).
fof(f9058,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))
| ~ spl73_6
| ~ spl73_11 ),
inference(forward_demodulation,[],[f9052,f4998]) ).
fof(f9059,plain,
( $false
| ~ spl73_6
| ~ spl73_11 ),
inference(forward_subsumption_resolution,[],[f9058,f8076]) ).
fof(f9060,plain,
( ~ spl73_6
| ~ spl73_11 ),
inference(avatar_contradiction_clause,[],[f9059]) ).
cnf(s5,plain,
( spl73_5
| spl73_6 ),
inference(sat_conversion,[],[f4993]) ).
cnf(s8,plain,
( spl73_9
| spl73_10 ),
inference(sat_conversion,[],[f5218]) ).
cnf(s12,plain,
( ~ spl73_5
| ~ spl73_10 ),
inference(sat_conversion,[],[f8130]) ).
cnf(s16,plain,
~ spl73_9,
inference(sat_conversion,[],[f8154]) ).
cnf(s17,plain,
( spl73_11
| spl73_12 ),
inference(sat_conversion,[],[f8179]) ).
cnf(s24,plain,
( ~ spl73_6
| ~ spl73_10
| ~ spl73_12 ),
inference(sat_conversion,[],[f9028]) ).
cnf(s25,plain,
( ~ spl73_6
| ~ spl73_11 ),
inference(sat_conversion,[],[f9060]) ).
cnf(s27,plain,
spl73_10,
inference(rat,[],[s8,s16]) ).
cnf(s29,plain,
~ spl73_5,
inference(rat,[],[s12,s27]) ).
cnf(s30,plain,
spl73_6,
inference(rat,[],[s5,s29]) ).
cnf(s31,plain,
~ spl73_11,
inference(rat,[],[s25,s30]) ).
cnf(s32,plain,
~ spl73_12,
inference(rat,[],[s24,s27,s30]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s17,s32,s31]) ).
fof(f9061,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW179+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n010.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 13:12:48 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 5.94/1.68 % (1915818)Detected formulas, will run a generic FOF schedule.
% 5.94/1.68 % (1915824)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=3837966861:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.94/1.68 % (1915828)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3083076785:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.94/1.68 % (1915827)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2310720554:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.94/1.68 % (1915823)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=2104909953:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.94/1.68 % (1915826)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1505100375:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.94/1.68 % (1915825)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=960721752:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.94/1.68 % (1915829)dis-21_1_sil=8000:lcm=predicate:random_seed=1561323221: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)
% 5.94/1.68 % (1915826)Instruction limit reached!
% 5.94/1.68 % (1915826)------------------------------
% 5.94/1.68 % (1915826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.68 % (1915826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.68 % (1915826)CaDiCaL version: 2.1.3
% 5.94/1.68 % (1915826)Termination reason: Instruction limit
% 5.94/1.68 % (1915826)Termination phase: Saturation
% 5.94/1.68 % (1915826)Time elapsed: 0.054 s
% 5.94/1.68 % (1915826)Peak memory usage: 90 MB
% 5.94/1.68 % (1915826)Instructions burned: 111 (million)
% 5.94/1.68 % (1915827)Instruction limit reached!
% 5.94/1.68 % (1915827)------------------------------
% 5.94/1.68 % (1915827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.68 % (1915827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.68 % (1915827)CaDiCaL version: 2.1.3
% 5.94/1.68 % (1915827)Termination reason: Instruction limit
% 5.94/1.68 % (1915827)Termination phase: Saturation
% 5.94/1.68 % (1915827)Time elapsed: 0.067 s
% 5.94/1.68 % (1915827)Peak memory usage: 89 MB
% 5.94/1.68 % (1915827)Instructions burned: 119 (million)
% 5.94/1.68 % (1915828)Instruction limit reached!
% 5.94/1.68 % (1915828)------------------------------
% 5.94/1.68 % (1915828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.68 % (1915828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.68 % (1915828)CaDiCaL version: 2.1.3
% 5.94/1.68 % (1915828)Termination reason: Instruction limit
% 5.94/1.68 % (1915828)Termination phase: Saturation
% 5.94/1.68 % (1915828)Time elapsed: 0.077 s
% 5.94/1.68 % (1915828)Peak memory usage: 91 MB
% 5.94/1.68 % (1915828)Instructions burned: 140 (million)
% 5.94/1.68 % (1915829)Instruction limit reached!
% 5.94/1.68 % (1915829)------------------------------
% 5.94/1.68 % (1915829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.68 % (1915829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.68 % (1915829)CaDiCaL version: 2.1.3
% 5.94/1.68 % (1915829)Termination reason: Instruction limit
% 5.94/1.68 % (1915829)Termination phase: Saturation
% 5.94/1.68 % (1915829)Time elapsed: 0.066 s
% 5.94/1.68 % (1915829)Peak memory usage: 91 MB
% 5.94/1.68 % (1915829)Instructions burned: 130 (million)
% 5.94/1.68 % (1915837)lrs+10_1_sil=8000:sp=occurrence:random_seed=1072225282:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.94/1.68 % (1915838)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4006523830:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.94/1.68 % (1915839)lrs+1011_1_sil=32000:sp=occurrence:random_seed=760390571:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.94/1.68 % (1915840)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=1169840814:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.94/1.68 % (1915838)Instruction limit reached!
% 5.94/1.68 % (1915838)------------------------------
% 5.94/1.68 % (1915838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.68 % (1915838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.68 % (1915838)CaDiCaL version: 2.1.3
% 5.94/1.68 % (1915838)Termination reason: Instruction limit
% 5.94/1.68 % (1915838)Termination phase: Saturation
% 5.94/1.68 % (1915838)Time elapsed: 0.090 s
% 5.94/1.68 % (1915838)Peak memory usage: 91 MB
% 5.94/1.68 % (1915838)Instructions burned: 157 (million)
% 5.94/1.68 % (1915840)Instruction limit reached!
% 5.94/1.68 % (1915840)------------------------------
% 5.94/1.68 % (1915840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.68 % (1915840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.68 % (1915840)CaDiCaL version: 2.1.3
% 5.94/1.68 % (1915840)Termination reason: Instruction limit
% 5.94/1.68 % (1915840)Termination phase: Saturation
% 5.94/1.68 % (1915840)Time elapsed: 0.141 s
% 5.94/1.68 % (1915840)Peak memory usage: 92 MB
% 5.94/1.68 % (1915840)Instructions burned: 248 (million)
% 5.94/1.68 % (1915837)Instruction limit reached!
% 5.94/1.68 % (1915837)------------------------------
% 5.94/1.68 % (1915837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.68 % (1915837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.68 % (1915837)CaDiCaL version: 2.1.3
% 5.94/1.68 % (1915837)Termination reason: Instruction limit
% 5.94/1.68 % (1915837)Termination phase: Saturation
% 5.94/1.68 % (1915837)Time elapsed: 0.182 s
% 5.94/1.68 % (1915837)Peak memory usage: 92 MB
% 5.94/1.68 % (1915837)Instructions burned: 286 (million)
% 5.94/1.68 % (1915845)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1741408324:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.94/1.68 % (1915839)Instruction limit reached!
% 5.94/1.68 % (1915839)------------------------------
% 5.94/1.68 % (1915839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.68 % (1915839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.68 % (1915839)CaDiCaL version: 2.1.3
% 5.94/1.68 % (1915839)Termination reason: Instruction limit
% 5.94/1.68 % (1915839)Termination phase: Saturation
% 5.94/1.68 % (1915839)Time elapsed: 0.205 s
% 5.94/1.68 % (1915839)Peak memory usage: 92 MB
% 5.94/1.68 % (1915839)Instructions burned: 326 (million)
% 5.94/1.68 % (1915848)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3799690107:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.94/1.68 % (1915849)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=88384557:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.94/1.68 % (1915851)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1708492412:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.94/1.68 % (1915849)Instruction limit reached!
% 5.94/1.68 % (1915849)------------------------------
% 5.94/1.68 % (1915849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.68 % (1915849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.68 % (1915849)CaDiCaL version: 2.1.3
% 5.94/1.68 % (1915849)Termination reason: Instruction limit
% 5.94/1.68 % (1915849)Termination phase: Saturation
% 5.94/1.68 % (1915849)Time elapsed: 0.058 s
% 5.94/1.68 % (1915849)Peak memory usage: 90 MB
% 5.94/1.68 % (1915849)Instructions burned: 114 (million)
% 5.94/1.68 % (1915845)Instruction limit reached!
% 5.94/1.68 % (1915845)------------------------------
% 5.94/1.68 % (1915845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.68 % (1915845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.68 % (1915845)CaDiCaL version: 2.1.3
% 5.94/1.68 % (1915845)Termination reason: Instruction limit
% 5.94/1.68 % (1915845)Termination phase: Saturation
% 5.94/1.68 % (1915845)Time elapsed: 0.170 s
% 5.94/1.68 % (1915845)Peak memory usage: 92 MB
% 5.94/1.68 % (1915845)Instructions burned: 294 (million)
% 5.94/1.68 % (1915851)Instruction limit reached!
% 5.94/1.68 % (1915851)------------------------------
% 5.94/1.68 % (1915851)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.68 % (1915851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.68 % (1915851)CaDiCaL version: 2.1.3
% 5.94/1.68 % (1915851)Termination reason: Instruction limit
% 5.94/1.68 % (1915851)Termination phase: Saturation
% 5.94/1.68 % (1915851)Time elapsed: 0.062 s
% 5.94/1.68 % (1915851)Peak memory usage: 90 MB
% 5.94/1.68 % (1915851)Instructions burned: 130 (million)
% 5.94/1.68 % (1915824)First to succeed.
% 5.94/1.68 % (1915824)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1915818"
% 5.94/1.68 % (1915855)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4208038918:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 5.94/1.68 % (1915856)lrs+10_1_sil=8000:sp=occurrence:random_seed=1949973709:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 5.94/1.68 % (1915857)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=412605340:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 5.94/1.68 % (1915855)Instruction limit reached!
% 5.94/1.68 % (1915855)------------------------------
% 5.94/1.68 % (1915855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.68 % (1915855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.68 % (1915855)CaDiCaL version: 2.1.3
% 5.94/1.68 % (1915855)Termination reason: Instruction limit
% 5.94/1.68 % (1915855)Termination phase: Saturation
% 5.94/1.68 % (1915855)Time elapsed: 0.058 s
% 5.94/1.68 % (1915855)Peak memory usage: 90 MB
% 5.94/1.68 % (1915855)Instructions burned: 115 (million)
% 5.94/1.68 % (1915824)Refutation found. Thanks to Tanya!
% 5.94/1.68 % SZS status Theorem for theBenchmark
% 5.94/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 7.51/1.87 % (1915824)------------------------------
% 7.51/1.87 % (1915824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.51/1.87 % (1915824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.51/1.87 % (1915824)CaDiCaL version: 2.1.3
% 7.51/1.87 % (1915824)Termination reason: Refutation
% 7.51/1.87 % (1915824)Time elapsed: 0.705 s
% 7.51/1.87 % (1915824)Peak memory usage: 145 MB
% 7.51/1.87 % (1915824)Instructions burned: 2112 (million)
% 7.51/1.87 % (1915824)------------------------------
% 7.51/1.87 % (1915824)------------------------------
% 7.51/1.87 % (1915818)Success in time 1.018 s
% 7.51/1.87 % Vampire exiting
%------------------------------------------------------------------------------