%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWW233+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 01:39:40 PM UTC 2026
% Result : Theorem 8.08s 1.54s
% Output : Refutation 8.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 77 ( 38 unt; 0 def)
% Number of atoms : 132 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 106 ( 51 ~; 42 |; 0 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 103 ( 103 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_h) ).
fof(f6,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(f7,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(f33,axiom,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
=> c_Groups_Oabs__class_Oabs(X1,X0) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
fof(f39,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(f41,axiom,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
fof(f113,axiom,
! [X0,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(f201,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(f202,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(f216,axiom,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
fof(f303,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(f326,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(f1112,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(f1127,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(f1137,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(f1144,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f1145,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f1150,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(f1171,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1261,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1262,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(negated_conjecture,[status(cth)],[f1261]) ).
fof(f1272,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(flattening,[],[f1262]) ).
fof(f1275,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,[],[f7]) ).
fof(f1276,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,[],[f1275]) ).
fof(f1316,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f1317,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(flattening,[],[f1316]) ).
fof(f1324,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f1412,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(ennf_transformation,[],[f113]) ).
fof(f1413,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(flattening,[],[f1412]) ).
fof(f1549,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f201]) ).
fof(f1550,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f202]) ).
fof(f1577,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f216]) ).
fof(f1578,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f1577]) ).
fof(f1690,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,[],[f303]) ).
fof(f1724,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,[],[f326]) ).
fof(f2374,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(cnf_transformation,[],[f4]) ).
fof(f2376,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,[],[f6]) ).
fof(f2377,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,[],[f1276]) ).
fof(f2409,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,X0) = X0 ),
inference(cnf_transformation,[],[f1317]) ).
fof(f2417,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f39]) ).
fof(f2419,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f1324]) ).
fof(f2506,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Opreorder(X2) ),
inference(cnf_transformation,[],[f1413]) ).
fof(f2631,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f1549]) ).
fof(f2632,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f1550]) ).
fof(f2648,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f1578]) ).
fof(f2772,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(cnf_transformation,[],[f1690]) ).
fof(f2802,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,[],[f1724]) ).
fof(f3929,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1112]) ).
fof(f3944,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1127]) ).
fof(f3954,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1137]) ).
fof(f3961,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1144]) ).
fof(f3962,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1145]) ).
fof(f3967,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1150]) ).
fof(f3988,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1171]) ).
fof(f4078,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(cnf_transformation,[],[f1272]) ).
fof(f5250,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),X1) = X0,
inference(resolution,[],[f2631,f3967]) ).
fof(f5254,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X1) = X0,
inference(resolution,[],[f2632,f3967]) ).
fof(f5331,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0)
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
inference(superposition,[],[f2772,f5250]) ).
fof(f5332,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0),
inference(forward_subsumption_resolution,[],[f5331,f3944]) ).
fof(f5335,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,[],[f2802,f3954]) ).
fof(f5343,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(resolution,[],[f5332,f2506]) ).
fof(f5345,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(forward_subsumption_resolution,[],[f5343,f3961]) ).
fof(f5363,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[],[f5345,f2648]) ).
fof(f5365,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0),
inference(forward_subsumption_resolution,[],[f5363,f3962]) ).
fof(f5686,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(superposition,[],[f5365,f5254]) ).
fof(f6200,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(forward_demodulation,[],[f2374,f2417]) ).
fof(f6207,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,X0) ),
inference(resolution,[],[f2377,f4078]) ).
fof(f6216,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(resolution,[],[f6207,f2419]) ).
fof(f6231,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(forward_subsumption_resolution,[],[f6216,f3988]) ).
fof(f6318,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r____),
inference(resolution,[],[f6231,f2376]) ).
fof(f6342,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| v_r____ = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) ),
inference(resolution,[],[f6318,f2409]) ).
fof(f6345,plain,
v_r____ = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),
inference(forward_subsumption_resolution,[],[f6342,f3929]) ).
fof(f6449,plain,
v_r____ = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____),
inference(superposition,[],[f6345,f2417]) ).
fof(f7910,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(forward_demodulation,[],[f6200,f6449]) ).
fof(f7911,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_r____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(forward_demodulation,[],[f7910,f5335]) ).
fof(f7912,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_r____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(resolution,[],[f7911,f6207]) ).
fof(f7919,plain,
$false,
inference(forward_subsumption_resolution,[],[f7912,f5686]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW233+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % 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 13:19:46 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.08/1.54 % (1773682)Will run a generic schedule for satisfiability detection.
% 8.08/1.54 % (1773693)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2981940535:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 8.08/1.54 % (1773688)% WARNING: option uhcvi not known.
% 8.08/1.54 % (1773687)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1920084269_2999 on theBenchmark for (2999ds/0Mi)
% 8.08/1.54 % (1773688)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1715675527:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 8.08/1.54 % (1773689)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1382932709:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 8.08/1.54 % (1773690)dis+10_1_sil=32000:sp=arity:random_seed=1836432454:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 8.08/1.54 % (1773691)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2064314329:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 8.08/1.54 % (1773692)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1039473474:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 8.08/1.54 % (1773693)Instruction limit reached!
% 8.08/1.54 % (1773693)------------------------------
% 8.08/1.54 % (1773693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773693)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773693)Termination reason: Instruction limit
% 8.08/1.54 % (1773693)Termination phase: Saturation
% 8.08/1.54 % (1773693)Time elapsed: 0.048 s
% 8.08/1.54 % (1773693)Peak memory usage: 16 MB
% 8.08/1.54 % (1773693)Instructions burned: 160 (million)
% 8.08/1.54 % (1773690)Instruction limit reached!
% 8.08/1.54 % (1773690)------------------------------
% 8.08/1.54 % (1773690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773690)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773690)Termination reason: Instruction limit
% 8.08/1.54 % (1773690)Termination phase: Saturation
% 8.08/1.54 % (1773690)Time elapsed: 0.052 s
% 8.08/1.54 % (1773690)Peak memory usage: 14 MB
% 8.08/1.54 % (1773690)Instructions burned: 106 (million)
% 8.08/1.54 % (1773691)Instruction limit reached!
% 8.08/1.54 % (1773691)------------------------------
% 8.08/1.54 % (1773691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773691)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773691)Termination reason: Instruction limit
% 8.08/1.54 % (1773691)Termination phase: Saturation
% 8.08/1.54 % (1773691)Time elapsed: 0.055 s
% 8.08/1.54 % (1773691)Peak memory usage: 14 MB
% 8.08/1.54 % (1773691)Instructions burned: 118 (million)
% 8.08/1.54 % (1773701)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1565670161:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 8.08/1.54 % (1773692)Instruction limit reached!
% 8.08/1.54 % (1773692)------------------------------
% 8.08/1.54 % (1773692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773692)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773692)Termination reason: Instruction limit
% 8.08/1.54 % (1773692)Termination phase: Saturation
% 8.08/1.54 % (1773692)Time elapsed: 0.066 s
% 8.08/1.54 % (1773692)Peak memory usage: 14 MB
% 8.08/1.54 % (1773692)Instructions burned: 131 (million)
% 8.08/1.54 % (1773702)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3265670082:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 8.08/1.54 % (1773704)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=135419554:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 8.08/1.54 % (1773705)ott-21_1_sil=16000:fs=off:random_seed=563206690:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 8.08/1.54 % (1773702)Instruction limit reached!
% 8.08/1.54 % (1773702)------------------------------
% 8.08/1.54 % (1773702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773702)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773702)Termination reason: Instruction limit
% 8.08/1.54 % (1773702)Termination phase: Saturation
% 8.08/1.54 % (1773702)Time elapsed: 0.061 s
% 8.08/1.54 % (1773702)Peak memory usage: 14 MB
% 8.08/1.54 % (1773702)Instructions burned: 131 (million)
% 8.08/1.54 % (1773709)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2985937313:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 8.08/1.54 % (1773705)Instruction limit reached!
% 8.08/1.54 % (1773705)------------------------------
% 8.08/1.54 % (1773705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773705)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773705)Termination reason: Instruction limit
% 8.08/1.54 % (1773705)Termination phase: Saturation
% 8.08/1.54 % (1773705)Time elapsed: 0.089 s
% 8.08/1.54 % (1773705)Peak memory usage: 14 MB
% 8.08/1.54 % (1773705)Instructions burned: 181 (million)
% 8.08/1.54 % (1773711)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3258869212:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 8.08/1.54 % (1773701)Instruction limit reached!
% 8.08/1.54 % (1773701)------------------------------
% 8.08/1.54 % (1773701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773701)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773701)Termination reason: Instruction limit
% 8.08/1.54 % (1773701)Termination phase: Finite model building preprocessing
% 8.08/1.54 % (1773701)Time elapsed: 0.184 s
% 8.08/1.54 % (1773701)Peak memory usage: 23 MB
% 8.08/1.54 % (1773701)Instructions burned: 716 (million)
% 8.08/1.54 % (1773713)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2702511242:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 8.08/1.54 % TRYING [1]
% 8.08/1.54 % TRYING [2]
% 8.08/1.54 % (1773704)Instruction limit reached!
% 8.08/1.54 % (1773704)------------------------------
% 8.08/1.54 % (1773704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773704)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773704)Termination reason: Instruction limit
% 8.08/1.54 % (1773704)Termination phase: Saturation
% 8.08/1.54 % (1773704)Time elapsed: 0.340 s
% 8.08/1.54 % (1773704)Peak memory usage: 16 MB
% 8.08/1.54 % (1773704)Instructions burned: 685 (million)
% 8.08/1.54 % (1773715)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3912710417:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 8.08/1.54 % (1773709)Instruction limit reached!
% 8.08/1.54 % (1773709)------------------------------
% 8.08/1.54 % (1773709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773709)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773709)Termination reason: Instruction limit
% 8.08/1.54 % (1773709)Termination phase: Saturation
% 8.08/1.54 % (1773709)Time elapsed: 0.295 s
% 8.08/1.54 % (1773709)Peak memory usage: 16 MB
% 8.08/1.54 % (1773709)Instructions burned: 477 (million)
% 8.08/1.54 % (1773717)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=950043989:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 8.08/1.54 % TRYING [1]
% 8.08/1.54 % TRYING [3]
% 8.08/1.54 % (1773711)Instruction limit reached!
% 8.08/1.54 % (1773711)------------------------------
% 8.08/1.54 % (1773711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773711)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773711)Termination reason: Instruction limit
% 8.08/1.54 % (1773711)Termination phase: Finite model building constraint generation
% 8.08/1.54 % (1773711)Time elapsed: 0.418 s
% 8.08/1.54 % (1773711)Peak memory usage: 31 MB
% 8.08/1.54 % (1773711)Instructions burned: 866 (million)
% 8.08/1.54 % (1773719)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4055973635:i=879:kws=inv_precedence:fsr=off_2993 on theBenchmark for (2993ds/879Mi)
% 8.08/1.54 % (1773713)Instruction limit reached!
% 8.08/1.54 % (1773713)------------------------------
% 8.08/1.54 % (1773713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773713)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773713)Termination reason: Instruction limit
% 8.08/1.54 % (1773713)Termination phase: Saturation
% 8.08/1.54 % (1773713)Time elapsed: 0.397 s
% 8.08/1.54 % (1773713)Peak memory usage: 22 MB
% 8.08/1.54 % (1773713)Instructions burned: 1182 (million)
% 8.08/1.54 % (1773721)fmb+10_1_sil=64000:random_seed=3563907793:i=22061:nm=2:gsp=on_2992 on theBenchmark for (2992ds/22061Mi)
% 8.08/1.54 % TRYING [1]
% 8.08/1.54 % (1773717)Instruction limit reached!
% 8.08/1.54 % (1773717)------------------------------
% 8.08/1.54 % (1773717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773717)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773717)Termination reason: Instruction limit
% 8.08/1.54 % (1773717)Termination phase: Saturation
% 8.08/1.54 % (1773717)Time elapsed: 0.387 s
% 8.08/1.54 % (1773717)Peak memory usage: 19 MB
% 8.08/1.54 % (1773717)Instructions burned: 692 (million)
% 8.08/1.54 % (1773715)Instruction limit reached!
% 8.08/1.54 % (1773715)------------------------------
% 8.08/1.54 % (1773715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773715)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773715)Termination reason: Instruction limit
% 8.08/1.54 % (1773715)Termination phase: Finite model building constraint generation
% 8.08/1.54 % (1773715)Time elapsed: 0.434 s
% 8.08/1.54 % (1773715)Peak memory usage: 44 MB
% 8.08/1.54 % (1773715)Instructions burned: 889 (million)
% 8.08/1.54 % (1773723)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=459466963:i=9515:nm=5_2990 on theBenchmark for (2990ds/9515Mi)
% 8.08/1.54 % TRYING [2]
% 8.08/1.54 % (1773724)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=116293063:fmbsr=1.7:i=920_2990 on theBenchmark for (2990ds/920Mi)
% 8.08/1.54 % (1773719)Instruction limit reached!
% 8.08/1.54 % (1773719)------------------------------
% 8.08/1.54 % (1773719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.54 % (1773719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.54 % (1773719)CaDiCaL version: 2.1.3
% 8.08/1.54 % (1773719)Termination reason: Instruction limit
% 8.08/1.54 % (1773719)Termination phase: Saturation
% 8.08/1.54 % (1773719)Time elapsed: 0.452 s
% 8.08/1.54 % (1773719)Peak memory usage: 21 MB
% 8.08/1.54 % (1773719)Instructions burned: 880 (million)
% 8.08/1.54 % (1773727)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2902518556:i=5131_2988 on theBenchmark for (2988ds/5131Mi)
% 8.08/1.54 % (1773727) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1773682-1773727"...
% 8.08/1.54 % (1773727)...printing done.
% 8.08/1.54 % (1773727)Refutation found. Thanks to Tanya!
% 8.08/1.54 % SZS status Theorem for theBenchmark
% 8.08/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 8.08/1.55 % (1773727)------------------------------
% 8.08/1.55 % (1773727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.08/1.55 % (1773727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/1.55 % (1773727)CaDiCaL version: 2.1.3
% 8.08/1.55 % (1773727)Termination reason: Refutation
% 8.08/1.55 % (1773727)Time elapsed: 0.126 s
% 8.08/1.55 % (1773727)Peak memory usage: 15 MB
% 8.08/1.55 % (1773727)Instructions burned: 214 (million)
% 8.08/1.55 % (1773682)Success in time 1.318 s
% 8.08/1.55 % Vampire exiting
%------------------------------------------------------------------------------