%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW218+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 : n008.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 01:29:52 PM UTC 2026
% Result : Theorem 4.25s 1.60s
% Output : Refutation 5.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 10 unt; 3 def)
% Number of atoms : 173 ( 27 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 198 ( 80 ~; 87 |; 24 &)
% ( 5 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 62 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
? [X0] :
! [X1] :
( ? [X2] :
( ? [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096) ).
fof(f1259,axiom,
( ? [X0] :
! [X1] :
( ? [X2] :
( ? [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) )
=> v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1260,conjecture,
v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f1261,negated_conjecture,
~ v_thesis____,
inference(negated_conjecture,[status(cth)],[f1260]) ).
fof(f1262,plain,
~ v_thesis____,
inference(flattening,[],[f1261]) ).
fof(f1269,plain,
( v_thesis____
| ! [X0] :
? [X1] :
( ? [X2] :
( ? [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) )
<~> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(ennf_transformation,[],[f1259]) ).
fof(f1309,plain,
( v_thesis____
| ! [X0] :
? [X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ! [X2] :
( ! [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ? [X2] :
( ? [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ) ) ) ),
inference(nnf_transformation,[],[f1269]) ).
fof(f1310,plain,
( v_thesis____
| ! [X0] :
? [X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ! [X2] :
( ! [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ? [X4] :
( ? [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X5)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X4) ) ) ) ),
inference(rectify,[],[f1309]) ).
fof(f1311,plain,
( v_thesis____
| ! [X0] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0)
| ! [X2] :
( ! [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X2) ) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0)
| ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK2(X0)),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK2(X0))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK1(X0))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),sK1(X0)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0(X0)),skolemize(X4,sK1(X0)),skolemize(X5,sK2(X0))],[f1310]) ).
fof(f1335,plain,
? [X0] :
! [X1] :
( ( ? [X2] :
( ? [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ! [X2] :
( ! [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f1336,plain,
? [X0] :
! [X1] :
( ( ? [X2] :
( ? [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ! [X4] :
( ! [X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X5)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X4) ) ) ),
inference(rectify,[],[f1335]) ).
fof(f1337,plain,
! [X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK11(X1)),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK11(X1))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK10(X1))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,sK10(X1)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,sK9) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,sK9)
| ! [X4] :
( ! [X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X5)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X4) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X2,sK10(X1)),skolemize(X3,sK11(X1))],[f1336]) ).
fof(f1345,plain,
! [X0] :
( v_thesis____
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f1311]) ).
fof(f1346,plain,
! [X0] :
( v_thesis____
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK2(X0))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK1(X0)) ),
inference(cnf_transformation,[],[f1311]) ).
fof(f1347,plain,
! [X0] :
( v_thesis____
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK2(X0)),v_r) ),
inference(cnf_transformation,[],[f1311]) ).
fof(f1348,plain,
! [X2,X3,X0] :
( v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X2) ),
inference(cnf_transformation,[],[f1311]) ).
fof(f1349,plain,
~ v_thesis____,
inference(cnf_transformation,[],[f1262]) ).
fof(f1424,plain,
! [X1,X4,X5] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,sK9)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5),v_r)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X5)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X4) ),
inference(cnf_transformation,[],[f1337]) ).
fof(f1425,plain,
! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,sK10(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,sK9) ),
inference(cnf_transformation,[],[f1337]) ).
fof(f1426,plain,
! [X1] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK11(X1))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK10(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,sK9) ),
inference(cnf_transformation,[],[f1337]) ).
fof(f1427,plain,
! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK11(X1)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,sK9) ),
inference(cnf_transformation,[],[f1337]) ).
fof(f1476,plain,
! [X2,X3] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r)
| sP19(X2) ),
inference(cnf_transformation,[],[f1476_D]) ).
fof(f1476_D,definition,
! [X2] :
( ! [X3] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),v_r) )
<=> ~ sP19(X2) ),
introduced(definition,[new_symbols(definition,[sP19])],[general_splitting_component_introduction]) ).
fof(f1477,plain,
! [X2,X0] :
( v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X2)
| ~ sP19(X2) ),
inference(general_splitting,[],[f1348,f1476_D]) ).
fof(f1478,plain,
! [X1,X4] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X4)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,sK9)
| sP20(X4) ),
inference(cnf_transformation,[],[f1478_D]) ).
fof(f1478_D,definition,
! [X4] :
( ! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X4)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,sK9) )
<=> ~ sP20(X4) ),
introduced(definition,[new_symbols(definition,[sP20])],[general_splitting_component_introduction]) ).
fof(f1479,plain,
! [X4,X5] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X5)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5),v_r)
| ~ sP20(X4) ),
inference(general_splitting,[],[f1424,f1478_D]) ).
fof(f1480,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),sK1(X0))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0) ),
inference(forward_subsumption_resolution,[],[f1345,f1349]) ).
fof(f1481,plain,
! [X0] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK2(X0))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK1(X0))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0) ),
inference(forward_subsumption_resolution,[],[f1346,f1349]) ).
fof(f1482,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK2(X0)),v_r)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0) ),
inference(forward_subsumption_resolution,[],[f1347,f1349]) ).
fof(f1483,plain,
! [X2,X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0)
| ~ sP19(X2) ),
inference(forward_subsumption_resolution,[],[f1477,f1349]) ).
fof(f1486,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),sK9)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0)
| sP20(sK1(X0)) ),
inference(resolution,[],[f1480,f1478]) ).
fof(f1496,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),sK9)
| ~ sP19(sK10(sK0(X0)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0) ),
inference(resolution,[],[f1483,f1425]) ).
fof(f1500,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK1(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK2(X0)),v_r)
| ~ sP20(X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0) ),
inference(superposition,[],[f1479,f1481]) ).
fof(f1505,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK1(X0))
| ~ sP20(X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0) ),
inference(forward_subsumption_resolution,[],[f1500,f1482]) ).
fof(f1518,definition,
( spl21_2
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(sK9),sK9) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
fof(f1519,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(sK9),sK9)
| spl21_2 ),
inference(avatar_component_clause,[],[f1518]) ).
fof(f1520,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(sK9),sK9)
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f1518]) ).
fof(f1522,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK10(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK11(X0)),v_r)
| sP19(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sK9) ),
inference(superposition,[],[f1476,f1426]) ).
fof(f1543,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK10(X0))
| sP19(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sK9) ),
inference(forward_subsumption_resolution,[],[f1522,f1427]) ).
fof(f1550,plain,
( ~ sP19(sK10(sK0(sK9)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(sK9),sK9)
| ~ spl21_2 ),
inference(resolution,[],[f1496,f1520]) ).
fof(f1551,plain,
( ~ sP19(sK10(sK0(sK9)))
| ~ spl21_2 ),
inference(forward_subsumption_resolution,[],[f1550,f1520]) ).
fof(f1554,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(X0),X0)
| ~ sP20(sK1(X0)) ),
inference(equality_resolution,[],[f1505]) ).
fof(f1677,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,sK9)
| sP19(sK10(X0)) ),
inference(equality_resolution,[],[f1543]) ).
fof(f1926,plain,
( sP19(sK10(sK0(sK9)))
| ~ spl21_2 ),
inference(resolution,[],[f1677,f1520]) ).
fof(f1944,plain,
( $false
| ~ spl21_2 ),
inference(forward_subsumption_resolution,[],[f1926,f1551]) ).
fof(f1945,plain,
~ spl21_2,
inference(avatar_contradiction_clause,[],[f1944]) ).
fof(f1972,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(sK9),sK9)
| sP20(sK1(sK9))
| spl21_2 ),
inference(resolution,[],[f1519,f1486]) ).
fof(f1981,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK0(sK9),sK9)
| spl21_2 ),
inference(forward_subsumption_resolution,[],[f1972,f1554]) ).
fof(f1982,plain,
( $false
| spl21_2 ),
inference(forward_subsumption_resolution,[],[f1981,f1519]) ).
fof(f1983,plain,
spl21_2,
inference(avatar_contradiction_clause,[],[f1982]) ).
cnf(s27,plain,
~ spl21_2,
inference(sat_conversion,[],[f1945]) ).
cnf(s35,plain,
spl21_2,
inference(sat_conversion,[],[f1983]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s27,s35]) ).
fof(f1984,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW218+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n008.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 13:19:24 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.28 Running first-order theorem proving
% 0.25/0.28 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
% 4.25/1.60 % (2244860)Detected formulas, will run a generic FOF schedule.
% 4.25/1.60 % (2244870)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4062169615:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.25/1.60 % (2244871)dis-21_1_sil=8000:lcm=predicate:random_seed=3337362848: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)
% 4.25/1.60 % (2244870)Instruction limit reached!
% 4.25/1.60 % (2244870)------------------------------
% 4.25/1.60 % (2244870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.60 % (2244870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.60 % (2244870)CaDiCaL version: 2.1.3
% 4.25/1.60 % (2244870)Termination reason: Instruction limit
% 4.25/1.60 % (2244870)Termination phase: Saturation
% 4.25/1.60 % (2244870)Time elapsed: 0.073 s
% 4.25/1.60 % (2244870)Peak memory usage: 91 MB
% 4.25/1.60 % (2244870)Instructions burned: 140 (million)
% 4.25/1.60 % (2244871)Instruction limit reached!
% 4.25/1.60 % (2244871)------------------------------
% 4.25/1.60 % (2244871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.60 % (2244871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.60 % (2244871)CaDiCaL version: 2.1.3
% 4.25/1.60 % (2244871)Termination reason: Instruction limit
% 4.25/1.60 % (2244871)Termination phase: Saturation
% 4.25/1.60 % (2244871)Time elapsed: 0.075 s
% 4.25/1.60 % (2244871)Peak memory usage: 90 MB
% 4.25/1.60 % (2244871)Instructions burned: 129 (million)
% 4.25/1.60 % (2244867)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=2274911656:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.25/1.60 % (2244868)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1597517437:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.25/1.60 % (2244865)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=3617380689:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.25/1.60 % (2244866)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=203823202:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.25/1.60 % (2244869)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4089082201:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.25/1.60 % (2244868)First to succeed.
% 4.25/1.60 % (2244868)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2244860"
% 4.25/1.60 % (2244869)Instruction limit reached!
% 4.25/1.60 % (2244869)------------------------------
% 4.25/1.60 % (2244869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.60 % (2244869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.60 % (2244869)CaDiCaL version: 2.1.3
% 4.25/1.60 % (2244869)Termination reason: Instruction limit
% 4.25/1.60 % (2244869)Termination phase: Saturation
% 4.25/1.60 % (2244869)Time elapsed: 0.110 s
% 4.25/1.60 % (2244869)Peak memory usage: 89 MB
% 4.25/1.60 % (2244869)Instructions burned: 119 (million)
% 4.25/1.60 % (2244874)lrs+10_1_sil=8000:sp=occurrence:random_seed=1969496656:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.25/1.60 % (2244879)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2617934626:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 4.25/1.60 % (2244879)Refutation not found, incomplete strategy
% 4.25/1.60 % (2244879)------------------------------
% 4.25/1.60 % (2244879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.60 % (2244879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.60 % (2244879)CaDiCaL version: 2.1.3
% 4.25/1.60 % (2244879)Termination reason: Refutation not found, incomplete strategy
% 4.25/1.60 % (2244879)Time elapsed: 0.018 s
% 4.25/1.60 % (2244879)Peak memory usage: 89 MB
% 4.25/1.60 % (2244879)Instructions burned: 18 (million)
% 4.25/1.60 % (2244874)Instruction limit reached!
% 4.25/1.60 % (2244874)------------------------------
% 4.25/1.60 % (2244874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.60 % (2244874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.60 % (2244874)CaDiCaL version: 2.1.3
% 4.25/1.60 % (2244874)Termination reason: Instruction limit
% 4.25/1.60 % (2244874)Termination phase: Saturation
% 4.25/1.60 % (2244874)Time elapsed: 0.165 s
% 4.25/1.60 % (2244874)Peak memory usage: 92 MB
% 4.25/1.60 % (2244874)Instructions burned: 285 (million)
% 4.25/1.60 % (2244881)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2173734084:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 4.25/1.60 % (2244868)Refutation found. Thanks to Tanya!
% 4.25/1.60 % SZS status Theorem for theBenchmark
% 4.25/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 5.79/1.78 % (2244868)------------------------------
% 5.79/1.78 % (2244868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.79/1.78 % (2244868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.79/1.78 % (2244868)CaDiCaL version: 2.1.3
% 5.79/1.78 % (2244868)Termination reason: Refutation
% 5.79/1.78 % (2244868)Time elapsed: 0.040 s
% 5.79/1.78 % (2244868)Peak memory usage: 91 MB
% 5.79/1.78 % (2244868)Instructions burned: 35 (million)
% 5.79/1.78 % (2244868)------------------------------
% 5.79/1.78 % (2244868)------------------------------
% 5.79/1.78 % (2244860)Success in time 0.761 s
% 5.79/1.78 % Vampire exiting
%------------------------------------------------------------------------------