%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU408+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:48:46 PM UTC 2026
% Result : Theorem 3.31s 1.93s
% Output : Refutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 76 ( 21 unt; 2 def)
% Number of atoms : 322 ( 45 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 396 ( 150 ~; 131 |; 96 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-6 aty)
% Number of variables : 107 ( 0 sgn 98 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [X0,X1,X2] :
( X2 = k2_xboole_0(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f54,axiom,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f281,axiom,
! [X0,X1] : k3_tarski(k2_tarski(X0,X1)) = k2_xboole_0(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_zfmisc_1) ).
fof(f444,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f2737,axiom,
! [X0,X1] : k2_relat_1(k10_finseq_1(X0,X1)) = k2_tarski(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_finseq_2) ).
fof(f4433,axiom,
! [X0,X1] :
( ( l1_orders_2(X0)
& l1_orders_2(X1) )
=> ( v1_orders_2(k1_latsum_1(X0,X1))
& l1_orders_2(k1_latsum_1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
fof(f4436,axiom,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( ( v1_orders_2(X2)
& l1_orders_2(X2) )
=> ( X2 = k1_latsum_1(X0,X1)
<=> ( u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
& u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_latsum_1) ).
fof(f4437,axiom,
! [X0,X1] :
( ( l1_orders_2(X0)
& ~ v3_struct_0(X1)
& l1_orders_2(X1) )
=> ( ~ v3_struct_0(k1_latsum_1(X0,X1))
& v1_orders_2(k1_latsum_1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_latsum_1) ).
fof(f4448,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v2_orders_2(X0)
& v3_orders_2(X0)
& v4_orders_2(X0)
& v1_lattice3(X0)
& l1_orders_2(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( r2_hidden(X2,u1_struct_0(X1))
=> m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_latsum_1) ).
fof(f4449,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v2_orders_2(X0)
& v3_orders_2(X0)
& v4_orders_2(X0)
& v1_lattice3(X0)
& l1_orders_2(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( r2_hidden(X2,u1_struct_0(X1))
=> m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) ) ) ),
inference(negated_conjecture,[status(cth)],[f4448]) ).
fof(f4528,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
& r2_hidden(X2,u1_struct_0(X1)) )
& ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
& ~ v3_struct_0(X0)
& v2_orders_2(X0)
& v3_orders_2(X0)
& v4_orders_2(X0)
& v1_lattice3(X0)
& l1_orders_2(X0) ),
inference(ennf_transformation,[],[f4449]) ).
fof(f4529,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
& r2_hidden(X2,u1_struct_0(X1)) )
& ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
& ~ v3_struct_0(X0)
& v2_orders_2(X0)
& v3_orders_2(X0)
& v4_orders_2(X0)
& v1_lattice3(X0)
& l1_orders_2(X0) ),
inference(flattening,[],[f4528]) ).
fof(f4570,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f444]) ).
fof(f4678,plain,
! [X0,X1] :
( ( ~ v3_struct_0(k1_latsum_1(X0,X1))
& v1_orders_2(k1_latsum_1(X0,X1)) )
| ~ l1_orders_2(X0)
| v3_struct_0(X1)
| ~ l1_orders_2(X1) ),
inference(ennf_transformation,[],[f4437]) ).
fof(f4679,plain,
! [X0,X1] :
( ( ~ v3_struct_0(k1_latsum_1(X0,X1))
& v1_orders_2(k1_latsum_1(X0,X1)) )
| ~ l1_orders_2(X0)
| v3_struct_0(X1)
| ~ l1_orders_2(X1) ),
inference(flattening,[],[f4678]) ).
fof(f4680,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k1_latsum_1(X0,X1)
<=> ( u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
& u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1))) ) )
| ~ v1_orders_2(X2)
| ~ l1_orders_2(X2) )
| ~ l1_orders_2(X1) )
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f4436]) ).
fof(f4681,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k1_latsum_1(X0,X1)
<=> ( u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
& u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1))) ) )
| ~ v1_orders_2(X2)
| ~ l1_orders_2(X2) )
| ~ l1_orders_2(X1) )
| ~ l1_orders_2(X0) ),
inference(flattening,[],[f4680]) ).
fof(f4682,plain,
! [X0,X1] :
( ( v1_orders_2(k1_latsum_1(X0,X1))
& l1_orders_2(k1_latsum_1(X0,X1)) )
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(ennf_transformation,[],[f4433]) ).
fof(f4683,plain,
! [X0,X1] :
( ( v1_orders_2(k1_latsum_1(X0,X1))
& l1_orders_2(k1_latsum_1(X0,X1)) )
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(flattening,[],[f4682]) ).
fof(f5803,plain,
( ~ m1_subset_1(sK45,u1_struct_0(k1_latsum_1(sK43,sK44)))
& r2_hidden(sK45,u1_struct_0(sK44))
& ~ v3_struct_0(sK44)
& v2_orders_2(sK44)
& v3_orders_2(sK44)
& v4_orders_2(sK44)
& v1_lattice3(sK44)
& l1_orders_2(sK44)
& ~ v3_struct_0(sK43)
& v2_orders_2(sK43)
& v3_orders_2(sK43)
& v4_orders_2(sK43)
& v1_lattice3(sK43)
& l1_orders_2(sK43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43,sK44,sK45]),skolemize(X0,sK43),skolemize(X1,sK44),skolemize(X2,sK45)],[f4529]) ).
fof(f5877,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k1_latsum_1(X0,X1)
| u1_struct_0(X2) != k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| u1_orders_2(X2) != k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1))) )
& ( ( u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
& u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1))) )
| k1_latsum_1(X0,X1) != X2 ) )
| ~ v1_orders_2(X2)
| ~ l1_orders_2(X2) )
| ~ l1_orders_2(X1) )
| ~ l1_orders_2(X0) ),
inference(nnf_transformation,[],[f4681]) ).
fof(f5878,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k1_latsum_1(X0,X1)
| u1_struct_0(X2) != k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| u1_orders_2(X2) != k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1))) )
& ( ( u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
& u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1))) )
| k1_latsum_1(X0,X1) != X2 ) )
| ~ v1_orders_2(X2)
| ~ l1_orders_2(X2) )
| ~ l1_orders_2(X1) )
| ~ l1_orders_2(X0) ),
inference(flattening,[],[f5877]) ).
fof(f6209,plain,
! [X0,X1,X2] :
( ( X2 = k2_xboole_0(X0,X1)
| ? [X3] :
( ( ( ~ r2_hidden(X3,X0)
& ~ r2_hidden(X3,X1) )
| ~ r2_hidden(X3,X2) )
& ( r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X0)
& ~ r2_hidden(X3,X1) ) )
& ( r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) ) )
| k2_xboole_0(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f6210,plain,
! [X0,X1,X2] :
( ( X2 = k2_xboole_0(X0,X1)
| ? [X3] :
( ( ( ~ r2_hidden(X3,X0)
& ~ r2_hidden(X3,X1) )
| ~ r2_hidden(X3,X2) )
& ( r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X0)
& ~ r2_hidden(X3,X1) ) )
& ( r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) ) )
| k2_xboole_0(X0,X1) != X2 ) ),
inference(flattening,[],[f6209]) ).
fof(f6211,plain,
! [X0,X1,X2] :
( ( X2 = k2_xboole_0(X0,X1)
| ? [X3] :
( ( ( ~ r2_hidden(X3,X0)
& ~ r2_hidden(X3,X1) )
| ~ r2_hidden(X3,X2) )
& ( r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| r2_hidden(X3,X2) ) ) )
& ( ! [X4] :
( ( r2_hidden(X4,X2)
| ( ~ r2_hidden(X4,X0)
& ~ r2_hidden(X4,X1) ) )
& ( r2_hidden(X4,X0)
| r2_hidden(X4,X1)
| ~ r2_hidden(X4,X2) ) )
| k2_xboole_0(X0,X1) != X2 ) ),
inference(rectify,[],[f6210]) ).
fof(f6212,plain,
! [X0,X1,X2] :
( ( X2 = k2_xboole_0(X0,X1)
| ( ( ( ~ r2_hidden(sK273(X0,X1,X2),X0)
& ~ r2_hidden(sK273(X0,X1,X2),X1) )
| ~ r2_hidden(sK273(X0,X1,X2),X2) )
& ( r2_hidden(sK273(X0,X1,X2),X0)
| r2_hidden(sK273(X0,X1,X2),X1)
| r2_hidden(sK273(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( r2_hidden(X4,X2)
| ( ~ r2_hidden(X4,X0)
& ~ r2_hidden(X4,X1) ) )
& ( r2_hidden(X4,X0)
| r2_hidden(X4,X1)
| ~ r2_hidden(X4,X2) ) )
| k2_xboole_0(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(X3,sK273(X0,X1,X2))],[f6211]) ).
fof(f6384,plain,
l1_orders_2(sK43),
inference(cnf_transformation,[],[f5803]) ).
fof(f6390,plain,
l1_orders_2(sK44),
inference(cnf_transformation,[],[f5803]) ).
fof(f6395,plain,
~ v3_struct_0(sK44),
inference(cnf_transformation,[],[f5803]) ).
fof(f6396,plain,
r2_hidden(sK45,u1_struct_0(sK44)),
inference(cnf_transformation,[],[f5803]) ).
fof(f6397,plain,
~ m1_subset_1(sK45,u1_struct_0(k1_latsum_1(sK43,sK44))),
inference(cnf_transformation,[],[f5803]) ).
fof(f6446,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f4570]) ).
fof(f6608,plain,
! [X0,X1] :
( v1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X0)
| v3_struct_0(X1)
| ~ l1_orders_2(X1) ),
inference(cnf_transformation,[],[f4679]) ).
fof(f6611,plain,
! [X2,X0,X1] :
( u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| k1_latsum_1(X0,X1) != X2
| ~ v1_orders_2(X2)
| ~ l1_orders_2(X2)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f5878]) ).
fof(f6613,plain,
! [X0,X1] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(cnf_transformation,[],[f4683]) ).
fof(f7747,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k3_tarski(k2_tarski(X0,X1)),
inference(cnf_transformation,[],[f281]) ).
fof(f7786,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[],[f54]) ).
fof(f7793,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X2)
| ~ r2_hidden(X4,X0)
| k2_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f6212]) ).
fof(f8046,plain,
! [X0,X1] : k2_tarski(X0,X1) = k2_relat_1(k10_finseq_1(X0,X1)),
inference(cnf_transformation,[],[f2737]) ).
fof(f8389,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k3_tarski(k2_relat_1(k10_finseq_1(X0,X1))),
inference(definition_unfolding,[],[f7747,f8046]) ).
fof(f8401,plain,
! [X2,X0,X1] :
( u1_struct_0(X2) = k3_tarski(k2_relat_1(k10_finseq_1(u1_struct_0(X0),u1_struct_0(X1))))
| k1_latsum_1(X0,X1) != X2
| ~ v1_orders_2(X2)
| ~ l1_orders_2(X2)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(definition_unfolding,[],[f6611,f8389]) ).
fof(f8646,plain,
! [X0,X1] : k3_tarski(k2_relat_1(k10_finseq_1(X0,X1))) = k3_tarski(k2_relat_1(k10_finseq_1(X1,X0))),
inference(definition_unfolding,[],[f7786,f8389,f8389]) ).
fof(f8654,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X2)
| ~ r2_hidden(X4,X0)
| k3_tarski(k2_relat_1(k10_finseq_1(X0,X1))) != X2 ),
inference(definition_unfolding,[],[f7793,f8389]) ).
fof(f8898,plain,
! [X0,X1] :
( u1_struct_0(k1_latsum_1(X0,X1)) = k3_tarski(k2_relat_1(k10_finseq_1(u1_struct_0(X0),u1_struct_0(X1))))
| ~ v1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(equality_resolution,[],[f8401]) ).
fof(f8977,plain,
! [X0,X1,X4] :
( r2_hidden(X4,k3_tarski(k2_relat_1(k10_finseq_1(X0,X1))))
| ~ r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f8654]) ).
fof(f9079,plain,
~ r2_hidden(sK45,u1_struct_0(k1_latsum_1(sK43,sK44))),
inference(resolution,[],[f6397,f6446]) ).
fof(f9097,definition,
( spl368_3
<=> l1_orders_2(k1_latsum_1(sK43,sK44)) ),
introduced(definition,[new_symbols(definition,[spl368_3])],[avatar_definition]) ).
fof(f9098,plain,
( l1_orders_2(k1_latsum_1(sK43,sK44))
| ~ spl368_3 ),
inference(avatar_component_clause,[],[f9097]) ).
fof(f9099,plain,
( ~ l1_orders_2(k1_latsum_1(sK43,sK44))
| spl368_3 ),
inference(avatar_component_clause,[],[f9097]) ).
fof(f9101,definition,
( spl368_4
<=> v1_orders_2(k1_latsum_1(sK43,sK44)) ),
introduced(definition,[new_symbols(definition,[spl368_4])],[avatar_definition]) ).
fof(f9102,plain,
( v1_orders_2(k1_latsum_1(sK43,sK44))
| ~ spl368_4 ),
inference(avatar_component_clause,[],[f9101]) ).
fof(f9103,plain,
( ~ v1_orders_2(k1_latsum_1(sK43,sK44))
| spl368_4 ),
inference(avatar_component_clause,[],[f9101]) ).
fof(f9118,plain,
( ~ l1_orders_2(sK43)
| ~ l1_orders_2(sK44)
| spl368_3 ),
inference(resolution,[],[f9099,f6613]) ).
fof(f9119,plain,
( ~ l1_orders_2(sK44)
| spl368_3 ),
inference(forward_subsumption_resolution,[],[f9118,f6384]) ).
fof(f9120,plain,
( $false
| spl368_3 ),
inference(forward_subsumption_resolution,[],[f9119,f6390]) ).
fof(f9121,plain,
spl368_3,
inference(avatar_contradiction_clause,[],[f9120]) ).
fof(f9123,plain,
( ~ l1_orders_2(sK43)
| v3_struct_0(sK44)
| ~ l1_orders_2(sK44)
| spl368_4 ),
inference(resolution,[],[f9103,f6608]) ).
fof(f9126,plain,
( v3_struct_0(sK44)
| ~ l1_orders_2(sK44)
| spl368_4 ),
inference(forward_subsumption_resolution,[],[f9123,f6384]) ).
fof(f9129,plain,
( ~ l1_orders_2(sK44)
| spl368_4 ),
inference(forward_subsumption_resolution,[],[f9126,f6395]) ).
fof(f9134,plain,
( $false
| spl368_4 ),
inference(forward_subsumption_resolution,[],[f9129,f6390]) ).
fof(f9135,plain,
spl368_4,
inference(avatar_contradiction_clause,[],[f9134]) ).
fof(f9142,plain,
( ~ r2_hidden(sK45,k3_tarski(k2_relat_1(k10_finseq_1(u1_struct_0(sK43),u1_struct_0(sK44)))))
| ~ v1_orders_2(k1_latsum_1(sK43,sK44))
| ~ l1_orders_2(k1_latsum_1(sK43,sK44))
| ~ l1_orders_2(sK44)
| ~ l1_orders_2(sK43) ),
inference(superposition,[],[f9079,f8898]) ).
fof(f9143,plain,
( ~ r2_hidden(sK45,k3_tarski(k2_relat_1(k10_finseq_1(u1_struct_0(sK43),u1_struct_0(sK44)))))
| ~ l1_orders_2(k1_latsum_1(sK43,sK44))
| ~ l1_orders_2(sK44)
| ~ l1_orders_2(sK43)
| ~ spl368_4 ),
inference(forward_subsumption_resolution,[],[f9142,f9102]) ).
fof(f9144,plain,
( ~ r2_hidden(sK45,k3_tarski(k2_relat_1(k10_finseq_1(u1_struct_0(sK43),u1_struct_0(sK44)))))
| ~ l1_orders_2(sK44)
| ~ l1_orders_2(sK43)
| ~ spl368_3
| ~ spl368_4 ),
inference(forward_subsumption_resolution,[],[f9143,f9098]) ).
fof(f9145,plain,
( ~ r2_hidden(sK45,k3_tarski(k2_relat_1(k10_finseq_1(u1_struct_0(sK43),u1_struct_0(sK44)))))
| ~ l1_orders_2(sK43)
| ~ spl368_3
| ~ spl368_4 ),
inference(forward_subsumption_resolution,[],[f9144,f6390]) ).
fof(f9146,plain,
( ~ r2_hidden(sK45,k3_tarski(k2_relat_1(k10_finseq_1(u1_struct_0(sK43),u1_struct_0(sK44)))))
| ~ spl368_3
| ~ spl368_4 ),
inference(forward_subsumption_resolution,[],[f9145,f6384]) ).
fof(f9147,plain,
( ~ r2_hidden(sK45,k3_tarski(k2_relat_1(k10_finseq_1(u1_struct_0(sK44),u1_struct_0(sK43)))))
| ~ spl368_3
| ~ spl368_4 ),
inference(forward_demodulation,[],[f9146,f8646]) ).
fof(f9635,plain,
( ~ r2_hidden(sK45,u1_struct_0(sK44))
| ~ spl368_3
| ~ spl368_4 ),
inference(resolution,[],[f9147,f8977]) ).
fof(f9644,plain,
( $false
| ~ spl368_3
| ~ spl368_4 ),
inference(forward_subsumption_resolution,[],[f9635,f6396]) ).
fof(f9645,plain,
( ~ spl368_3
| ~ spl368_4 ),
inference(avatar_contradiction_clause,[],[f9644]) ).
cnf(s3,plain,
spl368_3,
inference(sat_conversion,[],[f9121]) ).
cnf(s6,plain,
spl368_4,
inference(sat_conversion,[],[f9135]) ).
cnf(s34,plain,
( ~ spl368_3
| ~ spl368_4 ),
inference(sat_conversion,[],[f9645]) ).
cnf(s35,plain,
~ spl368_3,
inference(rat,[],[s34,s6]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s3,s35]) ).
fof(f9646,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU408+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 05:10:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.31/1.93 % (448319)Detected formulas, will run a generic FOF schedule.
% 3.31/1.93 % (448328)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1900089099:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 3.31/1.93 % (448326)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=3651181912:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 3.31/1.93 % (448329)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1256700263:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 3.31/1.93 % (448324)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=2698258328:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 3.31/1.93 % (448327)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1748485843:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 3.31/1.93 % (448330)dis-21_1_sil=8000:lcm=predicate:random_seed=2044755576:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 3.31/1.93 % (448325)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=2802364136:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 3.31/1.93 % (448328)Instruction limit reached!
% 3.31/1.93 % (448328)------------------------------
% 3.31/1.93 % (448328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.93 % (448328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.93 % (448328)CaDiCaL version: 2.1.3
% 3.31/1.93 % (448328)Termination reason: Instruction limit
% 3.31/1.93 % (448328)Termination phase: Saturation
% 3.31/1.93 % (448328)Time elapsed: 0.047 s
% 3.31/1.93 % (448328)Peak memory usage: 94 MB
% 3.31/1.93 % (448328)Instructions burned: 119 (million)
% 3.31/1.93 % (448327)Refutation not found, incomplete strategy
% 3.31/1.93 % (448327)------------------------------
% 3.31/1.93 % (448327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.93 % (448327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.93 % (448327)CaDiCaL version: 2.1.3
% 3.31/1.93 % (448327)Termination reason: Refutation not found, incomplete strategy
% 3.31/1.93 % (448327)Time elapsed: 0.020 s
% 3.31/1.93 % (448327)Peak memory usage: 93 MB
% 3.31/1.93 % (448327)Instructions burned: 24 (million)
% 3.31/1.93 % (448330)Instruction limit reached!
% 3.31/1.93 % (448330)------------------------------
% 3.31/1.93 % (448330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.93 % (448330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.93 % (448330)CaDiCaL version: 2.1.3
% 3.31/1.93 % (448330)Termination reason: Instruction limit
% 3.31/1.93 % (448330)Termination phase: Preprocessing 3
% 3.31/1.93 % (448330)Time elapsed: 0.091 s
% 3.31/1.93 % (448330)Peak memory usage: 95 MB
% 3.31/1.93 % (448330)Instructions burned: 130 (million)
% 3.31/1.93 % (448329)Instruction limit reached!
% 3.31/1.93 % (448329)------------------------------
% 3.31/1.93 % (448329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.93 % (448329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.93 % (448329)CaDiCaL version: 2.1.3
% 3.31/1.93 % (448329)Termination reason: Instruction limit
% 3.31/1.93 % (448329)Termination phase: Preprocessing 3
% 3.31/1.93 % (448329)Time elapsed: 0.091 s
% 3.31/1.93 % (448329)Peak memory usage: 95 MB
% 3.31/1.93 % (448329)Instructions burned: 139 (million)
% 3.31/1.93 % (448338)lrs+10_1_sil=8000:sp=occurrence:random_seed=400219021:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 3.31/1.93 % (448340)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1641484857:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 3.31/1.93 % (448339)lrs+10_1_sil=32000:urr=on:br=off:random_seed=907174908:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 3.31/1.93 % (448327)------------------------------
% 3.31/1.93 % (448327)------------------------------
% 3.31/1.93 % (448340)Instruction limit reached!
% 3.31/1.93 % (448340)------------------------------
% 3.31/1.93 % (448340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.93 % (448340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.93 % (448340)CaDiCaL version: 2.1.3
% 3.31/1.93 % (448340)Termination reason: Instruction limit
% 3.31/1.93 % (448340)Termination phase: Saturation
% 3.31/1.93 % (448340)Time elapsed: 0.118 s
% 3.31/1.93 % (448340)Peak memory usage: 96 MB
% 3.31/1.93 % (448340)Instructions burned: 327 (million)
% 3.31/1.93 % (448339)Instruction limit reached!
% 3.31/1.93 % (448339)------------------------------
% 3.31/1.93 % (448339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.93 % (448339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.93 % (448339)CaDiCaL version: 2.1.3
% 3.31/1.93 % (448339)Termination reason: Instruction limit
% 3.31/1.93 % (448339)Termination phase: Saturation
% 3.31/1.93 % (448339)Time elapsed: 0.084 s
% 3.31/1.93 % (448339)Peak memory usage: 94 MB
% 3.31/1.93 % (448339)Instructions burned: 158 (million)
% 3.31/1.93 % (448338)Instruction limit reached!
% 3.31/1.93 % (448338)------------------------------
% 3.31/1.93 % (448338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.93 % (448338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.93 % (448338)CaDiCaL version: 2.1.3
% 3.31/1.93 % (448338)Termination reason: Instruction limit
% 3.31/1.93 % (448338)Termination phase: Saturation
% 3.31/1.93 % (448338)Time elapsed: 0.201 s
% 3.31/1.93 % (448338)Peak memory usage: 97 MB
% 3.31/1.93 % (448338)Instructions burned: 285 (million)
% 3.31/1.93 % (448344)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=1310509917:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 3.31/1.93 % (448345)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3055946589:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 3.31/1.93 % (448346)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2306121494:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 3.31/1.93 % (448345)First to succeed.
% 3.31/1.93 % (448345)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-448319"
% 3.31/1.93 % (448347)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2005745414:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 3.31/1.93 % (448344)Instruction limit reached!
% 3.31/1.93 % (448344)------------------------------
% 3.31/1.93 % (448344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.93 % (448344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.93 % (448344)CaDiCaL version: 2.1.3
% 3.31/1.93 % (448344)Termination reason: Instruction limit
% 3.31/1.93 % (448344)Termination phase: Property scanning
% 3.31/1.93 % (448344)Time elapsed: 0.156 s
% 3.31/1.93 % (448344)Peak memory usage: 100 MB
% 3.31/1.93 % (448344)Instructions burned: 249 (million)
% 3.31/1.93 % (448347)Instruction limit reached!
% 3.31/1.93 % (448347)------------------------------
% 3.31/1.93 % (448347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.93 % (448347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.93 % (448347)CaDiCaL version: 2.1.3
% 3.31/1.93 % (448347)Termination reason: Instruction limit
% 3.31/1.93 % (448347)Termination phase: Saturation
% 3.31/1.93 % (448347)Time elapsed: 0.073 s
% 3.31/1.93 % (448347)Peak memory usage: 96 MB
% 3.31/1.93 % (448347)Instructions burned: 114 (million)
% 3.31/1.93 % (448345)Refutation found. Thanks to Tanya!
% 3.31/1.93 % SZS status Theorem for theBenchmark
% 3.31/1.93 % SZS output start Proof for theBenchmark
% See solution above
% 3.31/2.03 % (448345)------------------------------
% 3.31/2.03 % (448345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/2.03 % (448345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/2.03 % (448345)CaDiCaL version: 2.1.3
% 3.31/2.03 % (448345)Termination reason: Refutation
% 3.31/2.03 % (448345)Time elapsed: 0.064 s
% 3.31/2.03 % (448345)Peak memory usage: 98 MB
% 3.31/2.03 % (448345)Instructions burned: 185 (million)
% 3.31/2.03 % (448345)------------------------------
% 3.31/2.03 % (448345)------------------------------
% 3.31/2.03 % (448319)Success in time 1.072 s
% 3.31/2.03 % Vampire exiting
%------------------------------------------------------------------------------